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

arXiv:quant-ph/0012091 · Physical Review A

Nonlocal effects of partial measurements and quantum erasure

Avshalom C. Elitzur, Shahar Dolev

Published May 15, 2001• 29 citations
arXivHTMLPDF

Abstract

Partial measurement turns the initial superposition not into a definite outcome but into a greater probability for it. The probability can approach 100%, yet the measurement can undergo complete quantum erasure. In the Einstein-Podolsky-Rosen (EPR) setting, we prove that (i) every partial measurement nonlocally creates the same partial change in the distant particle, and (ii) every erasure inflicts the same erasure on the distant particle's state. This enables an EPR experiment where the nonlocal effect does not vanish after a single measurement but keeps ``traveling'' back and forth between particles. We study an experiment in which two distant particles are subjected to interferometry with a partial ``which path'' measurement. Such a measurement causes a variable amount of correlation between the particles. A new inequality is formulated for same-angle polarizations, extending Bell's inequality for different angles. The resulting nonlocality proof is highly visualizable, as it rests entirely on the interference effect. Partial measurement also gives rise to a new form of entanglement, where the particles manifest correlations of multiple polarization directions. Another novelty in that the measurement to be erased is fully observable, in contrast to prevailing erasure techniques in which it can never be observed. Some profound conceptual implications of our experiment are briefly pointed out.

DOI
10.1103/physreva.63.062109

Related papers

The Retrocausal Nature of Quantum Measurement Revealed by Partial and Weak Measurements

Avshalom C. Elitzur, Eliahu Cohen, Daniel P. Sheehan

Quantum measurement is sometimes more effective when its result is not definite. Partial measurement turns the initial superposition not into a certain state but to a greater probability for it, enabling probing the quantum state in cases where complete measurement makes the noncommuting variables inaccessible. It also enables full quantum erasure that, unlike prevailing method, can be carried out even on recorded results. Aharonov's weak measurement is another method of imprecisely measuring quantum variables, outsmarting the uncertainty principle in even subtler ways. Happily, the two methods complement and corroborate one another in several interesting ways. We gedankenly apply these measurements to the EPR case. A pair of entangled particles undergoes more than one pair of partial and weak measurements, which, unlike complete measurements, leave them partially correlated. Their erasure is then shown to be as nonlocal as measurement itself. Surprisingly, the temporal relations between such measurements in the EPR setting do not follow the temporal sequence perceived by an external observer. For each particle, the measurements performed on the other operate as if they occurred (with signs reversed) in its own past, and in reversed order. This fully accords with Cramer's transactional interpretation and Aharonov's two state‐vector formalism.

AIP conference proceedings•Jan 1, 2011•15 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

Filtering one-way Einstein-Podolsky-Rosen steering

Ze-Yan Hao, Yan Wang, Jia-Kun Li +8 more

Einstein-Podolsky-Rosen (EPR) steering, a fundamental concept of quantum nonlocality, describes one observer's capability to remotely affect another distant observer's state by local measurements. Unlike quantum entanglement and Bell nonlocality, both associated with the symmetric quantum correlation, EPR steering depicts the unique asymmetric property of quantum nonlocality. With the local filter operation in which some system components are discarded, quantum nonlocality can be distilled to enhance the nonlocal correlation and even the hidden nonlocality can be activated. However, asymmetric quantum nonlocality in the filter operation still lacks a well-rounded investigation, especially considering the discarded parts where quantum nonlocal correlations may still exist with probabilities. Here, in both theory and experiment, we investigate the effect of reusing the discarded particles from local filter. We observe all configurations of EPR steering simultaneously and other intriguing evolution of asymmetric quantum nonlocality, such as reversing the direction of one-way EPR steering. This work provides a perspective to answer ``what is the essential role of utilizing quantum steering as a resource?'' and demonstrates a practical toolbox for manipulating asymmetric quantum systems with significant potential applications in quantum information tasks.

