Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

There is no spooky action-at-a-distance in quantum correlations: Resolution of the Einstein-Podolsky-Rosen nonlocality puzzle

C. S. Unnikrishnan

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The long-standing puzzle of the nonlocal Einstein-Podolsky-Rosen correlations is resolved. The correct quantum mechanical correlations arise for the case of entangled particles when strict locality is assumed for the probability amplitudes instead of locality for probabilities. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Sixty five years ago, the most significant paper questioning a fundamental aspect of quantum phenomena was written by Einstein, Podolsky and Rosen (EPR) [1]. They addressed the question whether the wave-function represented a complete description of reality in quantum mechanics, and argued that it didn’t. Bohr’s reply to this paper [2] was not sufficient to resolve the fundamental issues raised by EPR. Decades later, Bohm rephrased the EPR problem [3] in terms of particles correlated in their spin and this helped enormously in analyzing the problem with clarity. John Bell analyzed the EPR problem in the early sixties and established the Bell’s inequalities obeyed by

Related papers

There is no spooky action-at-a-distance in quantum correlations: Resolution of the EPR nonlocality puzzle

C. S. Unnikrishnan

The long-standing puzzle of the nonlocal Einstein-Podolsky-Rosen correlations is resolved. The correct quantum mechanical correlations arise for the case of entangled particles when strict locality is assumed for the probability amplitudes instead of locality for probabilities. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state.

arXiv:quant-ph/0001112•Jan 31, 2000•3 citations

Quantum correlations from local amplitudes and the resolution of the Einstein-Podolsky-Rosen nonlocality puzzle

C. S. Unnikrishnan

The Einstein-Podolsky-Rosen (EPR) nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is more or less entirely resolved, if the quantum correlations are calculated directly from local quantities, which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes and calculate an amplitude correlation function. Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently “nonlocal” effects, such as quantum teleportation and entanglement swapping, are different from what is usually assumed. Bell-type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples, we derive the quantum correlations of two-particle maximally entangled states and the three-particle Greenberger-Horne-Zeilinger entangled state.

arXiv:quant-ph/0005103•Optics and Spectroscopy•Sep 1, 2001•0 citations

A Modest View of Bell's Theorem

S. P. Boughn

In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entanglement are a result of ordinary quantum superposition with no need to introduce nonlocality. The conclusion of the EPR paper wasn't that quantum mechanics is nonlocal but rather that it is an incomplete description of reality. For different reasons, many physicists, including me, agree with Einstein that quantum mechanics is necessarily an incomplete description of reality.

arXiv:1604.08529•Apr 28, 2016•3 citations

Nonlocality of the original Einstein-Podolsky-Rosen state

Oliver Cohen

We examine the properties and behavior of the original Einstein-Podolsky-Rosen (EPR) wave function [Phys. Rev. 47, 777 (1935)] and related Gaussian-correlated wave functions. We assess the degree of entanglement of these wave functions and consider an argument of Bell [Ann. (N.Y.) Acad. Sci. 480, 263 (1986)] based on the Wigner phase-space distribution [Phys. Rev. 40, 749 (1932)], which implies that the original EPR correlations can accommodate a local hidden-variable description. We extend Bell's analysis to the related Gaussian wave functions. We then show that it is possible to identify definite nonlocal aspects for the original EPR state and related states. We describe possible experiments that would demonstrate these nonlocal features through violations of Bell inequalities. The implications of our results, and in particular their relevance for the causal interpretation of quantum mechanics, are considered.

Physical Review A•Nov 1, 1997•24 citations

Einstein, Podolsky and Rosen versus Bohm and Bell

Andrei Yu. Khrennikov, Igor Vasil'evich Volovich

There is an opinion that the Bohm reformulation of the EPR paradox in terms of spin variables is equivalent to the original one. In this note we show that such an opinion is not justified. We apply to the original EPR problem the method which was used by Bell for the Bohm reformulation. He has shown that correlation function of two spins cannot be represented by classical correlation of separated bounded random processes. This Bell`s theorem has been interpreted as incompatibility of local realism with quantum mechanics. We show that, in contrast to Bell`s theorem for spin or polarization correlation functions, the correlation of positions (or momenta) of two particles, depending on the rotation angles, in the original EPR model always admits a representation in the form of classical correlation of separated random processes. In this sense there exists a local realistic representation for the original EPR model but there is no such a representation for the Bohm spin reformulation of the EPR paradox. It shows also that the phenomena of quantum nonlocality is based not only on the properties of entangled states but also on the using of particular bounded observables.

arXiv:quant-ph/0211078•Nov 13, 2002•4 citations

Neglecting non-locality: the response to EPR

Kristian Camilleri

Abstract The 1935 Einstein–Podolsky–Rosen (EPR) paper, “Can Quantum–Mechanical Description of Physical Reality Be Considered Complete?”, stands as a landmark in the foundational debates over quantum mechanics. While the paper has since become one of Einstein’s most cited works, it initially received little attention, and the feature of non-locality, which was central to the argument in the paper, was largely neglected for decades. In this paper, I offer two reasons for this early neglect of non-locality in the immediate aftermath of EPR. First, early responses to the EPR paper defended the completeness of quantum mechanics by reformulating the thought experiment the authors had presented, thereby obscuring the feature of quantum mechanics the authors had wished to highlight. Bohr’s influential reply, for instance, substituted the specific thought experiment presented by EPR with the two-slit experiment, thus suppressing the entanglement between spatially separated systems. A second reason for the marginalization of non-locality was the tendency to see Einstein’s critique of quantum mechanics as proceeding from a commitment to determinism, though this in fact played no role in the EPR paper or in his later writings and correspondence. This paper argues that the failure to recognize non-locality was partly a result of the rhetorical manoeuvring by EPR’s critics, but also to a broader philosophical climate dominated by concerns over determinism, which effectively eclipsed all other conceptual issues, Only with Bell’s theorem in the 1960s did non-locality return as a serious focus of foundational inquiry.

