A. S. Holevo: Probabilistical and statistical aspects of quantum theory, North-Holland (1982). Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Optimal Cloning of Pure States - Werner (1998) (7 citations) (Correct)
....construct devices which take several identically prepared quantum systems as an input, make a measurement, and thereby determine the density matrix describing the preparation to any desired degree of accuracy. This is the problem of quantum state estimation, which has been studied by many authors [Hol,Hel,MP,DBE] Of course, we can use this classical information to prepare many new systems ( clones ) in a state which is a close approximation of the input state. Clearly, the quality of the clones will depend on the number of initially available input systems. On the other hand, there will be no ....
....oe Omega N . But these are all density matrices on H Omega N : this can be seen by inserting the expansion (3:1) into oe Omega N = j Omega N ih Omega N j, and observing that from the resulting power series in and the coefficients jnihmj can be extracted. Hence (3:7) holds for all cloning maps T satisfying the assumptions stated at the beginning of this paragraph. As a corollary we obtain the equation fl(T RM TMN ) fl(T RM )fl(T MN ) for cloning in stages. Since the family of optimal cloners defined by (3:3) obviously satisfies the concatenation property b ....
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A.S. Holevo: Probabilistic and statistical aspects of quantum theory, North-Holland, Amsterdam 1982
On the Concentration of Quantum States in Phase Space - Werner (1993) (Correct)
....of Quantum Theory is taken seriously, or, on the technical side, whenever norm estimates of states or observables are desired. There is a well known alternative to the Wigner function avoiding these difficulties, which is variously known as the Husimi function [14] a phase space observable [5,7], a Berezin upper lower symbol [13] or convolution with a coherent state [16] One price to pay in all these approaches is that while the Wigner function has an intrinsic characterization in terms of the Weyl operators alone [10] these positive distribution functions depend on the choice of a ....
A.S. Holevo: Probabilistic and statistical aspects of quantum theory, North Holland, Amsterdam 1982
Computing with Quanta - Impacts of Quantum Theory on Computation - Hirvensalo (2000) Self-citation (Quantum) (Correct)
....functions f : A B , it is worth studying the physical systems which are used to represent the elements of A and B. For a physical system, one can associate the notion of a state. Here we will not enter into details, but merely outline the basic features. For more details, see [18] [16], or [8] for instance. In this section, we study the alphabet representations according to the classical physics, and the following section is devoted to the study of representing the alphabets with quantum physics in mind. 3.1 State Set A physical system CA which is capable to represent a ....
....representation (13) is not necessarily unique, as we have seen, cf. Remark 2. However, representation (13) is worth investigating. If T = jxihxj originally is some one dimensional projection, it turns out that then T is not expressible as convex combination of other one dimensional projections [16]. In other words: Proposition 6. The set of states of system QA is a convex set having onedimensional projections as extremals. De nition 2. A state T of system QA is pure, if T is a projection onto a one dimensional subspace. Otherwise, T is mixed. Remark 4. Let T = T 1 (1 )T 2 be a ....
A. S. Holevo: Probabilistical and statistical aspects of quantum theory, North-Holland (1982).
The Classical Limit of Quantum Theory - Werner (1995) Self-citation (Quantum) (Correct)
....in the textbooks. 2 For the mathematical formulation of the classical limit both readings amount to the same thing. The following are some of the features, which one might ask of a satisfactory explanation, and which the present paper aims to implement. a) The limit should be defined for the whole theory, not of certain isolated aspects. That is, we should define the limits of general states, observables, and expectation values, and these should go to their classical counterparts. b) The definition should be conceptually simple and general. That is, it should be appropriate for ....
....unsatisfactory from the conceptual point of view. Technically it means that operator norms (see (d) above) cannot be estimated without artificial smoothness assumptions [Dau] It is well known that by averaging Wigner functions with a suitable Gaussian [Bop,Car] these difficulties disappear [Dav,Hol,We1] Moreover, the Gaussians can be chosen such that in the classical limit this smearing out becomes negligible anyhow. In their averaged form Wigner functions play an important role in our approach. For a discussion of states that have positive Wigner functions all the way to the classical ....
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A.S. Holevo: Probabilistic and statistical aspects of quantum theory, North Holland, Amsterdam 1982
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