arXiv:2304.04210•Physical Review A•Feb 9, 2024•11 citations

EPR paradox, quantum nonlocality and physical reality

Marian Kupczyński

Eighty years ago Einstein, Podolsky and Rosen demonstrated that instantaneous reduction of wave function, believed to describe completely a pair of entangled physical systems, led to EPR paradox. The paradox disappears in statistical interpretation of quantum mechanics (QM) according to which a wave function describes only an ensemble of identically prepared physical systems. QM predicts strong correlations between outcomes of measurements performed on different members of EPR pairs in far-away locations. Searching for an intuitive explanation of these correlations John Bell analysed so called local realistic hidden variable models and proved that correlations consistent with these models satisfy Bell inequalities which are violated by some predictions of QM and by experimental data. Several different local models were constructed and inequalities proven. Some eminent physicists concluded that Nature is definitely nonlocal and that it is acting according to a law of nonlocal randomness. According to these law perfectly random, but strongly correlated events, can be produced at the same time in far away locations and a local and causal explanation of their occurrence cannot be given. We strongly disagree with this conclusion and we prove the contrary by analysing in detail some influential finite sample proofs of Bell and CHSH inequalities and so called Quantum Randi Challenges. We also show how one can win so called Bell's game without violating locality of Nature. Nonlocal randomness is inconsistent with local quantum field theory, with standard model in elementary particle physics and with causal laws and adaptive dynamics prevailing in the surrounding us world. The experimental violation of Bell-type inequalities does not prove the nonlocality of Nature but it only confirms a contextual character of quantum observables and gives a strong argument against counterfactual definiteness and against a point of view according to which experimental outcomes are produced in irreducible random way.

arXiv:1602.02959•Journal of Physics Conference Series•Mar 1, 2016•27 citations

Bell's Theorem Reexamined

Luiz Carlos Ryff

An Einstein-Podolsky-Rosen (EPR)-like argument using events separated by a time-like interval strongly suggestes that measuring the polarization state of a photon of an entangled pair changes the polarization state of the other distant photon. Trough a very simple demonstration, the Wigner-D'Espagnat inequality is used to show that in order to prove Bell's theorem neither the assumption that there is a well-defined space of complete states $λ$ of the particle pair and well-defined probability distribution $ρ(λ)$ over this space nor the use of counterfactuals is necessary. These results reinforce the viewpoint that quantum mechanics implicitly presupposes some sort of nonlocal connection between the particles of an entangled pair. As will become evident from our discussion, relinquishing realism and/or free will cannot solve this apparent puzzle.

