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

Physical Review A

Contradiction of quantum mechanics with local hidden variables for quadrature phase measurements on pair-coherent states and squeezed macroscopic superpositions of coherent states

Alexei Gilchrist, Piotr Deuar, M. D. Reid

Published Dec 1, 1999• 50 citations
Publisher

Abstract

We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (``position'' and ``momentum'') measurements. A contradiction is shown possible for two quantum states: a pair-coherent state, and a superpositions of two coherent states, where the superposition state has been squeezed by the action of a two-mode squeezing operator. In one case a contradiction is still possible for states of increasing photon number, though the effect becomes smaller and more difficult to observe. The high efficiency of the homodyne method of measurement of quadrature phase amplitudes may open a way for a loophole-free test of local hidden variable theories, and the effect of detection loss on the contradiction with local hidden variables is calculated.

DOI
10.1103/physreva.60.4259

Related papers

Contradiction of Quantum Mechanics with Local Hidden Variables for Quadrature Phase Amplitude Measurements

Alexei Gilchrist, Piotr Deuar, M. D. Reid

We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (``position'' and ``momentum'') measurements. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.

arXiv:quant-ph/0010024•Physical Review Letters•Apr 13, 1998•112 citations

New Tests of Macroscopic Local Realism using Continuous Variable Measurements

M. D. Reid

We show that quantum mechanics predicts an Einstein-Podolsky-Rosen paradox (EPR), and also a contradiction with local hidden variable theories, for photon number measurements which have limited resolving power, to the point of imposing an uncertainty in the photon number result which is macroscopic in absolute terms. We show how this can be interpreted as a failure of a new, very strong premise, called macroscopic local realism. We link this premise to the Schrodinger-cat paradox. Our proposed experiments ensure all fields incident on each measurement apparatus are macroscopic. We show that an alternative measurement scheme corresponds to balanced homodyne detection of quadrature phase amplitudes. The implication is that where either EPR correlations or failure of local realism is predicted for continuous variable (quadrature phase amplitude) measurements, one can perform a modified experiment which would lead to conclusions about the much stronger premise of macroscopic local realism.

arXiv:quant-ph/0101050•Jan 12, 2001•0 citations

Optical homodyne measurements and entangled coherent states

Barry C. Sanders, K. S. Lee, M. S. Kim

We show that optical homodyne measurements of coherent states, and of superpositions of coherent states, can be described using the joint photon-number distribution for entangled coherent states. The quadrature-phase distribution interference fringes for superpositions of macroscopically distinct coherent states (the so-called ``Schr\"odinger cat states'') are shown to arise from interference in the photon-number distribution for entangled coherent states. The entangled squeezed states are introduced here as squeezed superposition states which are optically mixed with an antisqueezed coherent local oscillator field (squeezing in the other quadrature) at a beam splitter, and we discuss the connection between entangled squeezed states and squeezed-state homodyne detection of squeezed light. Finally the relationship between interference in phase space and fringes in the joint photon-number distribution for the entangled squeezed state is explored.

Physical Review A•Jul 1, 1995•53 citations

Violations of entropic Bell inequalities with coarse-grained quadrature measurements for continuous-variable states

Zeng‐Bing Chen, Yao Fu, Yu-Kang Zhao

It is a long-standing belief, as pointed out by Bell in 1986, that it is impossible to use a two-mode Gaussian state possessing a positive-definite Wigner function to demonstrate nonlocality as the Wigner function itself provides a local hidden-variable model. In particular, when one performs continuous-variable (CV) quadrature measurements upon a routinely generated CV entanglement, namely, the two-mode squeezed vacuum (TMSV) state, the resulting Wigner function is positive-definite and as such, the TMSV state cannot violate any Bell inequality using CV quadrature measurements. We show here, however, that a Bell inequality for CV states in terms of entropies can be quantum mechanically violated by the TMSV state with two coarse-grained quadrature measurements per site within experimentally accessible parameter regime. The proposed CV entropic Bell inequality is advantageous for an experimental test, especially for a possible loophole-free test of nonlocality, as the quadrature measurements can be implemented with homodyne detections of nearly $100%$ detection efficiency under current technology.

arXiv:1409.0437•Physical Review A•Aug 26, 2014•5 citations

Violation of Bell’s Inequality Using Continuous Variable Measurements

Oliver Thearle, Jiří Janoušek, Seiji Armstrong +8 more

A Bell inequality is a fundamental test to rule out local hidden variable model descriptions of correlations between two physically separated systems. There have been a number of experiments in which a Bell inequality has been violated using discrete-variable systems. We demonstrate a violation of Bell's inequality using continuous variable quadrature measurements. By creating a four-mode entangled state with homodyne detection, we recorded a clear violation with a Bell value of B=2.31±0.02. This opens new possibilities for using continuous variable states for device independent quantum protocols.

arXiv:1801.03194•Physical Review Letters•Jan 25, 2018•35 citations

Complex two-mode quadratures -- a unified formalism for continuous-variable quantum optics