The European Physical Journal H•Aug 12, 2026•0 citations
The long-standing puzzle of the nonlocal Einstein-Podolsky-Rosen correlations is resolved. The correct quantum mechanical correlations arise for the case of entangled particles when strict locality is assumed for the probability amplitudes instead of locality for probabilities. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Sixty five years ago, the most significant paper questioning a fundamental aspect of quantum phenomena was written by Einstein, Podolsky and Rosen (EPR) [1]. They addressed the question whether the wave-function represented a complete description of reality in quantum mechanics, and argued that it didn’t. Bohr’s reply to this paper [2] was not sufficient to resolve the fundamental issues raised by EPR. Decades later, Bohm rephrased the EPR problem [3] in terms of particles correlated in their spin and this helped enormously in analyzing the problem with clarity. John Bell analyzed the EPR problem in the early sixties and established the Bell’s inequalities obeyed by
The Einstein-Podolsky-Rosen (EPR) nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is more or less entirely resolved, if the quantum correlations are calculated directly from local quantities, which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes and calculate an amplitude correlation function. Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently “nonlocal” effects, such as quantum teleportation and entanglement swapping, are different from what is usually assumed. Bell-type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples, we derive the quantum correlations of two-particle maximally entangled states and the three-particle Greenberger-Horne-Zeilinger entangled state.
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entanglement are a result of ordinary quantum superposition with no need to introduce nonlocality. The conclusion of the EPR paper wasn't that quantum mechanics is nonlocal but rather that it is an incomplete description of reality. For different reasons, many physicists, including me, agree with Einstein that quantum mechanics is necessarily an incomplete description of reality.
We examine the properties and behavior of the original Einstein-Podolsky-Rosen (EPR) wave function [Phys. Rev. 47, 777 (1935)] and related Gaussian-correlated wave functions. We assess the degree of entanglement of these wave functions and consider an argument of Bell [Ann. (N.Y.) Acad. Sci. 480, 263 (1986)] based on the Wigner phase-space distribution [Phys. Rev. 40, 749 (1932)], which implies that the original EPR correlations can accommodate a local hidden-variable description. We extend Bell's analysis to the related Gaussian wave functions. We then show that it is possible to identify definite nonlocal aspects for the original EPR state and related states. We describe possible experiments that would demonstrate these nonlocal features through violations of Bell inequalities. The implications of our results, and in particular their relevance for the causal interpretation of quantum mechanics, are considered.
There is an opinion that the Bohm reformulation of the EPR paradox in terms of spin variables is equivalent to the original one. In this note we show that such an opinion is not justified. We apply to the original EPR problem the method which was used by Bell for the Bohm reformulation. He has shown that correlation function of two spins cannot be represented by classical correlation of separated bounded random processes. This Bell`s theorem has been interpreted as incompatibility of local realism with quantum mechanics. We show that, in contrast to Bell`s theorem for spin or polarization correlation functions, the correlation of positions (or momenta) of two particles, depending on the rotation angles, in the original EPR model always admits a representation in the form of classical correlation of separated random processes. In this sense there exists a local realistic representation for the original EPR model but there is no such a representation for the Bohm spin reformulation of the EPR paradox. It shows also that the phenomena of quantum nonlocality is based not only on the properties of entangled states but also on the using of particular bounded observables.
Abstract The 1935 Einstein–Podolsky–Rosen (EPR) paper, “Can Quantum–Mechanical Description of Physical Reality Be Considered Complete?”, stands as a landmark in the foundational debates over quantum mechanics. While the paper has since become one of Einstein’s most cited works, it initially received little attention, and the feature of non-locality, which was central to the argument in the paper, was largely neglected for decades. In this paper, I offer two reasons for this early neglect of non-locality in the immediate aftermath of EPR. First, early responses to the EPR paper defended the completeness of quantum mechanics by reformulating the thought experiment the authors had presented, thereby obscuring the feature of quantum mechanics the authors had wished to highlight. Bohr’s influential reply, for instance, substituted the specific thought experiment presented by EPR with the two-slit experiment, thus suppressing the entanglement between spatially separated systems. A second reason for the marginalization of non-locality was the tendency to see Einstein’s critique of quantum mechanics as proceeding from a commitment to determinism, though this in fact played no role in the EPR paper or in his later writings and correspondence. This paper argues that the failure to recognize non-locality was partly a result of the rhetorical manoeuvring by EPR’s critics, but also to a broader philosophical climate dominated by concerns over determinism, which effectively eclipsed all other conceptual issues, Only with Bell’s theorem in the 1960s did non-locality return as a serious focus of foundational inquiry.