#### DMCA

## Quantum mechanics as quantum information (and only a little more), Quantum Theory: Reconsideration of Foundations (2002)

Citations: | 111 - 8 self |

### Citations

12166 |
Elements of Information Theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ...y that one’s uncertainty about a hypothesis can be expected to decrease upon the acquisition of data. This can be made rigorous, for instance, by gauging uncertainty with the Shannon entropy function =-=[80]-=-, S(H) = − � P(h)log P(h) . (75) h 30sThis number is bounded between 0 and the logarithm of the number of hypotheses in H, and there are several reasons to think of it as a good measure of uncertainty... |

2439 |
The Foundations of Statistics
- Savage
- 1954
(Show Context)
Citation Context ...in the completely mixed state ρ = 1 I and remains that way. 2 16 The repetition in these footnotes is not a typographical error. 17 I adopt this terminology to be similar to L. J. Savage’s book, Ref. =-=[43]-=-, Chapter 2, where he discusses the terms “the person,” “the world,” “consequences,” “acts,” and “decisions,” in the context of rational decision theory. “A consequence is anything that may happen to ... |

1479 | Bayesian Theory
- Bernardo, Smith
- 1994
(Show Context)
Citation Context ...ng to make sense of the remainder of quantum mechanics, one strategy ought to be to seek guidance [74] from the most developed avenue of “rational-decision theory” to date—Bayesian probability theory =-=[75, 76, 77]-=-. Indeed, the very aim of Bayesian theory is to develop reliable methods of reasoning and making decisions in the light of incomplete information. To what extent does that structure mesh with the seem... |

1153 |
Can Quantum-Mechanical Description of Physical Reality be Considered
- Einstein, Podolsky, et al.
- 1935
(Show Context)
Citation Context ...by interacting with a part of the world that should have no causal connection with the system of interest. The paradigm here is of course the one well known through the Einstein, Podolsky, Rosen paper=-=[34]-=-, but simpler versions of the train of thought had a long pre-history with Einstein [35] himself. The best was in essence this. Take two spatially separated systems A and B prepared in some entangled ... |

960 |
Quantum Cryptography: Public Key Distribution and Coin Tossing
- Bennett, Brassard
- 1984
(Show Context)
Citation Context ...paper in quantum information that does not make use of it. Unknown quantum states are teleported [23], protected with quantum error correcting codes [101], and used to check for quantum eavesdropping =-=[102]-=-. The list of uses grows each day. But what can the term mean? In an information-based interpretation of quantum mechanics, it is an oxymoron: If quantum states, by their very definition, are states o... |

935 |
Quantum Theory: Concepts and Methods
- Peres
- 1993
(Show Context)
Citation Context ...everal variations of it) are indeed violated by the physical world. The Kochen-Specker no-go theorems have been meticulously clarified to the point where simple textbook pictures can be drawn of them =-=[39]-=-. Incompleteness, it seems, is here to stay: The theory prescribes that no matter how much we know about a quantum system—even when we have maximal information about it 13 —there will always be a stat... |

754 |
Matrix Analysis
- Bhatia
- 1997
(Show Context)
Citation Context ...ainly innumerable ways to combine two Hilbert spaces HA and HB to obtain a third HAB. We could take the direct sum of the two spaces HAB = HA ⊕ HB. We could take their Grassmann product HAB = HA ∧ HB =-=[66]-=-. We could take scads of other things. But instead we take their tensor product, HAB = HA ⊗ HB . (41) Why? Could it arise from the selfsame considerations as of the previous section—namely, from a non... |

642 | Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen
- Bennett, Brassard, et al.
- 1993
(Show Context)
Citation Context ...jective information—the information one has about a quantum system. It has no objective reality in and of itself. 9 The argument is then refined by considering the phenomenon of quantum teleportation =-=[23]-=-. In Section 4 “Information About What?,” I tackle that very question [24] head-on. The answer is “the potential consequences of our experimental interventions into nature.” Once freed from the notion... |

336 |
Information Theory
- Ash
- 1965
(Show Context)
Citation Context ...ortant of these is that it quantifies the number of binary-valued questions one expects to ask (per instance of H) if one’s only means to ascertain the outcome is from a colleague who knows the result=-=[81]-=-. Under this quantification, the lower the Shannon entropy, the more predictable a measurement’s outcomes. Because the function f(x) = −xlog x is concave on the interval [0,1], it follows that, S(H) =... |

322 |
Scheme for reducing decoherence in quantum computer memory
- Shor
- 1995
(Show Context)
Citation Context ...It is the unknown quantum state. There is hardly a paper in quantum information that does not make use of it. Unknown quantum states are teleported [23], protected with quantum error correcting codes =-=[101]-=-, and used to check for quantum eavesdropping [102]. The list of uses grows each day. But what can the term mean? In an information-based interpretation of quantum mechanics, it is an oxymoron: If qua... |

291 |
effects, and operations: Fundamental notions in quantum theory
- States
- 1983
(Show Context)
Citation Context ...orthogonal projectors. In quantum information theory it has been found to be extremely convenient to expand the notion of measurement to also include general positive operator-valued measures (POVMs) =-=[39, 50]-=-. In other words, in place of the usual textbook notion 19 Pronounced ding-ables. 14sof measurement, any set {Ed} of positive-semidefinite operators on H D that forms a resolution of the identity, i.e... |

271 |
Completely positive linear maps on complex matrices
- Choi
- 1975
(Show Context)
Citation Context ...e trace preserving completely positive linear maps Φ over a D-dimensional vector space can be placed in a one-to-one correspondence with density operators on a D 2 -dimensional space via the relation =-=[79, 99, 100]-=- where |ψ ME〉 signifies a maximally entangled state on H D ⊗ H D, Υ = I ⊗ Φ(|ψ ME〉〈ψ ME|) (116) |ψ ME〉 = 1 √ D D� |i〉|i〉 . (117) i=1 This is usually treated as a convenient representation theorem only... |

215 |
An Investigation of the Laws of thought
- Boole
- 1854
(Show Context)
Citation Context ...ule? 34 The answer is, “Of course not!” Bayes’ rule—and beyond it all of probability theory—is a tool that stands above the details of physics. George Boole called probability theory a law of thought =-=[94]-=-. Its calculus specifies the optimal way an agent should reason and make decisions when faced with incomplete information. In this way, probability theory is a generalization of Aristotelian logic 35 ... |

