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:1604.00623

Interpreting the macroscopic pointer by analyzing the Einstein-Podolsky-Rosen steering of an entangled macroscopic superposition state

M. D. Reid

Published Apr 3, 2016• 1 citation
arXivHTMLPDF

Abstract

We examine Einstein-Podolsky-Rosen's (EPR) steering nonlocality for two realisable Schrodinger cat-type states where a meso/ macroscopic system (called the "cat"-system) is entangled with a spin-$1/2$ system. For large cat-systems, we show that a local hidden state model is near-satisfied, meaning that the cat-system can be consistent with being in a mixture of "dead" and "alive" states despite that it is entangled with the spin system. We justify that a rigorous signature of the Schrodinger cat-type paradox is the EPR-steering of the cat-system and provide two experimental signatures. This leads to a hybrid quantum/ classical interpretation of the macroscopic pointer of a measurement device and suggests many Schrodinger cat-type paradoxes can be explained by microscopic nonlocality.

DOI
10.48550/arxiv.1604.00623

Related papers

Interpreting the macroscopic pointer via the elements of reality of a Schrodinger cat

M. D. Reid

We examine Einstein-Podolsky-Rosen's (EPR) steering nonlocality for two realisable Schrodinger cat-type states where a meso/ macroscopic system (called the cat-system) is entangled with a spin-$1/2$ system. For large cat-systems, we show that a local hidden state model is near-satisfied, meaning that the cat-system can be consistent with being in a mixture of dead and alive states despite that it is entangled with the spin system. We justify that a rigorous signature of the Schrodinger cat-type paradox is the EPR-steering of the cat-system and provide two experimental signatures. This leads to a hybrid quantum/ classical interpretation of the macroscopic pointer of a measurement device and suggests many Schrodinger cat-type paradoxes can be explained by microscopic nonlocality.

•Apr 3, 2016•0 citations

Interpreting the macroscopic pointer by analysing the elements of reality of a Schrödinger cat

M. D. Reid

Abstract We examine Einstein–Podolsky–Rosen’s (EPR) steering nonlocality for two realisable Schrödinger cat-type states where a meso/macroscopic system (called the ‘cat’-system) is entangled with a microscopic spin- 1 / 2 system. We follow EPR’s argument and derive the predictions for ‘elements of reality’ that would exist to describe the cat-system, under the assumption of EPR’s local realism. By showing that those predictions cannot be replicated by any local quantum state description of the cat-system, we demonstrate the EPR-steering of the cat-system. For large cat-systems, we find that a local hidden state model is near-satisfied, meaning that a local quantum state description exists (for the cat) whose predictions differ from those of the elements of reality by a vanishingly small amount. For such a local hidden state model, the EPR-steering of the cat vanishes, and the cat-system can be regarded as being in a mixture of ‘dead’ and ‘alive’ states despite it being entangled with the spin system. We therefore propose that a rigorous signature of the Schrödinger cat-type paradox is the EPR-steering of the cat-system and provide two experimental signatures. This leads to a hybrid quantum/classical interpretation of the macroscopic pointer of a measurement device and suggests that many Schrödinger cat-type paradoxes may be explained by microscopic nonlocality.

Journal of Physics A Mathematical and Theoretical•Aug 22, 2017•15 citations

Einstein-Podolsky-Rosen steering nonlocality in pulsed optomechanics and macroscopic atomic ensembles

Qiongyi He, M. D. Reid

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 for a massive system. In that case, EPR's of reality are defined for the oscillator, and it is these elements of that are falsified (if quantum mechanics is complete). For this sort of paradox, we show that a thermal barrier exists, meaning that a threshold level of pulse-oscillator interaction is required for a given thermal occupation n_0 of the oscillator. We find there is no equivalent thermal barrier for the entanglement of the pulse with the oscillator, nor for the EPR paradox that addresses the local of the optical system. Finally, we examine the possibility of an EPR paradox between two entangled oscillators. Our work highlights the asymmetrical effect of thermal noise on quantum nonlocality.

