J. Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1(3):195--200, 1964.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is the erasure of phase states. Just as a single qubit is a computational resource due to superposition of states, an ebit is also a computational resource because it encodes exactly one classical bit of information (one bit being erased) even if the qubits are separated by a large distance [11]. The ebit s property is that of an Einstein Podolsky Rosen (EPR) communications resource. A 0 B 0 (SA SB ) A B 0 A 0 B = a0 b0 0 a0 b1 0 a1 b0 a1 b1 = a0 b0 a1 b1 (13) The number of spinors s=2 contains only even factors, so s 3 = 1 0, so 0 occurs only when 1 1= 0 18 ....

J. Bell (1964), "On the Einstein-Podolsky-Rosen Paradox", Physics, Vol. 1, pp. 195-200.

....group at NIST, Boulder has entangled four ions, shown exceedingly long coherence times for a single qubit, demonstrated high efficiency readout, initialized four atoms into their ground state, and multiplexed atoms between two traps. They have also shown violations of the Bell s inequalities [Bell64] and had many other successes. Their remarkable success and leadership of this effort blazes new frontiers in the experimental approaches to quantum computation, and their progress shows no signs of slowing. Ions of beryllium are held single file. Laser pulses flip individual ions. To implement a ....

John Stewart Bell, "On the Einstein-Podolsky-Rosen Paradox", Physics, Vol. 1 (1964). pp. 195-200.

....adherents such as Gerard t Hooft [18] When one surveys the field though, one finds that despite great effort, a satisfactory derivation of quantum mechanics from a hidden variable perspective still eludes researchers. First in the list of problems which must be overcome is Bell s theorem [19 21] which states that a hidden variable model must have nonlocality or superluminal connections built into it. Bell s theorem is usually thought to be the most decisive objection to hidden variable models. Tachyons certainly provide for the possibility of nonlocality. But then the tachyon theory must ....

John Bell, "On the Einstein-Podolsky-Rosen Paradox", Physics Vol 1, pp. 195 (1964)

....1. It appears that information, i.e. the outcome of Alice s measurement, has somehow traveled to earth instantaneously. Since nothing can travel faster than the speed of light something must be wrong. The EPR paradox has been, and still is, a subject of dispute. Much progress was made when Bell [Bel64] came up with a test that would, in case quantum mechanics was correct, show correlations that could not be explained with just classical reasoning. This test has been done in the lab [ADR82] and these nonclassical correlations have been observed. In the following we will see that this EPR ....

J.S. Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1, 1964. 14

.... communication may exceed the speed of light Nonlocal e#ects were alluded to in a famous 1935 paper by Einstein, Podolsky, and Rosen [13] Einstein later referred to this as spukhafte Fernwirkungen (spooky actions at a distance) see [12, 25, 30] for more historical background) In 1964, Bell [3] formalized the notion of two particle nonlocality in terms of correlations among probabilities in a scenario where one of a number of a measurements are performed on each particle. He showed that the results of the measurements that occur quantum physically can be correlated in a way that cannot ....

J.S. Bell, On the Einstein-Podolsky-Rosen paradox, Physics, 1 (1964), pp. 195--200.

....of an independent quantum reality , in favor of nonlocality or action at a distance , Einstein challenged the quantum theory with a hypothetical experiment known as the EPR experiment [10] The experiment was reformulated by John Bell based on a modi cation by David Bohm. In 1964, Bell s theorem [2] pointed to the existence of quantum correlations larger than the corresponding bound imposed by local reality assumptions, and which could hopefully be discerned experimentally. Subsequent experimental results have largely supported the nonlocal assumptions, even though critics have attempted to ....

J. Bell, \On the Einstein Podolsky Rosen Paradox", Physica, 1964.

.... the fact that the predictions of quantum theory are correct in experiments of this kind actually show that information must be transferred 12 instantaneously, in some (Lorentz) frame of reference The usual arguments that connect these experiments to nonlocal action stem from the work of John Bell (1964). What Bell did was this. He noted that the argument of Einstein, Podolsky, and Rosen was based on a certain assumption, namely that Physical Reality , whatever it was, should have at least one key property: What is physically real in one region cannot depend upon which experiment an experimenter ....

Bell, J. 1964 On the Einstein Podolsky Rosen Paradox.

....entanglement and no communication, but which would require communication in the classical world. They also give upper and lower bounds on the amount of classical communication needed to simulate EPR pairs. Their results may be viewed as quantitative extensions of the famous Bell inequalities [6]. ffl Las Vegas protocols. In this paper we just considered two modes of computation: exact and bounded error. An intermediate type of protocols are zero error or Las Vegas protocols. These never output an incorrect answer, but may claim ignorance with probability at most 1 2. Some quantum14 ....

