We argue that the so-called entangled states in quantum theory are not something exceptional, deserving a special attention in our efforts to understand conceptual foundations of quantum world. They appear by constructing the basis states of a compound system via the basis states of entering subsystems and describe it as a wholeness. While a system is considered as a wholeness, the individual members, forming the entangled state, have no physical meaning. In consequence, there is no physical ground for Einstein, Podolsky and Rosen (EPR) correlations arising in a process of decaying the system, being in the entangled state, into its constituent parts. The same regards to Bell's introduced non-locality of quantum world.
The EPR paradox and the meaning of the Bell inequality are discussed. It is shown that considering the quantum objects as carrying with them ''instruction kits'' telling them what to do when meeting a measurement apparatus any paradox disappears. In this view the quantum state is characterized by the prescribed behaviour rather than by the specific value a parameter assumes as a result of an interaction.
We exhibit a classical model free from any paradox which exactly simulates the spin EPR test. We conclude that Bell's inequality violation is a strictly classical phenomenon, contrary to a general belief.
A new interpretation offers a consistent conceptual basis for nonrelativistic quantum mechanics. The Einstein-Podolsky-Rosen (EPR) paradox is solved and the violation of Bell's inequality is explained by maintaining realism, inductive inference and Einstein separability.
The paradoxes of the double-slit and the EPR experiments with particles are shown to originate in the implicit assumption that the particles are always located in the classical space. It is demonstrated that there exists a natural substitute for this assumption that provides a method of resolving the paradoxes.
The purpose of this manuscript is to provide a short pedagogical explanation why "quantum collapse" is not a metaphysical event, by pointing out the analogy with a "classical collapse" which is associated with the Monty Hall Paradox.
We present a unified approach, based on the use of quantum uncertainty relations, for arriving at criteria for the demonstration of the EPR paradox and macroscopic superpositions. We suggest to view each criterion as a means to demonstrate an EPR-type paradox, where there is an inconsistency between the assumptions of a form of realism, either macroscopic realism (MR) or local realism (LR), and the completeness of quantum mechanics.
The EPR (Einstein, Podolsky, Rosen) argument and the Schrodinger cat paradox are revisited in relation with modern quantum optics and atomic physics and with the concept of decoherence. It is shown that the questions raised fifty years ago are still at the heart of our understanding of quantum physics today.
The orthodox quantum mechanics has been commonly regarded as being supported decisively by the polarization EPR experiments, in which Bell's inequalities have been violated. The given conclusion has been based, however, on several mistakes that have not been yet commonly known and sufficiently analyzed. The whole problem will be newly discussed and a corresponding solution will be proposed.
Backward causation in which future events affect the past is formalized in a way consistent with Special Relativity and shown to restore locality to nonrelativistic quantum mechanics. It can explain the correlations of the EPR paradox without using hidden variables. It also restores time-symmetry to microphysics. Quantum Mechanics has the right properties to allow for backward causation. The new model is probably untestable experimentally but it has profound philosophical implications concerning reality.
We obtain criteria for entanglement and the EPR paradox for spin-entangled particles and analyse the effects of decoherence caused by absorption and state purity errors. For a two qubit photonic state, entanglement can occur for all transmission efficiencies. In this case, the state preparation purity must be above a threshold value. However, Bohm's spin EPR paradox can be achieved only above a critical level of loss. We calculate a required efficiency of 58%, which appears achievable with current quantum optical technologies. For a macroscopic number of particles prepared in a correlated stat…
A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for measurements with continuous variable outcomes is presented to establish criteria for the demonstration of the EPR paradox, for situations where the correlation between spatially separated subsystems is not perfect. Two types of criteria for EPR correlations are determined. The first type are based on measurements of the variances of conditional probability distributions and are necessary to reflect directly the situation of the original EPR paradox. The second weaker set of EPR criteria are based on the proven failure of …
In the normal presentation of the EPR problem a comparison is made between the (weak) Copenhagen interpretation of quantum mechanics which seems to suggest that at times action at a distance may take place, and the hidden parameter interpretation which must satisfy Bell's inequality, in contradiction to the predictions of quantum mechanics. In this paper, we consider a relativistic approach to the paradox. However, the frame of reference under consideration is not the usual Lorenz frame but rather the spin frame of reference which is invariant with respect to the SU(2) group.
Relativistic bipartite entangled quantum states is studied to show that Nature doesn't favor nonlocality for massive particles in the ultra-relativistic limit. We found that to an observer (Bob) in a moving frame S', the entangled Bell state shared by Alice and Bob appears as the superposition of the Bell bases in the frame S' due to the requirement of the special relativity. It is shown that the entangled pair satisfies the Bell's inequality when the boost speed approaches the speed of light, thus providing a counter example for nonlocality of Einstein-Podolsky-Rosen(EPR) paradox.