168 |
Speakable and Unspeakable
- Bell
- 1987
(Show Context)
Citation Context ...otential consequences of our experimental interventions into nature.” Once freed from the notion that quantum measurement ought to be about revealing traces of some preexisting property[25] (or beable=-=[26]-=-), one finds no particular reason to take the standard account of measurement (in terms of complete sets of orthogonal projection operators) as a basic notion. Indeed quantum information theory, with ... |

144 |
The Emperor’s New Mind. Concerning Computers
- Penrose
- 1990
(Show Context)
Citation Context ...interest—i.e., one of the four Pauli rotations—Alice can sharpen her predictability to complete certainty for any YES-NO observable she wishes. Roger Penrose argues in his book The Emperor’s New Mind =-=[42]-=- that when a system “has” a state |ψ〉 there ought to be some property in the system (in and of itself) that corresponds to its “|ψ〉’ness.” For how else could the system be prepared to reveal a YES in ... |

139 |
The Transactional Interpretation of Quantum Mechanics
- Cramer
- 1986
(Show Context)
Citation Context ..., and it is like being in a holy city in great tumult. You will find all the religions with all their priests pitted in holy war—the Bohmians [3], the Consistent Historians [4], the Transactionalists =-=[5]-=-, the Spontaneous Collapseans [6], the Einselectionists [7], the Contextual Objectivists [8], the outright Everettics [9, 10], and many more beyond that. They all declare to see the light, the ultimat... |

139 |
Interpreting the Quantum World
- Bub
- 1997
(Show Context)
Citation Context ...nswer is “the potential consequences of our experimental interventions into nature.” Once freed from the notion that quantum measurement ought to be about revealing traces of some preexisting property=-=[25]-=- (or beable[26]), one finds no particular reason to take the standard account of measurement (in terms of complete sets of orthogonal projection operators) as a basic notion. Indeed quantum informatio... |

116 |
Norm ideals of completely continuous operators
- Schatten
- 1960
(Show Context)
Citation Context ...the same eigenvalues! To see the impact of this, let us once again explore the content of Eqs. (73) and (74). A common way to describe their meaning is to use the operator polar-decomposition theorem =-=[87]-=- to rewrite Eq. (73) in the form ρd = 1 1/2 UdE P(d) d ρE1/2 d † U d , (90) where Ud is a unitary operator. Since—subject only to the constraint of efficiency—the operators Ad are not determined any f... |

111 |
Quantum cryptography without Bell’s theorem
- Bennett, Brassard, et al.
- 1992
(Show Context)
Citation Context ...anguage built up in the previous sections. For quantum key distribution it is essential to be able to prepare a physical system in one or another quantum state drawn from some fixed nonorthogonal set =-=[102, 107]-=-. These nonorthogonal states are used to encode a potentially secret cryptographic key to be shared between the sender and receiver. The information an eavesdropper seeks is about which quantum state ... |

110 |
Quantum Theory From Five Reasonable Axioms
- Hardy
- 2001
(Show Context)
Citation Context ...perators Πd into a proper POVM. This can be done by considering the positive semidefinite operator G defined by D G = 2 � Πd . (36) 22 This idea has its roots in L. Hardy’s two important papers Refs. =-=[58]-=- and [59]. d=1 21sIt is straightforward to show that 〈ψ|G|ψ〉 > 0 for all |ψ〉 �= 0, thus establishing that G is positive definite (i.e., Hermitian with positive eigenvalues) and hence invertible. Apply... |

92 |
Finetti, Theory of probability
- de
- 1975
(Show Context)
Citation Context ...probability from the results of repeated trials on “identically prepared systems.” The way to eliminate unknown probabilities from this situation was introduced by Bruno de Finetti in the early 1930s =-=[104]-=-. His method was simply to focus on the equivalence of the repeated trials— namely, that what is really important is that the systems are indistinguishable as far as probabilistic predictions are conc... |

87 |
The Shaky Game: Einstein, Realism, and the Quantum Theory (University of
- Fine
- 1986
(Show Context)
Citation Context ...ystem of interest. The paradigm here is of course the one well known through the Einstein, Podolsky, Rosen paper[34], but simpler versions of the train of thought had a long pre-history with Einstein =-=[35]-=- himself. The best was in essence this. Take two spatially separated systems A and B prepared in some entangled quantum state |ψ AB 〉. By performing the measurement of one or another of two observable... |

86 |
A complete classification of quantum ensembles having a given density matrix
- Hughston, Jozsa, et al.
- 1993
(Show Context)
Citation Context ... of states: only that when the states are weighted by their probabilities, they mix together to form the initial density operator for system B alone. For a precise statement of this freedom, see Ref. =-=[36]-=-. 9sWhat relation is there between the “state” (“quantum state”) described by a function ψ and a real deterministic situation (that we call the “real state”)? Does the quantum state characterize compl... |

77 |
General properties of entropy”, Rev
- Wehrl
- 1978
(Show Context)
Citation Context ...is: With respect to a given density operator ρ, which measurement P will give the most predictability over its outcomes? As it turns out, the answer is any P that forms a set of eigenprojectors for ρ =-=[82]-=-. When this obtains, the Shannon entropy of the measurement outcomes reduces to simply the von Neumann entropy of the density operator. The von Neumann entropy, then, signifies the amount of impredict... |

76 |
Enk, private communication
- van
(Show Context)
Citation Context ...does it mean to accept quantum mechanics? Does it mean accepting (in essence) the existence of an “expert” whose probabilities we should strive to possess whenever we strive to be maximally rational? =-=[93]-=- The key to answering this question comes from combining the previous discussion of Bayes’ rule with the considerations of the standard quantum-measurement device of Section 4.2. For, contemplating th... |

67 | Unknown quantum states: The quantum de Finetti representation
- Caves, Fuchs, et al.
- 1999
(Show Context)
Citation Context ...solution, at least in the case of quantum-state tomography [31], is found through a quantum mechanical version of de Finetti’s classic theorem on “unknown probabilities.” This reports work from Refs. =-=[32]-=- and [33]. Maybe one of the most interesting things about the theorem is that it fails for Hilbert spaces over the field of real numbers, suggesting that perhaps the whole discipline of quantum inform... |