J. S. Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1:195--200, 1965.

....separated regions (1987c) 2. Bell s inequality is maximally violated in many eld theories in every normal state (for appropriate spacelike separated regions) 1987c) It is well known, however, that the problem of local hidden variables has been associated with Bell s inequalities since Bell s work (1964, 1966, 1971) The typical core of reasoning in Bell type papers is this: T is an Einstein local hidden variable theory of quantum mechanics 1 T is Bell local 2 Bell s inequalities hold; but Bell s inequalities 3 are violated by quantum mechanics (and, as far as we can tell on the basis of ....

Bell, J.S. (1964), \On the Einstein-Podolsky-Rosen Paradox", Physics 1: 195-200.

....mean values over many instances of quantities with the same stochastic behavior within a single system. Precise concepts and traditional results about complementarity, uncertainty and nonlocality follow with a minimum of technicalities. In particular, nonlocal correlations predicted by Bell [2] and rst detected by Aspect [1] are shown to be already consequences of the nature of quantum mechanical ensembles and do not depend on hidden variables or on counterfactual reasoning. The concept of probability itself is derived from that of an ensemble by means 3 of a formula motivated from ....

....The LORD, according to Isaiah, ca. 540 B.C. 37] Before they call I will answer; while they are still speaking I will hear. The LORD, according to Isaiah, ca. 540 B.C. 38] A famous feature of quantum physics is its intrinsic nonlocality, expressed by so called Bell inequalities (cf. Bell [2], Clauser Shimony [12] The formulation given here depends on the most orthodox part of quantum mechanics only; it does not, as is usually done, refer to hidden variables, and involves no counterfactual reasoning. 6.1 Theorem. Let f k (k = 1; 2; 3; 4) be Hermitian quantities satisfying f 2 ....

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J.S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1 (1964), 195-200. (Reprinted in [76].)

....The most interesting feature of quantum information is contained not in individual qubits, but in correlations amongst them, often referred to as entanglements. Bell showed that there exist quantum entanglements which cannot be realised by any classical probabilistic local hidden variable theory [9]. Such entanglements originate from complex superposition coefficients, and exemplify physically possible tasks which no classical computer can perform. With the reduced density matrices defined as partial traces, the entanglement entropy for pure quantum states is E(X : Y ) S(ae X ) S(ae Y ) ....

J. Bell, On the Einstein-Podolsky-Rosen Paradox, Physics 1 (1964) 195.

....state of its own; the state of the system is not a tensor product of the states of each particle, but is some superposition which describes quantum correlations between these particles. Such particles are said to be quantumly entangled. The Einstein Podolski Rosen paradox[89] and Bell inequalities[25, 26, 68, 108], correspond to this puzzling quantum feature by which a quantum particle does not have a state of its own. Because of the entanglement or quantum correlations between the n quantum particles, the state of the system cannot be specified by simply describing the state of each of the n particles. ....

Bell J S On the Einstein-Podolsky-Rosen paradox, Physics 1 195--200, 1964

....revealed to me the importance of the restricted additivity (R6) as the key to a realistic interpretation of quantum mechanics. 36] also indicates how the double slit experiment conforms with such a cautious realistic interpretation. iii) In a similar way, the violation of Bell inequalities (Bell [1], Clauser Shimony [8] Pitowsky [46] can be explained by a failure of additivity of weak equations involving noncommuting quantities, too. iv) On the other hand, EPR type experiments about nonlocality [14] get a trivial explanation by the underlying deterministic dynamics and the fact that in ....

J.S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1 (1964), 195-200. (Reprinted in [60].)

.... systems [2] the parametric down conversion techniques crucial for these experiments have also been used to verify violation of Bell s inequality directly [3] Although the Bell CHSH inequalities were originally derived in the context of EPR B experiments [4] and (local) hidden variable theories [5,6], the present concern is with the differences in information processing capability between classical and quantum systems. Analyses of EPR B experiments from the very first [8] have been concerned with limitations in, for example, detector efficiency [6] The observed violations of Bell CHSH ....

J. S. Bell, "On the Einstein-Podolsky-Rosen paradox", Physics 1 (1964) 195--200.

.... systems [2] the parametric down conversion techniques crucial for these experiments have also been used to verify violation of Bell s inequality directly [3] Although the Bell CHSH inequalities were originally derived in the context of EPR B experiments [4] and (local) hidden variable theories [5,6], the present concern is with the differences in information processing capability between classical and quantum systems. Analyses of EPR B experiments from the very first [8] have been concerned with limitations in, for example, detector efficiency [6] The observed violations of Bell CHSH ....