The concept of steering was introduced by Schrodinger in 1935 as a generalization of the EPR paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and Isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell-nonlocality. …
We show that EPR's criterion of reality leads to contradictions in quantum mechanics. When locality is assumed, an inequality involving only one particle is violated, while when parameter and outcome dependence are assumed, EPR-realism is shown to be not Lorentz invariant. Quantum mechanics is both non-local and non-realistic.
The violation of local uncertainty relations is a valuable tool for detecting entanglement, especially in multi-dimensional systems. The orbital angular momentum of light provides such a multi-dimensional system. We study quantum correlations for the conjugate variables of orbital angular momentum and angular position. We determine an experimentally testable criterion for the demonstration of an angular version of the EPR paradox. For the interpretation of future experimental results from our proposed setup, we include a model for the indeterminacies inherent to the angular position measuremen…
In 1935, Albert Einstein, Boris Podolsky, and Nathan Rosen ('EPR') reported on a thought experiment that they believed showed that quantum theory provided an incomplete description of reality. Today we know that quantum theory is a complete and correct description of Nature (in flat space-time). The EPR thought experiment is predicted by quantum theory and has since been experimentally confirmed. However, EPR experiments have no physical pictorial explanation, and are considered part of a "paradox". Here I resolve the "paradox". I show independently of any interpretation of quantum theory that…
We review both the Einstein, Podolsky, Rosen (EPR) paper about the completeness of quantum theory, and Schrodinger's responses to the EPR paper. We find that both the EPR paper and Schrodinger's responses, including the cat paradox, are not consistent with the current understanding of quantum theory and thermodynamics. Because both the EPR paper and Schrodinger's responses play a leading role in discussions of the fascinating and promising fields of quantum computation and quantum information, we hope our review will be helpful to researchers in these fields.
Einstein-Podolsky-Rosen (EPR) paradox is considered in a relation to a measurement of an arbitrary quantum system . It is shown that the EPR paradox always appears in a gedanken experiment with two successively joined measuring devices.
The Einstein-Podolsky-Rosen (EPR) paradox was enunciated in 1935 and since then it has made a lot of ink flow. Being a subtle result, it has also been largely misunderstood. Indeed, if questioned about its solution, many physicists will still affirm today that the paradox has been solved by the Bell-test experimental results, which have shown that entangled states are real. However, this remains a wrong view, as the validity of the EPR ex-absurdum reasoning is independent from the Bell-test experiments, and the possible structural shortcomings it evidenced cannot be eliminated. These were corr…
We prove that by adopting a strict interpretation of the Einstein-Podolsky-Rosen criterion of reality, the proofs of the known non-locality theorems fail in showing that quantum mechanics violates the principle of locality and reality.
Local realism has been knocked down by the experiments with entangled pairs of particles based on Bell's theorem(J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964)). However, there has been continuing debate on whether locality or realism is the problem. In this work, we analyzed the Einstein-Podolsky-Rosen thought experiment of Bohm's version using information theory and thermodynamics. The inference of non-locality from EPR experiments will be against the principle of non-realism of quantum mechanics. Therefore, the experiments about quantum entanglement cannot provide any proof to a…
Most physicists agree that the Einstein-Podolsky-Rosen-Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell's inequality are locality and counterfactual definiteness, but not scientific realism, determinism, or hidden …
Experiments have reported the entanglement of two spatially separated macroscopic atomic ensembles at room temperature (Krauter et al 2011 Phys. Rev. Lett. 107 080503; Julsgaard et al 2001 Nature 413 400). We show how an Einstein-Podolsky-Rosen (EPR) paradox is realizable with this experiment. Our proposed test involves violation of an inferred Heisenberg uncertainty principle, which is a sufficient condition for an EPR paradox. This is a stronger test of nonlocality than entanglement. Our proposal would enable the first definitive confirmation of quantum EPR paradox correlations between two m…
In the paper, the EPR paradox is explored by the approach of quantum supervaluationism that leads to a "gappy" semantics with the propositions giving rise to truth-value gaps. Within this approach, the statement, which asserts that in the singlet state the system of two (i.e., A and B) spin-1/2 particles possesses the a priori property "spin A is up and spin B is down along the same axis" or "spin A is down and spin B is up along the same axis", does not have the truth-value at all. Consequently, after the verification of, say, the proposition "spin A is up along the z-axis", the statistical p…