•Nov 8, 2012•0 citations

Criteria to detect macroscopic quantum coherence, macroscopic quantum entanglement, and an Einstein-Podolsky-Rosen paradox for macroscopic superposition states

M. D. Reid

According to classical theory, a system with two or more macroscopically distinct states available to it is in one of those states at all times. Quantum mechanics gives a different interpretation where the system can be in a superposition of such states. In this paper, we derive criteria in the form of inequalities to detect this effect, referred to as mesoscopic quantum coherence, where the states are (at least) mesoscopically distinct. Such criteria are also signatures of a mesoscopic Schr\"odinger cat paradox. We extend the treatment to consider definitions and criteria for mesoscopically entangled states, which are a subset of the states exhibiting mesoscopic quantum coherence. It is shown how the criteria (referred to as type I criteria) can be applied to detect the mesoscopic entanglement of systems prepared in NOON states, Greenberger-Horne-Zeilinger states, and entangled cat states involving coherent states. Here, a larger system $C$ is entangled with a second system $S$, which can be small. The proposed definition of mesoscopic (macroscopic) entanglement involves the Schmidt decomposition, and can be applied to systems in a superposition of many states, only some pairs of which are mesoscopically (macroscopically) distinguishable. We prove that a higher-order Hillery-Zubairy entanglement criterion will detect mesoscopic entanglement of this type, and use this to demonstrate the mesoscopic entanglement of the ground state of a two-mode Bose-Einstein condensate. Finally, we explain how a subset of the type I criteria (called type II criteria) are EPR steering inequalities allowing realization of a mesoscopic or macroscopic version of the Einstein-Podolsky-Rosen paradox for macroscopic superposition states. Where the two systems $C$ and $S$ are spatially separated, we then use results from the literature to point out it is not possible to complete quantum mechanics using hidden-variable theories compatible with the assumption of locality between the two systems. The violation of certain Bell inequalities is sufficient to prove this result, which gives a stricter signature of the Schr\"odinger cat paradox and of mesoscopic quantum coherence. We call such signatures type III criteria.

Physical Review A•Nov 25, 2019•9 citations

Revealing Hidden Einstein-Podolsky-Rosen Nonlocality

Stephen Patrick Walborn, A. Salles, Rafael M. Gomes +2 more

Steering is a form of quantum nonlocality that is intimately related to the famous Einstein-Podolsky-Rosen (EPR) paradox that ignited the ongoing discussion of quantum correlations. Within the hierarchy of nonlocal correlations appearing in nature, EPR steering occupies an intermediate position between Bell nonlocality and entanglement. In continuous variable systems, EPR steering correlations have been observed by violation of Reid's EPR inequality, which is based on inferred variances of complementary observables. Here we propose and experimentally test a new criterion based on entropy functions, and show that it is more powerful than the variance inequality for identifying EPR steering. Using the entropic criterion our experimental results show EPR steering, while the variance criterion does not. Our results open up the possibility of observing this type of nonlocality in a wider variety of quantum states.

Physical Review Letters•Mar 30, 2011•308 citations

Einstein-Podolsky-Rosen paradox and quantum steering in pulsed optomechanics

Qiongyi He, M. D. Reid

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 Schr\"odinger 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, meaning that a threshold level of pulse-oscillator interaction is required for a given thermal occupation ${n}_{0}$ of the oscillator. We find there is no equivalent thermal barrier for the entanglement of the pulse with the oscillator or for the EPR paradox that addresses the local reality of the optical system. Finally, we examine the possibility of an EPR paradox between two entangled oscillators. Our work highlights the asymmetrical effect of thermal noise on quantum nonlocality.

