Dual form of the phase-space classical simulation problem in quantum optics

Abstract

In quantum optics, nonclassicality of quantum states is commonly associated with negativities of phase-space quasiprobability distributions. We argue that the impossibility of any classical simulations with phase-space functions is a necessary and sufficient condition of nonclassicality. The problem of such phase-space classical simulations for particular measurement schemes is analysed in the framework of Einstein-Podolsky-Rosen-Bell's principles of physical reality. The dual form of this problem results in an analogue of Bell inequalities. Their violations imply the impossibility of phase-space classical simulations and, as a consequence, nonclassicality of quantum states. We apply this technique to emblematic optical measurements such as photocounting, including the cases of realistic photon-number resolution and homodyne detection in unbalanced, balanced, and eight-port configurations.

arXiv comment21 pages, 5 figures

References in corpus (35)

• Bell nonlocality
• Device-independent security of quantum cryptography against collective attacks
• Symmetric Informationally Complete Quantum Measurements
• Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency
• Negativity of the Wigner function as an indicator of nonclassicality
• Violations of local realism by two entangled quNits are stronger than for two qubits
• Positive Wigner functions render classical simulation of quantum computation efficient
• Efficient Classical Simulation of Continuous Variable Quantum Information Processes
• The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
• Photon number resolution using a time-multiplexed single-photon detector
• A computable measure of nonclassicality for light
• Fiber-assisted detection with photon number resolution
• Sufficient Conditions for Efficient Classical Simulation of Quantum Optics
• True photo-counting statistics of multiple on-off detectors
• Multiple-photon resolving fiber-loop detector
• Informationally complete measurements and groups representation
• Density Matrix From Photon Number Tomography
• Nonclassicality filters and quasiprobabilities
• Sub-binomial light
• Statistical mixtures of states can be more quantum than their superpositions: Comparison of nonclassicality measures for single-qubit states
• Direct observation of sub-binomial light
• Reduced Deadtime and Higher Rate Photon-Counting Detection using a Multiplexed Detector Array
• Quasiprobability representation of quantum coherence
• Necessity of negativity in quantum theory
• Increasing relative nonclassicality quantified by standard entanglement potentials by dissipation and unbalanced beam splitting
• Phase-space inequalities beyond negativities
• Nonclassicality of states and measurements by breaking classical bounds on statistics
• Quasiprobability distributions for quantum-optical coherence and beyond
• Probing nonclassicality with matrices of phase-space distributions
• Homodyne Detection and Quantum State Reconstruction
• Probabilistic quantum phase-space simulation of Bell violations and their dynamical evolution
• Quantum probabilistic sampling of multipartite 60-qubit Bell inequality violations
• Quasistates and quasiprobabilities
• Simulating Bell violations without quantum computers
• Probabilistic simulation of mesoscopic "Schrödinger cat" states

Cited by in corpus (6)

• Photon-number resolution with microwave Josephson photomultipliers
• Tight inequalities for nonclassicality of measurement statistics
• Nonclassical correlations of radiation in relation to Bell nonlocality
• Time correlations in atmospheric quantum channels
• Nonclassical photocounting statistics with a single on-off detector
• Latent optical nonclassicality of conditionally prepared states