64 |
Many-Worlds Interpretation of Quantum Mechanics
- Vaidman
(Show Context)
Citation Context ...oly war—the Bohmians [3], the Consistent Historians [4], the Transactionalists [5], the Spontaneous Collapseans [6], the Einselectionists [7], the Contextual Objectivists [8], the outright Everettics =-=[9, 10]-=-, and many more beyond that. They all declare to see the light, the ultimate light. Each tells us that if we will accept their solution as our savior, then we too will see the light. 1 This paper, tho... |

51 |
A foundational principle for quantum mechanics
- Zeilinger
- 1999
(Show Context)
Citation Context ...ns, ask me over a beer sometime. 8 There have been other soundings of the idea that information and computation theory can tell us something deep about the foundations of quantum mechanics. See Refs. =-=[17], [18], -=-[19], and in particular Ref. [20]. 9 In the previous version of this paper, quant-ph/0106166, I variously called quantum states “information” and “states of knowledge” and did not emphasize so... |

45 |
Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase
- Vogel, Risken
- 1989
(Show Context)
Citation Context ...ng the system being measured or manipulated, and that what we are doing is grounding the phenomenon with respect to his state of belief. The solution, at least in the case of quantum-state tomography =-=[31]-=-, is found through a quantum mechanical version of de Finetti’s classic theorem on “unknown probabilities.” This reports work from Refs. [32] and [33]. Maybe one of the most interesting things about t... |

44 |
Einstein: The Life and Times
- Clark
- 1971
(Show Context)
Citation Context ...weringly to anyone who admires these principles. Einstein’s move effectively stopped all further debate on the origins of the Lorentz transformations. Outside of the time of the Nazi regime in Germany=-=[12]-=-, I suspect there have been less than a handful of conferences devoted to “interpreting” them. Most importantly, with the supreme simplicity of Einstein’s principles, physics became ready for “the nex... |

44 |
Linear transformations which preserve trace and positive semidefiniteness of operators
- Jamiolkowski
- 1972
(Show Context)
Citation Context ...e trace preserving completely positive linear maps Φ over a D-dimensional vector space can be placed in a one-to-one correspondence with density operators on a D 2 -dimensional space via the relation =-=[79, 99, 100]-=- where |ψ ME〉 signifies a maximally entangled state on H D ⊗ H D, Υ = I ⊗ Φ(|ψ ME〉〈ψ ME|) (116) |ψ ME〉 = 1 √ D D� |i〉|i〉 . (117) i=1 This is usually treated as a convenient representation theorem only... |

41 |
Degrees of concealment and bindingness in quantum bit commitment protocols
- Spekkens, Rudolph
- 2001
(Show Context)
Citation Context ...ropper and the consequent disturbance she must induce to the quantum states in the process. As the information gathered goes up, the necessary disturbance also goes up in a precisely formalizable way =-=[108, 109]-=-. Note the two ingredients that appear in this scenario. First, the information gathering or measurement is grounded with respect to one observer (in this case, the eavesdropper), while the 49sdisturb... |

40 | Decoherence, Einselection and the Existential Interpretation (the Rough Guide
- Zurek
- 1998
(Show Context)
Citation Context ...will find all the religions with all their priests pitted in holy war—the Bohmians [3], the Consistent Historians [4], the Transactionalists [5], the Spontaneous Collapseans [6], the Einselectionists =-=[7]-=-, the Contextual Objectivists [8], the outright Everettics [9, 10], and many more beyond that. They all declare to see the light, the ultimate light. Each tells us that if we will accept their solutio... |

40 |
Quantum Nonlocality without Entanglement,” Phys
- Bennett, DiVincenzo, et al.
- 1999
(Show Context)
Citation Context ... Eqs. (42) and (43). This, of course, is not the most general kind of local measurement one can imagine—more sophisticated measurements could involve multiple ping-pongings between A and B as in Ref. =-=[69]-=-—but the present restricted class is already sufficient for fixing that the probability rule for local measurements must come from a tensor-product structure. The theorem 27 is this: If f satisfies Eq... |

37 | Finite Precision Measurement Nullifies the Kochen-Specker Theorem
- Meyer
- 1999
(Show Context)
Citation Context ...tant thing is that the theorem works for Hilbert spaces over the rational number field: one does not need to invoke the full power of the continuum. This contrasts with the surprising result of Meyer =-=[54]-=- that the standard Gleason theorem fails in such a setting. The present theorem hints at a kind of resiliency to the structure of quantum mechanics that falls through the mesh of the standard Gleason ... |

36 | Quantum Probability from Decision Theory
- Barnum, Caves, et al.
- 2000
(Show Context)
Citation Context ... rule comes by way of Andrew Gleason’s amazing 1957 theorem [30]. For, it states that the standard rule is the only rule that satisfies a very simple kind of noncontextuality for measurement outcomes =-=[48]-=-. In particular, if one contemplates measuring two distinct observables {Πi} and {Γi} which happen to share a single projector Πk, then the probability of outcome k is independent of which observable ... |

31 |
Quantum Information: How much information in a state vector, in The Dilemma of Einstein, Podolsky and
- Caves, Fuchs
- 1995
(Show Context)
Citation Context ...e a statistical residue. There will always be questions that we can ask of a system for which we cannot predict the outcomes. In quantum theory, maximal information is simply not complete information =-=[40]-=-. But neither can it be completed. As Wolfgang Pauli once wrote to Markus Fierz [41], “The well-known ‘incompleteness’ of quantum mechanics (Einstein) is certainly an existent fact somehow-somewhere, ... |

29 |
The Fabric of reality: The science of parallel universes - and its implications (Penguin
- Deutsch
- 1998
(Show Context)
Citation Context ...oly war—the Bohmians [3], the Consistent Historians [4], the Transactionalists [5], the Spontaneous Collapseans [6], the Einselectionists [7], the Contextual Objectivists [8], the outright Everettics =-=[9, 10]-=-, and many more beyond that. They all declare to see the light, the ultimate light. Each tells us that if we will accept their solution as our savior, then we too will see the light. 1 This paper, tho... |