arXiv:1211.1779•Physical Review A•Nov 19, 2013•92 citations
We examine Einstein-Podolsky-Rosen's (EPR) steering nonlocality for two realisable Schrodinger cat-type states where a meso/ macroscopic system (called the "cat"-system) is entangled with a spin-1/21/21/2 system. For large cat-systems, we show that a local hidden state model is near-satisfied, meaning that the cat-system can be consistent with being in a mixture of "dead" and "alive" states despite that it is entangled with the spin system. We justify that a rigorous signature of the Schrodinger cat-type paradox is the EPR-steering of the cat-system and provide two experimental signatures. This leads to a hybrid quantum/ classical interpretation of the macroscopic pointer of a measurement device and suggests many Schrodinger cat-type paradoxes can be explained by microscopic nonlocality.
We examine Einstein-Podolsky-Rosen's (EPR) steering nonlocality for two realisable Schrodinger cat-type states where a meso/ macroscopic system (called the cat-system) is entangled with a spin-1/21/21/2 system. For large cat-systems, we show that a local hidden state model is near-satisfied, meaning that the cat-system can be consistent with being in a mixture of dead and alive states despite that it is entangled with the spin system. We justify that a rigorous signature of the Schrodinger cat-type paradox is the EPR-steering of the cat-system and provide two experimental signatures. This leads to a hybrid quantum/ classical interpretation of the macroscopic pointer of a measurement device and suggests many Schrodinger cat-type paradoxes can be explained by microscopic nonlocality.
Abstract We examine Einstein–Podolsky–Rosen’s (EPR) steering nonlocality for two realisable Schrödinger cat-type states where a meso/macroscopic system (called the ‘cat’-system) is entangled with a microscopic spin- 1 / 2 system. We follow EPR’s argument and derive the predictions for ‘elements of reality’ that would exist to describe the cat-system, under the assumption of EPR’s local realism. By showing that those predictions cannot be replicated by any local quantum state description of the cat-system, we demonstrate the EPR-steering of the cat-system. For large cat-systems, we find that a local hidden state model is near-satisfied, meaning that a local quantum state description exists (for the cat) whose predictions differ from those of the elements of reality by a vanishingly small amount. For such a local hidden state model, the EPR-steering of the cat vanishes, and the cat-system can be regarded as being in a mixture of ‘dead’ and ‘alive’ states despite it being entangled with the spin system. We therefore propose that a rigorous signature of the Schrödinger cat-type paradox is the EPR-steering of the cat-system and provide two experimental signatures. This leads to a hybrid quantum/classical interpretation of the macroscopic pointer of a measurement device and suggests that many Schrödinger cat-type paradoxes may be explained by microscopic nonlocality.
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 for a massive system. In that case, EPR's of reality are defined for the oscillator, and it is these elements of that are falsified (if quantum mechanics is complete). For this sort of paradox, we show that a thermal barrier exists, meaning that a threshold level of pulse-oscillator interaction is required for a given thermal occupation n_0 of the oscillator. We find there is no equivalent thermal barrier for the entanglement of the pulse with the oscillator, nor for the EPR paradox that addresses the local of the optical system. Finally, we examine the possibility of an EPR paradox between two entangled oscillators. Our work highlights the asymmetrical effect of thermal noise on quantum nonlocality.
According to classical theory, a system with two or more macroscopically distinct states available to it is in one of those states at all times. Quantum mechanics gives a different interpretation where the system can be in a superposition of such states. In this paper, we derive criteria in the form of inequalities to detect this effect, referred to as mesoscopic quantum coherence, where the states are (at least) mesoscopically distinct. Such criteria are also signatures of a mesoscopic Schr\"odinger cat paradox. We extend the treatment to consider definitions and criteria for mesoscopically entangled states, which are a subset of the states exhibiting mesoscopic quantum coherence. It is shown how the criteria (referred to as type I criteria) can be applied to detect the mesoscopic entanglement of systems prepared in NOON states, Greenberger-Horne-Zeilinger states, and entangled cat states involving coherent states. Here, a larger system CCC is entangled with a second system SSS, which can be small. The proposed definition of mesoscopic (macroscopic) entanglement involves the Schmidt decomposition, and can be applied to systems in a superposition of many states, only some pairs of which are mesoscopically (macroscopically) distinguishable. We prove that a higher-order Hillery-Zubairy entanglement criterion will detect mesoscopic entanglement of this type, and use this to demonstrate the mesoscopic entanglement of the ground state of a two-mode Bose-Einstein condensate. Finally, we explain how a subset of the type I criteria (called type II criteria) are EPR steering inequalities allowing realization of a mesoscopic or macroscopic version of the Einstein-Podolsky-Rosen paradox for macroscopic superposition states. Where the two systems CCC and SSS are spatially separated, we then use results from the literature to point out it is not possible to complete quantum mechanics using hidden-variable theories compatible with the assumption of locality between the two systems. The violation of certain Bell inequalities is sufficient to prove this result, which gives a stricter signature of the Schr\"odinger cat paradox and of mesoscopic quantum coherence. We call such signatures type III criteria.
Steering is a form of quantum nonlocality that is intimately related to the famous Einstein-Podolsky-Rosen (EPR) paradox that ignited the ongoing discussion of quantum correlations. Within the hierarchy of nonlocal correlations appearing in nature, EPR steering occupies an intermediate position between Bell nonlocality and entanglement. In continuous variable systems, EPR steering correlations have been observed by violation of Reid's EPR inequality, which is based on inferred variances of complementary observables. Here we propose and experimentally test a new criterion based on entropy functions, and show that it is more powerful than the variance inequality for identifying EPR steering. Using the entropic criterion our experimental results show EPR steering, while the variance criterion does not. Our results open up the possibility of observing this type of nonlocality in a wider variety of quantum states.
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 Schr\"odinger 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, meaning that a threshold level of pulse-oscillator interaction is required for a given thermal occupation n0{n}_{0}n0​ of the oscillator. We find there is no equivalent thermal barrier for the entanglement of the pulse with the oscillator or for the EPR paradox that addresses the local reality of the optical system. Finally, we examine the possibility of an EPR paradox between two entangled oscillators. Our work highlights the asymmetrical effect of thermal noise on quantum nonlocality.