We describe how to generate an Einstein-Podolsky-Rosen (EPR) paradox between a mesoscopic mechanical oscillator and an optical pulse. We find two types of paradox, defined by whether it is the oscillator or the pulse that shows the effect Schrodinger called "steering". Only the oscillator paradox addresses the question of mesoscopic local reality for a massive system. In that case, EPR's "elements of reality" are defined for the oscillator, and it is these elements of reality that are falsified (if quantum mechanics is complete). For this sort of paradox, we show that a thermal barrier exists,…
In spite of the fact that statistical predictions of quantum theory (QT) can only be tested if large amount of data is available a claim has been made that QT provides the most complete description of an individual physical system. Einstein's opposition to this claim and the paradox he presented in the article written together with Podolsky and Rosen in 1935 inspired generations of physicists in their quest for better understanding of QT. Seventy years after EPR article it is clear that without deep understanding of the character and limitations of QT one may not hope to find a meaningful unif…
This Colloquium examines the field of the EPR Gedankenexperiment, from the original paper of Einstein, Podolsky and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. We analyze the relationship with entanglement and Bell's theorem, and summarize the progress to date towards experimental confirmation of the EPR paradox, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fibre quantum soli…
Quantum experiments detect particles, but they reveal information about wave properties. No matter how quanta are detected, they always express the local net state of the corresponding wave-function. The mechanism behind this process is still a mystery. However, quantum wave-functions evolve like classical waves. If they determine all the observations, why do they entail "weird" phenomena? In particular, why do they produce conceptual problems, such as the EPR paradox? It turns out that all the major interpretations in quantum mechanics are particle-based ontologies. Variables of fundamental i…
We model measuring processes of a single spin-1/2 object and of a pair of spin-1/2 objects in the EPR-Bohm state by systems of differential equations. Our model is a local model with hidden-variables of the EPR-Bohm Gedankenexperiment. Although there is no dynamical interaction between a pair of spin-1/2 objects, the model can reproduce approximately the quantum-mechanical correlations by the coincidence counting. Hence the Bell inequality is violated. This result supports the idea that the coincidence counting is the source of the non-locality in the EPR-Bohm Gedankenexperiment.
We give a conceptually simple proof of nonlocality using only the perfect correlations between results of measurements on distant systems discussed by Einstein, Podolsky and Rosen---correlations that EPR thought proved the incompleteness of quantum mechanics. Our argument relies on an extension of EPR by Schrödinger.
The Einstein-Podolsky-Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of "quantum nonlocality", which manifests itself by three different types: quantum entanglement, quantum steering, and Bell nonlocality. Although Bell nonlocality is more often used to show the "quantum nonlocality", the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality,thus making it…
This article shows that the there is no paradox. Violation of Bell's inequalities should not be identified with a proof of non locality in quantum mechanics. A number of past experiments is reviewed, and it is concluded that the experimental results should be re-evaluated. The results of the experiments with atomic cascade are shown not to contradict the local realism. The article points out flaws in the experiments with down-converted photons. The experiments with neutron interferometer on measuring the "contextuality" and Bell-like inequalities are analyzed, and it is shown that the experime…
We report on a momentum-position realization of the EPR paradox using direct detection in the near and far fields of the photons emitted by collinear type-II phase-matched parametric downconversion. Using this approach we achieved a measured two-photon momentum-position variance product of $0.01\hbar^2$, which dramatically violates the bounds for the EPR and separability criteria.
Monogamy inequalities for the way bipartite EPR steering can be distributed among N systems are derived. One set of inequalities is based on witnesses with two measurement settings, and may be used to demonstrate correlation of outcomes between two parties, that cannot be shared with more parties. It is shown that the monogamy for steering is directional. Two parties cannot independently demonstrate steering of a third system, using the same two-setting steering witness, but it is possible for one party to steer two independent systems. This result explains the monogamy of two-setting Bell ine…
We give an introduction to an entangled massive system, specifically the neutral kaon system, which has similarities to the entangled two photon system, but, however, also challenging differences.