27 |
Lower bound for accessible information in quantum mechanics
- Jozsa, Robb, et al.
- 1994
(Show Context)
Citation Context ...easurements P [83]. Using this measure leads to the following quantity � S(ρ) = H(Π)dΩP � = −D (trρΠ) log (trρΠ) dΩΠ , (79) which is intimately connected to the so-called quantum “subentropy” of Ref. =-=[84]-=-. This mean entropy can be evaluated explicitly in terms of the eigenvalues of ρ and takes on the expression S(ρ) = 1 � � 1 1 1 + + · · · + + Q(ρ) (80) ln 2 2 3 D where the subentropy Q(ρ) is defined ... |

27 |
Locally normal symmetric states and an analogue of de Finetti’s theorem. Z. Wahrscheinlichkeitstheorie und Verw
- Hudson, Moody
(Show Context)
Citation Context ...bout the structure of the whole sequence of states ρ (N) : Each of the states ρ (N) has a kind of permutation invariance over its factors. The content of the quantum de Finetti representation theorem =-=[32, 105]-=- is that a sequence of states ρ (N) can have these properties, which are said to make it an exchangeable sequence, if and only if each term in it can also be written in the form ρ (N) � = P(ρ)ρ ⊗N dρ ... |

26 |
Relational quantum mechanics. Int
- Rovelli
- 1996
(Show Context)
Citation Context ...according to the Schrödinger equation. . “But what nonsense is this,” you must be asking. “Where else could they start?” The main issue is this, and no one has said it more clearly than Carlo Rovelli =-=[11]-=-. Where present-day quantumfoundation studies have stagnated in the stream of history is not so unlike where the physics of length contraction and time dilation stood before Einstein’s 1905 paper on s... |

24 |
On a characterization of the state space of quantum mechanics
- Araki
- 1980
(Show Context)
Citation Context ...iβjtr L(Ei ⊗ Fj) = tr ij � � L(E ⊗ F) . (58) For complex Hilbert spaces HA and HB, the uniqueness of L follows because the set {Ei ⊗ Fj} forms a complete basis for the Hermitian operators on HA ⊗ HB. =-=[71]-=- For real Hilbert spaces, however, the analog of the Hermitian operators are the symmetric operators. The dimensionality of the space of symmetric operators on a real Hilbert space HD is 1 2D(D + 1), ... |

23 |
Quantum theory needs no ‘interpretation’, Physics Today
- Fuchs, Peres
- 2000
(Show Context)
Citation Context ...ing reality—independent of our experimental interventions, then we must be prepared for that too. That is where quantum theory in its most minimal and conceptually simplest dispensation seems to stand=-=[46]-=-. It is a theory whose terms refer predominately to our interface with the world. It is a theory that cannot go the extra step that classical physics did without “writing songs I can’t 18 But I must s... |

20 | Quantum foundations in the light of quantum information
- Fuchs
- 2001
(Show Context)
Citation Context ... Each tells us that if we will accept their solution as our savior, then we too will see the light. 1 This paper, though substantially longer, should be viewed as a continuation and amendment to Ref. =-=[1]-=-. Details of the changes can be found in the Appendix to the present paper, Section 11. Substantial further arguments defending a transition from the “objective Bayesian” stance implicit in Ref. [1] t... |

20 |
Philosophical Profiles
- Bernstein
- 1986
(Show Context)
Citation Context ...h the measurement. Expressed in the language of Einstein, the quantum state cannot be a “complete” description of the quantum system. Here is the way Einstein put it to Michele Besso in a 1952 letter =-=[37]-=-: 10 Dash, verve, vigor, vim, zip, pep, punch, pizzazz! 11 Generally there need be hardly any relation between the two sets of states: only that when the states are weighted by their probabilities, th... |

20 | Physical justification for using the tensor product to describe two quantum systems as one joint system” Helv
- Aerts, Daubechies
- 1978
(Show Context)
Citation Context ... Alex Wilce brought to my attention that there is a significant amount of literature in the quantum logic community devoted to similar ways of motivating the tensor-product rule. See for example Ref. =-=[68]-=- and the many citations therein. 24 jsSuppose now that—just as with the POVM-version of Gleason’s theorem in Section 4—the joint probability P(i,j) for the outcomes of such a measurement should not de... |

19 |
Measures on the Closed Subspaces of a Hilbert
- Gleason
- 1957
(Show Context)
Citation Context ...gly simple Gleason-like derivation of the quantum probability rule recently found by Paul Busch [28] and, independently, by Joseph Renes and collaborators [29]. Contrary to Gleason’s original theorem =-=[30]-=-, this theorem works just as well for two-dimensional Hilbert spaces, and even for Hilbert spaces over the field of rational numbers. In Section 4.1, I give a strengthened argument for the noncontextu... |

19 |
Information-theoretical aspects of quantum measurement
- Prugovečki
- 1977
(Show Context)
Citation Context ...n finding a measurement for which the probabilities of outcomes completely specify a unique density operator. Such measurements are called informationally complete and have been studied for some time =-=[60, 61, 62]-=-. Here however, the picture is most pleasing if we consider a slightly refined version of the notion—that of the minimal informationally complete measurement [32]. The space of Hermitian operators on ... |

18 |
An elementary proof of Gleason's theorem
- COOKE, |MORAN
- 1985
(Show Context)
Citation Context ...., that it corresponds to the convex set of density operators). In itself this is no small feat, but the thing that makes the theorem an “amazing” theorem is the sheer difficulty required to prove it =-=[49]-=-. Note that no restrictions have been placed upon the function f beyond the ones mentioned above. There is no assumption that it need be differentiable, nor that it even need be continuous. All of tha... |

17 |
Information-theoretical aspects of quantum measurement, Problemy Peredachi Informatsii 9(2), 31–42
- Holevo
- 1973
(Show Context)
Citation Context ... in turn learns something about the system of real interest. Indirect though it may seem, this can be a powerful technique, sometimes revealing information that could not have been revealed otherwise =-=[51]-=-. A very simple example is where a sender has only a single qubit available for the sending one of three potential messages. She therefore has a need to encode the message in one of three preparations... |