J. S. Bell, "On the Einstein-Podolsky-Rosen paradox", Physics 1 (1964) 195--200.

....compelling; the discussion of observability is complex but shows that the results of the mathematics cannot be in con ict with what can in principle be measured by experiment. Further support for the positive e ect of the separation of meaning from observability is given by Bell s inequality (Bell [2], Clauser Shimony [12] a purely algebraic statement whose clarity is compelling, and the subsequent veri cation of its violation through experiments by Aspect [1] Finally, it seems that measurement problems can be adequately analysed by generalized observables de ned as positive operator ....

J.S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1 (1964), 195-200. (Reprinted in [36].)

.... entailed communication may exceed the speed of light Nonlocal effects were alluded to in a famous 1935 paper by Einstein, Podolsky, and Rosen [5] Einstein later referred to this as spukhafte Fernwirkungen [spooky actions at a distance] see [2, 9] for more historical background) In 1964, Bell [1] formalized the notion of two particle nonlocality in terms of correlations among probabilities in a scenario where one of a number of a measurements are performed on each particle. He showed that the results of the measurements that occur quantum physically can be correlated in a way that cannot ....

J.S. Bell, "On the Einstein-Podolsky-Rosen paradox", Physics, Vol. 1, 1964, pp. 195--200.

....state, a constant number of bits of communication is always sufficient regardless of the number of measurements under consideration. We also show that, in the case of a system of n Bell states, a constant times 2 n bits of communication are necessary. 1 Introduction Bell s celebrated theorem [1] shows that certain scenarios involving bipartite quantum measurements result in correlations that are impossible to simulate with a classical system if the measurement events are space like separated. If the measurement events are time like separated then classical simulation is possible, at the ....

....the underlying physics governing the behaviour of the system is quantum (in the sense that it can be based on entangled quantum states, rather than correlated random variables) then behaviour can occur that is impossible in the classical case. This is a natural way of interpreting Bell s theorem [1, 3]. To formalize and later generalize this, we shall define quantum measurement scenarios and (classical) local hidden variable schemes. 2 Definitions and preliminary results Define a quantum measurement scenario as a triple of the form (j Psii AB ; MA ; MB ) where j Psii AB is a bipartite ....

J.S. Bell, "On the Einstein-Podolsky-Rosen paradox", Physics, Vol. 1, 1964, pp. 195--200.

....cellular automaton model is modified as far as local physical measurements are incorporated into the model. Non locality is introduced into the model via entangled quantum mechanical two particle states. Keywords: 1 Introduction Non locality is a fascinating feature of quantum mechanics ( 13] [4], 5] Non locality was confirmed by a big number of experiments (e.g. 1] 2] 3] 16] These experiments are based on a Bell type inequality (e.g. 4] 10] and the outcomes of the measurements are shown to violate this inequality. Despite the fact that non locality is not the only possible ....

....entangled quantum mechanical two particle states. Keywords: 1 Introduction Non locality is a fascinating feature of quantum mechanics ( 13] 4] 5] Non locality was confirmed by a big number of experiments (e.g. 1] 2] 3] 16] These experiments are based on a Bell type inequality (e.g. [4], 10] and the outcomes of the measurements are shown to violate this inequality. Despite the fact that non locality is not the only possible explanation, it is the one which is usually used. We take in this paper also this point of view. This paper presents a cellular automaton that uses the ....

J. S. Bell. On the Einstein Podolsky Rosen Paradox. Physics, 1:195--200, 1964.

....non classical properties of quantum mechanics. Such properties are of considerable current interest in connection with their potential application to the securing of communication channels[7, 8, 9] Moreover, since entangled states also enter into the other Bell no hidden variable theorem[10] (predicated on locality) one anticipates a linking of non contextuality and non locality at a fundamental level. In particular the fact[6, 11] that there are examples that serve simultaneously as counter examples to both types of no hidden variable theorem is not too surprising. ....

Bell, J. S. 1964, "On the Einstein-Podolsky-Rosen paradox," Physics 1, 195-300.

....we were otherwise somehow attracted by the granting to measurement of an extraordinary status. 2 For an analysis of why von Neumann s and related impossibility proofs are not nearly so physically relevant as frequently imagined, see Bell s article [2] See also the celebrated article of Bell [3] for an impossibility proof which does have physical significance. See as well [6] For a recent, and comprehensive, account of Bohm s ideas see [20] function itself guiding this motion. Thus the hidden variables for Bohmian mechanics are simply the particle positions themselves. ....