Einstein, Podolski and Rosen (EPR) have shown that any wave function (subject to the Schrödinger equation) can describe the physical reality completely, and any two observables associated to two non-commuting operators can have simultaneous reality. In contrast, quantum theory claims that the wave function can capture the physical reality completely, and the physical quantities associated to two non-commuting operators cannot have simultaneous reality. The above contradiction is known as the EPR paradox. Here, we unambiguously expose that there is a hidden assumption made by EPR, which gives r…
In an empirical logic, an experimentally verifiable proposition P relating to a quantum system is assigned the value of either true of false if the system is in the pure state that belongs or, respectively, does not belong to the Hilbert subspace that represents P. Determined in such a way truth or falsity of P can be termed a factual truth-value of P. In the present paper, it is proposed to consider a counter-factual truth-value of P, i.e., either of the values, true or false, that would have been taken by P if the system had been in a pure state belonging to a Hilbert subspace that does not …
Quantum mechanics is very odd. It presents both an immensely practical and a deeply troubling conception of the physical world. As such, its uses stretch from optimizing nanoelectronics to examining the very nature of reality. In this article we will see how quantum mechanics forces us into a dramatic rethinking of one of the most fundamental tenets of modern science, locality. The article is written in a popular style for anyone interested in this subject.
In a previous paper certain measurable criteria have been derived, that are sufficient to demonstrate the existence of Einstein-Podolsky-Rosen (EPR) correlations for measurements with continuous variable outcomes. Here it is shown how such EPR criteria, which do not demand perfect EPR correlations, can be used to prove the extent of security for continuous variable quantum cryptographic schemes (in analogy to that proposed by Ekert) where Alice and Bob hope to construct a secure sequence of values from measurements performed on continuous-variable EPR-correlated fields sent from a distant sour…
Einstein, Podolsky and Rosen (EPR) pointed out that the quantum-mechanical description of "physical reality" implied an unphysical, instantaneous action between distant measurements. To avoid such an action at a distance, EPR concluded that Quantum Mechanics had to be incomplete. However, its extensions involving additional "hidden variables", allowing for the recovery of determinism and locality, have been disproved experimentally (Bell's theorem). Here, I present an opposite solution of the paradox based on the greater indeterminism of the modern Quantum Field Theory (QFT) description of Par…
Formulas for calculating the joint probability of outcomes of measurements performed on mutually non-interacting component systems of a combined system prepared in an entangled state are presented. The formulas are based on non-relativistic quantum mechanics. An interpretation of the joint probability which conforms to the principle of local causality is proposed. The joint probability of outcomes of spin measurements performed on the well-known system of two spatially separated spin-1/2 particles prepared initially in the singlet state is used to illustrate the proposed interpretation of theo…
It is shown that the absence of an objective existence of the results of quantum measurements cannot be proved by known experiments. There are also general arguments confirming this conclusion.
What is the momentum spectrum of a particle moving in an infinite deep square well? Einstein, Pauli and Yukawa had adopted different point of view than that in usual text books. The theoretical and experimental implication of this problem is discussed.
The original version of Einstein-Podolsky-Rosen (EPR) paradox and the Klein paradox of Klein-Gordon (KG) equation are discussed to show the necessity of existence of antiparticle with its wavefunction being fixed unambiguously. No concept of "hole" is needed.
The original version of Einstein-Podolsky-Rosen (EPR) paradox is discussed to show the completeness of Quantum Mechanics (QM). The unique solution leads to the wave function of antiparticle unambiguously, which implies the essential conformity between QM and Special Relativity (SR).
In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell's nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR's original scenario is "steering", i.e., the no…
We demonstrate the appearance of Einstein-Podolsky-Rosen (EPR) paradox when a radiation field impinges on a movable mirror. The, the possibility of a local realism test within a pendular Fabry-Perot cavity is shown to be feasible.
We study multi-partite entanglement, the generation of EPR states and quantum steering in a three-mode optomechanical system composed of an atomic ensemble located inside a single-mode cavity with a movable mirror. The cavity mode is driven by a short laser pulse, has a nonlinear parametric-type interaction with the mirror and a linear beamsplitter-type interaction with the atomic ensemble. There is no direct interaction of the mirror with the atomic ensemble. A threshold effect for the dynamics of the system is found, above which the system works as an amplifier and below which as an attenuat…
We formally link the concept of steering (a concept created by Schrodinger but only recently formalised by Wiseman, Jones and Doherty [Phys. Rev. Lett. 98, 140402 (2007)] and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid [Phys. Rev. A, 40, 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variables observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-ty…
Spatially entangled twin photons provide a test of the Einstein-Podolsky-Rosen (EPR) paradox in its original form of position (image plane) versus impulsion (Fourier plane). We show that recording a single pair of images in each plane is sufficient to safely demonstrate an EPR paradox. On each pair of images, we have retrieved the fluctuations by subtracting the fitted deterministic intensity shape and then have obtained an intercorrelation peak with a sufficient signal to noise ratio to safely distinguish this peak from random fluctuations. A 95% confidence interval has been determined, confi…