16 |
Remarks concerning the essays brought together in this co-operative volume
- Einstein
- 1949
(Show Context)
Citation Context ...tant to recognize that the first issue does not entail the second. Einstein had that firmly in mind, but he wanted more. His reason for going the further step was, I think, well justified at the time =-=[38]-=-: There exists . . . a simple psychological reason for the fact that this most nearly obvious interpretation is being shunned. For if the statistical quantum theory does not pretend to describe the in... |

16 |
Quantum state disturbance vs. information gain: Uncertainty relations for quantum information, Phys
- Fuchs, Peres
- 1996
(Show Context)
Citation Context ...ropper and the consequent disturbance she must induce to the quantum states in the process. As the information gathered goes up, the necessary disturbance also goes up in a precisely formalizable way =-=[108, 109]-=-. Note the two ingredients that appear in this scenario. First, the information gathering or measurement is grounded with respect to one observer (in this case, the eavesdropper), while the 49sdisturb... |

14 |
Sending quantum entanglement through noisy channels”, Phys
- Schumacher
- 1996
(Show Context)
Citation Context ...f. [78]. 30 As an aside, it should be clear from the construction in Eq. (68) that there are many equally good representations of ρd. For a precise statement of the latitude of this freedom, see Ref. =-=[79]-=-. 29sbe almost orthogonal to each other. In density-operator language, there is no sense in which Πi is contained in ρ: the two states are in distinct places of the operator space. That is, ρ �= � P(i... |

12 |
Von Neumann’s projection postulate as a probability conditionalization rule in quantum mechanics
- Bub
- 1977
(Show Context)
Citation Context ...e state |ψAB 〉 whose Schmidt decomposition takes the form |ψ AB 〉 = � � λi|ai〉|bi〉 . (98) i 32 Other similarities between quantum collapse and Bayesian conditionalization have been discussed in Refs. =-=[89, 90, 91]-=-. 33 This should be contrasted with the usual picture of a “minimally disturbing” measurement of some POVM. In our case, a minimal disturbance version of a POVM {Ed} corresponds to taking Vd = I for a... |

11 |
Information tradeoff relations for finite-strength quantum measurements
- Fuchs, Jacob
- 2001
(Show Context)
Citation Context ...81), which becomes a quantification of uncertainty in its own right. The way to get at a quantum statement of Eq. (76) is to make use of the fact that S(ρ) and Q(ρ) are both concave in the variable ρ.=-=[85]-=- That is, for either function, we have F(t˜ρ0 + (1 − t)˜ρ1) ≥ tF(˜ρ0) + (1 − t)F(˜ρ1) , (83) for any density operators ˜ρ0 and ˜ρ1 and any real number t ∈ [0,1]. Therefore, one might hope that F(ρ) ≥ ... |

11 |
Characterizing mixing and measurement in quantum mechanics
- Nielsen
- 2001
(Show Context)
Citation Context ...tion” or “feedback” on the measured system [88]: σd −→ ρd = UdσdU † d . (92) 31 By differing methods, a strengthening of this result in terms of a majorization property can be found in Refs. [85] and =-=[86]-=-. 33sBut this breakdown of the transition is a purely conceptual game. Since the Ud are arbitrary to begin with, we might as well break down the state-change process into the following (nonstandard) c... |

10 |
Entanglement and Quantum Computation”, The Geometric Universe
- Jozsa
- 1998
(Show Context)
Citation Context ...is not a spelling mistake. 23sQuantum entanglement has certainly captured the attention of our community. By most accounts it is the main ingredient in quantum information theory and quantum computing=-=[64]-=-, and it is the main mystery of the quantum foundations [65]. But what is it? Where does it come from? The predominant purpose it has served in this paper has been as a kind of background. For it, mor... |

10 |
Boojums all the way through: communicating science in a prosaic age (Cambridge
- Mermin
- 1990
(Show Context)
Citation Context ...inly captured the attention of our community. By most accounts it is the main ingredient in quantum information theory and quantum computing[64], and it is the main mystery of the quantum foundations =-=[65]-=-. But what is it? Where does it come from? The predominant purpose it has served in this paper has been as a kind of background. For it, more than any other ingredient in quantum mechanics, has clinch... |

9 |
Resource Letter IQM-1 on the Interpretation of Quantum Mechanics
- DeWitt, Graham
- 1971
(Show Context)
Citation Context ...g to come to terms with the ‘world out there’ by methods which, however imaginative and refined, involve in essence the same element of contact as a well-placed kick.” — B. S. DeWitt and R. N. Graham =-=[14]-=- 5sfrom the chaff. If the quantum state represents subjective information, then how much of its mathematical support structure might be of that same character? Some of it, maybe most of it, but surely... |

9 |
Informationally complete sets of physical quantities
- Busch
- 1991
(Show Context)
Citation Context ...n finding a measurement for which the probabilities of outcomes completely specify a unique density operator. Such measurements are called informationally complete and have been studied for some time =-=[60, 61, 62]-=-. Here however, the picture is most pleasing if we consider a slightly refined version of the notion—that of the minimal informationally complete measurement [32]. The space of Hermitian operators on ... |

8 |
Contextual Objectivity: a Realistic Interpretation of Quantum
- Grangier
- 2000
(Show Context)
Citation Context ...all their priests pitted in holy war—the Bohmians [3], the Consistent Historians [4], the Transactionalists [5], the Spontaneous Collapseans [6], the Einselectionists [7], the Contextual Objectivists =-=[8]-=-, the outright Everettics [9, 10], and many more beyond that. They all declare to see the light, the ultimate light. Each tells us that if we will accept their solution as our savior, then we too will... |

8 |
Notes on a Paulian Idea
- Fuchs
- 2003
(Show Context)
Citation Context ...oices of the master set are equally interesting once we have settled on noncontextuality for the probability assignments. 21 But quantum mechanics, of course, is particularly interesting! 21 See Ref. =-=[56]-=-, pp. 86–88, and Ref. [57] for some examples in that regard. 20s4.2 Le Bureau International des Poids et Mesures à Paris There is still one further, particularly important, advantage to thinking of PO... |

7 |
A foundational principle for quantum mechanics Found
- Zeilinger
- 1999
(Show Context)
Citation Context ...ns, ask me over a beer sometime. 8 There have been other soundings of the idea that information and computation theory can tell us something deep about the foundations of quantum mechanics. See Refs. =-=[17]-=-, [18], [19], and in particular Ref. [20]. 9 In the previous version of this paper, quant-ph/0106166, I variously called quantum states “information” and “states of knowledge” and did not emphasize so... |