arXiv:quant-ph/0510101•Oct 13, 2005•0 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
Partial measurement turns the initial superposition not into a definite outcome but into a greater probability for it. The probability can approach 100%, yet the measurement can undergo complete quantum erasure. In the Einstein-Podolsky-Rosen (EPR) setting, we prove that (i) every partial measurement nonlocally creates the same partial change in the distant particle, and (ii) every erasure inflicts the same erasure on the distant particle's state. This enables an EPR experiment where the nonlocal effect does not vanish after a single measurement but keeps traveling'' back and forth between particles. We study an experiment in which two distant particles are subjected to interferometry with a partial which path'' measurement. Such a measurement causes a variable amount of correlation between the particles. A new inequality is formulated for same-angle polarizations, extending Bell's inequality for different angles. The resulting nonlocality proof is highly visualizable, as it rests entirely on the interference effect. Partial measurement also gives rise to a new form of entanglement, where the particles manifest correlations of multiple polarization directions. Another novelty in that the measurement to be erased is fully observable, in contrast to prevailing erasure techniques in which it can never be observed. Some profound conceptual implications of our experiment are briefly pointed out.
Quantum measurement is sometimes more effective when its result is not definite. Partial measurement turns the initial superposition not into a certain state but to a greater probability for it, enabling probing the quantum state in cases where complete measurement makes the noncommuting variables inaccessible. It also enables full quantum erasure that, unlike prevailing method, can be carried out even on recorded results. Aharonov's weak measurement is another method of imprecisely measuring quantum variables, outsmarting the uncertainty principle in even subtler ways. Happily, the two methods complement and corroborate one another in several interesting ways. We gedankenly apply these measurements to the EPR case. A pair of entangled particles undergoes more than one pair of partial and weak measurements, which, unlike complete measurements, leave them partially correlated. Their erasure is then shown to be as nonlocal as measurement itself. Surprisingly, the temporal relations between such measurements in the EPR setting do not follow the temporal sequence perceived by an external observer. For each particle, the measurements performed on the other operate as if they occurred (with signs reversed) in its own past, and in reversed order. This fully accords with Cramer's transactional interpretation and Aharonov's two state‐vector formalism.
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.
Einstein-Podolsky-Rosen (EPR) steering, a fundamental concept of quantum nonlocality, describes one observer's capability to remotely affect another distant observer's state by local measurements. Unlike quantum entanglement and Bell nonlocality, both associated with the symmetric quantum correlation, EPR steering depicts the unique asymmetric property of quantum nonlocality. With the local filter operation in which some system components are discarded, quantum nonlocality can be distilled to enhance the nonlocal correlation and even the hidden nonlocality can be activated. However, asymmetric quantum nonlocality in the filter operation still lacks a well-rounded investigation, especially considering the discarded parts where quantum nonlocal correlations may still exist with probabilities. Here, in both theory and experiment, we investigate the effect of reusing the discarded particles from local filter. We observe all configurations of EPR steering simultaneously and other intriguing evolution of asymmetric quantum nonlocality, such as reversing the direction of one-way EPR steering. This work provides a perspective to answer ``what is the essential role of utilizing quantum steering as a resource?'' and demonstrates a practical toolbox for manipulating asymmetric quantum systems with significant potential applications in quantum information tasks.
Eighty years ago Einstein, Podolsky and Rosen demonstrated that instantaneous reduction of wave function, believed to describe completely a pair of entangled physical systems, led to EPR paradox. The paradox disappears in statistical interpretation of quantum mechanics (QM) according to which a wave function describes only an ensemble of identically prepared physical systems. QM predicts strong correlations between outcomes of measurements performed on different members of EPR pairs in far-away locations. Searching for an intuitive explanation of these correlations John Bell analysed so called local realistic hidden variable models and proved that correlations consistent with these models satisfy Bell inequalities which are violated by some predictions of QM and by experimental data. Several different local models were constructed and inequalities proven. Some eminent physicists concluded that Nature is definitely nonlocal and that it is acting according to a law of nonlocal randomness. According to these law perfectly random, but strongly correlated events, can be produced at the same time in far away locations and a local and causal explanation of their occurrence cannot be given. We strongly disagree with this conclusion and we prove the contrary by analysing in detail some influential finite sample proofs of Bell and CHSH inequalities and so called Quantum Randi Challenges. We also show how one can win so called Bell's game without violating locality of Nature. Nonlocal randomness is inconsistent with local quantum field theory, with standard model in elementary particle physics and with causal laws and adaptive dynamics prevailing in the surrounding us world. The experimental violation of Bell-type inequalities does not prove the nonlocality of Nature but it only confirms a contextual character of quantum observables and gives a strong argument against counterfactual definiteness and against a point of view according to which experimental outcomes are produced in irreducible random way.
An Einstein-Podolsky-Rosen (EPR)-like argument using events separated by a time-like interval strongly suggestes that measuring the polarization state of a photon of an entangled pair changes the polarization state of the other distant photon. Trough a very simple demonstration, the Wigner-D'Espagnat inequality is used to show that in order to prove Bell's theorem neither the assumption that there is a well-defined space of complete states λλλ of the particle pair and well-defined probability distribution ρ(λ)ρ(λ)ρ(λ) over this space nor the use of counterfactuals is necessary. These results reinforce the viewpoint that quantum mechanics implicitly presupposes some sort of nonlocal connection between the particles of an entangled pair. As will become evident from our discussion, relinquishing realism and/or free will cannot solve this apparent puzzle.
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.