Leon Bello, Yoad Michael, M. Rosenbluh +2 more

Quantum squeezing, a major resource for quantum information processing and quantum metrology, is best analyzed in terms of the field quadratures - the quantum optical analogues of position and momentum, which form the continuous-variable formalism of quantum light. Degenerate squeezing admits a very helpful and simple description in terms of the single-mode quadrature operators, but the non-degenerate case, i.e. when the squeezing involves pairs of modes, requires a more complicated treatment involving correlations between the quadratures of the different modes. We introduce a generalized set of complex quadrature operators that treats degenerate and non-degenerate squeezing on equal footing. We describe the mode-pairs (and photon-pairs) as a single entity, generalizing the concept of single-mode quadrature operators to two-mode fields of any bandwidth. These complex operators completely describe the SU(1,1) algebra of two-photon devices and directly relate to observable physical quantities, like power and visibility. Based on this formalism, we discuss the measurement of optically-broad squeezed signals with direct detection, and present a compact set of phase-dependent observables that completely and intuitively determine the two-mode squeezed state, and quantify the degree of inseparability and entanglement between the modes.

•Nov 16, 2020•1 citation
We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (position'' and momentum'') measurements. A contradiction is shown possible for two quantum states: a pair-coherent state, and a superpositions of two coherent states, where the superposition state has been squeezed by the action of a two-mode squeezing operator. In one case a contradiction is still possible for states of increasing photon number, though the effect becomes smaller and more difficult to observe. The high efficiency of the homodyne method of measurement of quadrature phase amplitudes may open a way for a loophole-free test of local hidden variable theories, and the effect of detection loss on the contradiction with local hidden variables is calculated.
We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (``position'' and ``momentum'') measurements. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.
We show that quantum mechanics predicts an Einstein-Podolsky-Rosen paradox (EPR), and also a contradiction with local hidden variable theories, for photon number measurements which have limited resolving power, to the point of imposing an uncertainty in the photon number result which is macroscopic in absolute terms. We show how this can be interpreted as a failure of a new, very strong premise, called macroscopic local realism. We link this premise to the Schrodinger-cat paradox. Our proposed experiments ensure all fields incident on each measurement apparatus are macroscopic. We show that an alternative measurement scheme corresponds to balanced homodyne detection of quadrature phase amplitudes. The implication is that where either EPR correlations or failure of local realism is predicted for continuous variable (quadrature phase amplitude) measurements, one can perform a modified experiment which would lead to conclusions about the much stronger premise of macroscopic local realism.
We show that optical homodyne measurements of coherent states, and of superpositions of coherent states, can be described using the joint photon-number distribution for entangled coherent states. The quadrature-phase distribution interference fringes for superpositions of macroscopically distinct coherent states (the so-called ``Schr\"odinger cat states'') are shown to arise from interference in the photon-number distribution for entangled coherent states. The entangled squeezed states are introduced here as squeezed superposition states which are optically mixed with an antisqueezed coherent local oscillator field (squeezing in the other quadrature) at a beam splitter, and we discuss the connection between entangled squeezed states and squeezed-state homodyne detection of squeezed light. Finally the relationship between interference in phase space and fringes in the joint photon-number distribution for the entangled squeezed state is explored.
It is a long-standing belief, as pointed out by Bell in 1986, that it is impossible to use a two-mode Gaussian state possessing a positive-definite Wigner function to demonstrate nonlocality as the Wigner function itself provides a local hidden-variable model. In particular, when one performs continuous-variable (CV) quadrature measurements upon a routinely generated CV entanglement, namely, the two-mode squeezed vacuum (TMSV) state, the resulting Wigner function is positive-definite and as such, the TMSV state cannot violate any Bell inequality using CV quadrature measurements. We show here, however, that a Bell inequality for CV states in terms of entropies can be quantum mechanically violated by the TMSV state with two coarse-grained quadrature measurements per site within experimentally accessible parameter regime. The proposed CV entropic Bell inequality is advantageous for an experimental test, especially for a possible loophole-free test of nonlocality, as the quadrature measurements can be implemented with homodyne detections of nearly 100100%100 detection efficiency under current technology.
A Bell inequality is a fundamental test to rule out local hidden variable model descriptions of correlations between two physically separated systems. There have been a number of experiments in which a Bell inequality has been violated using discrete-variable systems. We demonstrate a violation of Bell's inequality using continuous variable quadrature measurements. By creating a four-mode entangled state with homodyne detection, we recorded a clear violation with a Bell value of B=2.31±0.02. This opens new possibilities for using continuous variable states for device independent quantum protocols.
Quantum squeezing, a major resource for quantum information processing and quantum metrology, is best analyzed in terms of the field quadratures - the quantum optical analogues of position and momentum, which form the continuous-variable formalism of quantum light. Degenerate squeezing admits a very helpful and simple description in terms of the single-mode quadrature operators, but the non-degenerate case, i.e. when the squeezing involves pairs of modes, requires a more complicated treatment involving correlations between the quadratures of the different modes. We introduce a generalized set of complex quadrature operators that treats degenerate and non-degenerate squeezing on equal footing. We describe the mode-pairs (and photon-pairs) as a single entity, generalizing the concept of single-mode quadrature operators to two-mode fields of any bandwidth. These complex operators completely describe the SU(1,1) algebra of two-photon devices and directly relate to observable physical quantities, like power and visibility. Based on this formalism, we discuss the measurement of optically-broad squeezed signals with direct detection, and present a compact set of phase-dependent observables that completely and intuitively determine the two-mode squeezed state, and quantify the degree of inseparability and entanglement between the modes.