7 | 2000]: ‘Quantum Mechanics as a Principle Theory
- Bub
(Show Context)
Citation Context ... no objective reality in and of itself. 9 The argument is then refined by considering the phenomenon of quantum teleportation [23]. In Section 4 “Information About What?,” I tackle that very question =-=[24]-=- head-on. The answer is “the potential consequences of our experimental interventions into nature.” Once freed from the notion that quantum measurement ought to be about revealing traces of some preex... |

7 |
Cirac, “Storage of quantum dynamics on quantum states: A quasi-perfect programmable quantum gate,” Preprint arXiv: quant-ph/0012067
- Vidal, I
- 2000
(Show Context)
Citation Context ...n the same way as in Section 3: Namely, by considering the teleportation of quantum dynamics. I will for the moment, however, leave that as an exercise for the reader. See the many references in Ref. =-=[98]-=- for appropriate background. 40sIt has long been known that the trace preserving completely positive linear maps Φ over a D-dimensional vector space can be placed in a one-to-one correspondence with d... |

7 | Climbing Mount Scalable: PhysicalResource Requirements for a Scalable Quantum Computer
- Blume-Kohout, Caves, et al.
- 2002
(Show Context)
Citation Context ... only) a quantum measurement ever does is gather a piece of data by which we update our subjective probabilities for something else. It causes us to change our subjective probability 44 Cf. also Ref. =-=[110]-=-. 45 Cf. also the final paragraphs of Section 1. 51sassignments P(h) for some hypothesis h to a posterior assignment Pd(h) conditioned on the data d. 6. As noted in Footnote 9, this paper is a bit of ... |

6 | 2001) From classical state swapping to quantum teleportation - Mermin |

6 | Quantum State Reduction and the Quantum Bayes Principle
- Ozawa
- 1997
(Show Context)
Citation Context ...e state |ψAB 〉 whose Schmidt decomposition takes the form |ψ AB 〉 = � � λi|ai〉|bi〉 . (98) i 32 Other similarities between quantum collapse and Bayesian conditionalization have been discussed in Refs. =-=[89, 90, 91]-=-. 33 This should be contrasted with the usual picture of a “minimally disturbing” measurement of some POVM. In our case, a minimal disturbance version of a POVM {Ed} corresponds to taking Vd = I for a... |

5 |
Quantum states: What the hell are they? (The Post-Växjö Phase Transition). http://netlib.bell-labs.com/who/cafuchs
- Fuchs
- 2002
(Show Context)
Citation Context ...or is the subspace spanned by its eigenvectors with nonzero eigenvalues. 40 Such a statement, in fact, is not so dissimilar to the one found in Ref. [95]. For several rebuttals of that idea, see Ref. =-=[2]-=- and [96]. 39sFigure 3: One can use a slight modification of Einstein’s argument for the subjectivity of the quantum state to draw the same conclusion for quantum time evolutions. By performing measur... |

5 |
The tensor product of frame manuals
- Wilce
- 1990
(Show Context)
Citation Context ...nd establish the full probability rule for local quantum measurements—i.e., that L must be a density operator. Unfortunately, our assumptions are not strong enough for that. Here is a counterexample. =-=[72]-=- Consider a linear operator that is proportional to the swap operator on the two Hilbert spaces: LS(E ⊗ F) = 1 F ⊗ E . (61) D 2 This clearly satisfies the conditions of our theorem, but it is not equi... |

5 |
Quantum state of an ideal propagating laser field, arXiv: quant-ph/0111157
- Enk, Fuchs
(Show Context)
Citation Context ...ar optical medium driven by a laser, repeatedly prepares many instances of a quantum system, say many temporally distinct modes of the electromagnetic field, in a fixed quantum state ρ, pure or mixed =-=[103]-=-. An experimentalist who wishes to characterize the operation of the device or to calibrate it for future use may be able to perform measurements on the systems it prepares even if he cannot get at th... |

5 |
Quantum Theory in Real Hilbert Space Helv Phys Acta 33
- Stueckelberg, G
- 1960
(Show Context)
Citation Context ...that the quantum de Finetti theorem and the conclusions just drawn from it work only within the framework of complex vector-space quantum mechanics. For quantum mechanics based on real Hilbert spaces =-=[106]-=-, the connection between exchangeable density operators and unknown quantum states does not hold. A simple counterexample is the following. Consider the N-system state where ρ (N) = 1 2 ρ⊗N + + 1 2 ρ⊗... |

4 |
Consistent Histories and Quantum Measurements, Phys
- Griffiths, Omnès
- 1999
(Show Context)
Citation Context ...solution: Go to any meeting, and it is like being in a holy city in great tumult. You will find all the religions with all their priests pitted in holy war—the Bohmians [3], the Consistent Historians =-=[4]-=-, the Transactionalists [5], the Spontaneous Collapseans [6], the Einselectionists [7], the Contextual Objectivists [8], the outright Everettics [9, 10], and many more beyond that. They all declare to... |

4 |
Gleason’s Theorem with POVMs,” unpublished, 2000
- Caves, Fuchs, et al.
- 1957
(Show Context)
Citation Context ... point of view is demonstrated by the enticingly simple Gleason-like derivation of the quantum probability rule recently found by Paul Busch [28] and, independently, by Joseph Renes and collaborators =-=[29]-=-. Contrary to Gleason’s original theorem [30], this theorem works just as well for two-dimensional Hilbert spaces, and even for Hilbert spaces over the field of rational numbers. In Section 4.1, I giv... |

4 |
Physics and Beyond: Encounters and Conversations, translated by Arnold Pomerans
- Heisenberg
- 1971
(Show Context)
Citation Context ... It is just that, in a sense, they are by necessity at least one theory behind. No one got closer to the salient point than Heisenberg (in a quote he attributed to Einstein many years after the fact) =-=[45]-=-: It is quite wrong to try founding a theory on observable magnitudes alone. In reality the very opposite happens. It is the theory which decides what we can observe. You must appreciate that observat... |