J. S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1 (1964), 195--200, reprinted in [58] and in [10].

....question involves, of course, an enormous amount of detailed work. However a few general points are visible from the following examples. 3.1 EPR type phenomena and the division problem for objects Let us consider the example first proposed by D. Bohm which led J. Bell to his famous inequality [9]. An instable particle of spin 0 decays into two particles with spin 1 2 (event 0) On each of these particles the spin orientation is measured by a SternGerlach device. The orientation of the two Stern Gerlach magnets (unit vectors e; f) is set at some time (events 1 and 2) The subsequent ....

J. Bell, "On the Einstein-Podolsky-Rosen Paradox", Physics 1, 195 (1964).

....and hence destroy the information. In other words, the eavesdropper s acts will definitely cause a change in the signal between the legitimate users, which therefore reveals the presence of the eavesdropper. On the other hand it has been demonstrated that EPR and Bell s theorem or inequality [3] are also useful in quantum cryptography. Protocols based EPR and Bell s theorem exploit the properties of quantum correlated particles [10] A further simplified protocol which does not use Bell s inequality has been proposed by Bennett et al.[8] Although there are some other interesting ....

Bell, J. S.: On the Einstein Podolsky Rosen Paradox. Physics (N.Y.) 1 (1964) 195.

....1. Introduction Motivated by the desire to bring into the realm of testable hypotheses at least some of the important matters concerning the interpretation of quantum mechanics evoked in the controversy surrounding the EinsteinPodolsky Rosen paradox [18] 5] Bell discovered the first example [3][4] of a family of inequalities which are now generally called Bell s inequalities. These inequalities provide an upper bound on the strength of correlations between systems which are no longer interacting but have interacted in the past. Stated briefly, Bell showed that if the correlation ....

J.S. Bell, On the Einstein-Podolsky-Rosen paradox, Physics, 1 (1964), 195-200.

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John S. Bell, On the Einstein Podolsky Rosen paradox, ' ' Physics 1, 195 200 ( 1964). Reprinted in Ref. 25, pp. 403 408.

.... the EinsteinPodolsky Rosen problem [1] A pair of spin 1 2 particles initially in j Psi in i = jk 1 k 2i Omega 1 p 2 (j 1 # 2 i;j# 1 2 i) # (1) where 1 and 2 are the particle labels and k stands for the particle spatial mode, is split apart [2] Delimited by Bell s inequality [3], a set of spin measurements along specic directions leads to a conAEict between the predictions of quantum mechanics and the concepts of reality and locality as originally de ned in [1] Yet, experimental imperfection tends to erase the contradiction, and auxiliary assumptions are required to ....

J. S. Bell. On the Einstein Podolsky Rosen Paradox.Physics,1(3), 195, (1964).

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Bell, J. S. On the Einstein-Podolsky-Rosen paradox. Physics 1, 195-200 (1965).

....can find in the mathematical physics literature a number of theorems that, given an empirically observed set of probabilities, allow to state whether they admit a classical or alternatively a nonclassical probabilistic model. The most popular of such criteria where derived in the sixties by Bell (1964) within the specific physical context of the so called Einstein Podolsky Rosen paradox: they are universally referred to as Bell inequalities . 1 I received substantial help from my father Enrico G. a theoretical physicist at the University of Genoa (Italy) Many thanks to Domenico Costantini ....

Bell, J. S. (1964): "On the Einstein-Podolsky-Rosen Paradox," Physics, 1, 195-200.

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J. Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1(3):195--200, 1964.

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J.S. Bell, "On the Einstein-Podolsky-Rosen paradox", Physics, Vol. 1, 1964, pp. 195--200.

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J. S. Bell, On the Einstein-Podolsky-Rosen paradox, Physics, Vol. 1, pp. 195--200, 1964.

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J.S. Bell, "On the Einstein-Podolsky-Rosen paradox," Physics. 1, (1964.

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J.S. Bell. On the Einstein-Podolsky-Rosen paradox. Physics, 1:195--200, 1964.

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J.S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1 (1964), 195-200. (Reprinted in [82].)

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J.S. Bell, "On the Einstein-Podolsky-Rosen paradox", Physics, Volume 1, pp. 195--200, 1964.

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J. Bell. "On the Einstein-Podolsky-Rosen Paradox". Physics. Vol. 1, pp. 195-200, 1964.

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Bell J S On the Einstein-Podolsky-Rosen paradox, Physics 1 195--200, 1964

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Bell, J. S., "On the Einstein Podolsky Rosen Paradox," Physics 1, 195--200 (1964).

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S. Bell, J. S. On the Einstein Podolsky Rosen paradox, Physics, 1 #1964#, 195#200. Reprinted in #19# pp. 403#408, and in #2# pp. 14#21.

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J.S. Bell (1964), On the Einstein Podolsky Rosen paradox, Physics 1, 195--200.

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J.S. Bell. On the einstein-podolsky-rosen paradox. Physics, 1:195, 1964.

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