3 |
Dynamical reduction theories: Changing quantum theory so the statevector represents reality
- Ghirardi, Pearle
- 1990
(Show Context)
Citation Context ...city in great tumult. You will find all the religions with all their priests pitted in holy war—the Bohmians [3], the Consistent Historians [4], the Transactionalists [5], the Spontaneous Collapseans =-=[6]-=-, the Einselectionists [7], the Contextual Objectivists [8], the outright Everettics [9, 10], and many more beyond that. They all declare to see the light, the ultimate light. Each tells us that if we... |

3 |
Relativity for the Million
- Gardner
- 1962
(Show Context)
Citation Context ...l structure? Those principles should be crisp; they should be compelling. They should stir the soul. When I was in junior high school, I sat down with Martin Gardner’s book Relativity for the Million =-=[13]-=- and came away with an understanding of the subject that sustains me today: The concepts were strange, but they were clear enough that I could get a grasp on them knowing little more mathematics than ... |

3 |
Quantum States as Effect Valuations: Giving Operational Content to von Neumann’s No-Hidden-Variables Theorem,” quant-ph/9909073
- Busch
(Show Context)
Citation Context ...ities as the basic notion instead. The productivity of this point of view is demonstrated by the enticingly simple Gleason-like derivation of the quantum probability rule recently found by Paul Busch =-=[28]-=- and, independently, by Joseph Renes and collaborators [29]. Contrary to Gleason’s original theorem [30], this theorem works just as well for two-dimensional Hilbert spaces, and even for Hilbert space... |

3 |
An unentangled Gleason’s theorem, quant-ph/0002058
- Wallach
(Show Context)
Citation Context ...s as of the previous section—namely, from a noncontextuality property for measurement-outcome probabilities? The answer is yes, and the theorem I am about demonstrate owes much in inspiration to Ref. =-=[67]-=-. 26 Here is the scenario. Suppose we have two quantum systems, and we can make a measurement on each. On the first, we can measure any POVM on the DA-dimensional Hilbert space HA; on the second, we c... |

3 |
Probability Theory: The Logic of Science, available for download on the World Wide Web at http://bayes.wustl.edu/. This huge book was unfortunately never finished due
- Jaynes
- 1998
(Show Context)
Citation Context ...ng to make sense of the remainder of quantum mechanics, one strategy ought to be to seek guidance [74] from the most developed avenue of “rational-decision theory” to date—Bayesian probability theory =-=[75, 76, 77]-=-. Indeed, the very aim of Bayesian theory is to develop reliable methods of reasoning and making decisions in the light of incomplete information. To what extent does that structure mesh with the seem... |

3 |
Using feedback to eliminate back-action in quantum measurements
- Wiseman
- 1995
(Show Context)
Citation Context ...n, subject to the details of the measurement interaction and the particular outcome d, one imagines the measuring device enforcing a further kind of “back-action” or “feedback” on the measured system =-=[88]-=-: σd −→ ρd = UdσdU † d . (92) 31 By differing methods, a strengthening of this result in terms of a majorization property can be found in Refs. [85] and [86]. 33sBut this breakdown of the transition i... |

3 |
The Nature of Information
- Duvenhage
(Show Context)
Citation Context ...ility theory) to explain how the transition Bayes’ rule signifies comes about within the mind of the agent. 34 This point was recently stated much more eloquently by Rocco Duvenhage in his paper Ref. =-=[92]-=-: In classical mechanics a measurement is nothing strange. It is merely an event where the observer obtains information about some physical system. A measurement therefore changes the observer’s infor... |

2 |
Quantum Information Processing and Quantum Logic: Towards Mutual Illumination
- Barnum
- 2002
(Show Context)
Citation Context ...have been other soundings of the idea that information and computation theory can tell us something deep about the foundations of quantum mechanics. See Refs. [17], [18], [19], and in particular Ref. =-=[20]-=-. 9 In the previous version of this paper, quant-ph/0106166, I variously called quantum states “information” and “states of knowledge” and did not emphasize so much the “radical” Bayesian idea that th... |

2 |
Various vibes
- Bennett, Brun, et al.
- 2001
(Show Context)
Citation Context ...y. However, if the reader finds that this gives him a sense of butterflies in the stomach—or fears that I will become a solipsist [21] or a crystal-toting New Age practitioner of homeopathic medicine =-=[22]-=-—I hope he will keep in mind that this attempt to be absolutely frank about the subjectivity of some of the terms in quantum theory is part of a larger program to delimit the terms that can be interpr... |

2 |
letter to M. Fierz dated 10 August 1954, reprinted and translated
- Pauli
- 1988
(Show Context)
Citation Context ...for which we cannot predict the outcomes. In quantum theory, maximal information is simply not complete information [40]. But neither can it be completed. As Wolfgang Pauli once wrote to Markus Fierz =-=[41]-=-, “The well-known ‘incompleteness’ of quantum mechanics (Einstein) is certainly an existent fact somehow-somewhere, but certainly cannot be removed by reverting to classical field physics.” Nor, I wou... |

2 |
The Experiment in Classical and in Quantum Physics
- Jammer
- 1984
(Show Context)
Citation Context ... basis of all which we try to describe with science. But an experiment is an active intervention into the course of nature on the part of the experimenter; it is not contemplation of nature from afar =-=[44]-=-. We set up this or that experiment to see how nature reacts. It is the conjunction of myriads of such interventions and their consequences that we record into our data books. 18 We tell ourselves tha... |

2 |
Kathy’s Song
- Simon
- 1965
(Show Context)
Citation Context ...ering the whole path from the phenomenon to our consciousness—function in such a way that we can rely upon them and hence speak of “observation.” 13sbelieve, with words that tear and strain to rhyme” =-=[47]-=-. It is a theory not about observables, not about beables, but about “dingables.” 19 We tap a bell with our gentle touch and listen for its beautiful ring. So what are the ways we can intervene on the... |

2 |
Enk, Quantum and Classical Game Strategies, Phys
- van
- 2000
(Show Context)
Citation Context ...e logic from working when D = 2. This is quite nice because much of the community has gotten into the habit of thinking that 18sthere is nothing particularly “quantum mechanical” about a single qubit.=-=[52]-=- Indeed, because orthogonal projectors on H2 can be mapped onto antipodes of the Bloch sphere, it is known that the measurement-outcome statistics for any standard measurement can be mocked-up through... |

1 |
The Sentiment of Rationality,” in The Writings of William James: A Comprehensive Edition, edited with an introduction by
- James
- 1967
(Show Context)
Citation Context ...zing all the things within gravitational and motional phenomena that should be viewed as consequences of our coordinate choices. It was in identifying all the things that are “numerically additional” =-=[15]-=- to the observer-free situation—i.e., those things that come about purely by bringing the observer (scientific agent, coordinate system, etc.) back into the picture. This was a true breakthrough. For ... |

1 |
Towards a Unification of Physics and Information Theory,” quant-ph/0112166
- Devetak, Staples
(Show Context)
Citation Context ...k me over a beer sometime. 8 There have been other soundings of the idea that information and computation theory can tell us something deep about the foundations of quantum mechanics. See Refs. [17], =-=[18]-=-, [19], and in particular Ref. [20]. 9 In the previous version of this paper, quant-ph/0106166, I variously called quantum states “information” and “states of knowledge” and did not emphasize so much ... |

1 |
The Contemplation of Quantum Computation
- Mermin
- 2000
(Show Context)
Citation Context ...ver a beer sometime. 8 There have been other soundings of the idea that information and computation theory can tell us something deep about the foundations of quantum mechanics. See Refs. [17], [18], =-=[19]-=-, and in particular Ref. [20]. 9 In the previous version of this paper, quant-ph/0106166, I variously called quantum states “information” and “states of knowledge” and did not emphasize so much the “r... |

1 |
private communication
- Grangier
- 2001
(Show Context)
Citation Context ...the number of jaws that will drop from the adoption of this terminology. However, if the reader finds that this gives him a sense of butterflies in the stomach—or fears that I will become a solipsist =-=[21]-=- or a crystal-toting New Age practitioner of homeopathic medicine [22]—I hope he will keep in mind that this attempt to be absolutely frank about the subjectivity of some of the terms in quantum theor... |

1 |
Kochen-Specker-like Noncolorability for Trine Measurements on a Qubit,” long overdue, but still in preparation
- Fuchs, Renes
- 1997
(Show Context)
Citation Context ...er to derive a noncolorability result along the lines of Kochen and Specker for a single qubit. Considering only 3-outcome POVMs of the so-called “trine” or “MercedesBenz” type already does the trick.=-=[53]-=- 19s4.1 Noncontextuality In point of fact, there is: For, one can argue that the noncontextuality of probability assignments for measurement outcomes is more basic than even the particular structure o... |

1 |
Barnum for pointing out the similarities between this line of thought and that
- Howard
- 1963
(Show Context)
Citation Context ...urements (i.e., that they be POVMs). Noncontextuality bears more on how we identify what we are measuring than anything to do with a measurement’s invasiveness upon nature. Here is a way to see that. =-=[55]-=- Forget about quantum mechanics for the moment and consider a more general world—one that, skipping the details of quantum mechanics, still retains the notions of systems, machines, actions, and conse... |

1 |
Why Quantum Theory?,” to appear
- Hardy
- 2002
(Show Context)
Citation Context ...Πd into a proper POVM. This can be done by considering the positive semidefinite operator G defined by D G = 2 � Πd . (36) 22 This idea has its roots in L. Hardy’s two important papers Refs. [58] and =-=[59]-=-. d=1 21sIt is straightforward to show that 〈ψ|G|ψ〉 > 0 for all |ψ〉 �= 0, thus establishing that G is positive definite (i.e., Hermitian with positive eigenvalues) and hence invertible. Applying the (... |

1 |
Unsharpness in Measurement Yields Informational Completeness,” in Symposium on the Foundations of Modern Physics 1990: Quantum Theory of Measurement and Related Philosophical Problems, edited by
- Phys
- 1989
(Show Context)
Citation Context ...n finding a measurement for which the probabilities of outcomes completely specify a unique density operator. Such measurements are called informationally complete and have been studied for some time =-=[60, 61, 62]-=-. Here however, the picture is most pleasing if we consider a slightly refined version of the notion—that of the minimal informationally complete measurement [32]. The space of Hermitian operators on ... |

1 |
Compatible Quantum States: Coming to Agreement and Uncovering Disagreement,” in preparation
- Caves, Fuchs, et al.
(Show Context)
Citation Context ...e subspace spanned by its eigenvectors with nonzero eigenvalues. 40 Such a statement, in fact, is not so dissimilar to the one found in Ref. [95]. For several rebuttals of that idea, see Ref. [2] and =-=[96]-=-. 39sFigure 3: One can use a slight modification of Einstein’s argument for the subjectivity of the quantum state to draw the same conclusion for quantum time evolutions. By performing measurements on... |

1 |
private communication, as early as 10
- Caves
- 1999
(Show Context)
Citation Context ...t, “The time evolution operator Φ on the control qubit is only an ‘effective’ evolution for it. The ‘true’ evolution for the system is the unitary evolution specified by the complete quantum circuit.”=-=[97]-=- In my opinion, however, moves like this are just prostrations to the Everettic temple. One could dismiss the original Einsteinian argument in the same way: “The observer toggles nothing with his loca... |

1 |
The de Finetti System of Probability,” in Appendix A, “Other Approaches to Probability Theory,” of Ref. [76
- Jaynes
(Show Context)
Citation Context ...tency and value of the “radically” subjective Bayesian paradigm for probability theory. That is, I have become much more inclined to the view of Bruno de Finetti [104], say, than that of Edwin Jaynes =-=[111]-=-. To that end, I have stopped calling probability distributions “states of knowledge” and been more true to the conception that they are “states of belief” whose cash-value is determined by the way an... |

1 |
Muddling Through: Pursuing Science and Truths
- Fortun, Bernstein
- 1998
(Show Context)
Citation Context ...esirable consequences you must act in the following way.” 20. Section 10.1, which argues for the nonsubjectivity of Hilbert-space dimension, is new. 21. One can read about the term “Realitty” in Ref. =-=[112]-=-. 12 Acknowledgments I thank Carl Caves, Greg Comer, David Mermin, and Rüdiger Schack for the years of correspondence that led to this view, Jeff Bub and Lucien Hardy for giving me courage in general,... |