On the Concentration of Quantum States in Phase Space

Abstract In this work, we study the Wigner phase-space representation of qubit states encoded in continuous variables (CV) by using the Gottesman–Kitaev–Preskill (GKP) mapping. We explore a possible connection between resources for universal quantum computation in discrete-variable (DV) systems, i.e. non-stabilizer states, and negativity of the Wigner function in CV architectures, which is a necessary requirement for quantum advantage. In particular, we show that the lowest Wigner logarithmic negativity corresponds to encoded stabilizer states, while the maximum negativity is associated with the most non-stabilizer states, H-type and T-type quantum states.

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

New Journal of Physics ◽

10.1088/1367-2630/ac40cc ◽

2021 ◽

Author(s):

Andrii A. Semenov ◽

Andrei B Klimov

Keyword(s):

Phase Space ◽

Quantum Optics ◽

Photon Number ◽

Bell Inequalities ◽

Physical Reality ◽

Quantum States ◽

Optical Measurements ◽

Dual Form ◽

Einstein Podolsky Rosen ◽

Simulation Problem

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.

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Quantum Statistics of Light Emitted from a Pillar Microcavity

10.21203/rs.3.rs-423805/v1 ◽

2021 ◽

Author(s):

Timur A. Khudaiberganov ◽

Sergei M. Arakelian

Keyword(s):

Correlation Function ◽

Phase Space ◽

Quantum States ◽

Dissipative Effects ◽

Exciton Polaritons ◽

Quantum Behavior ◽

Population Ratio ◽

Domain Of Parameters ◽

Quasiprobability Functions ◽

Bistability Regime

Abstract A quantum behavior of the light emitted by exciton polaritons excited in a pillar semiconductor microcavity with embedded quantum well is investigated. Considering the bare excitons and photon modes as coupled quantum oscillators allows for an accurate accounting of the nonlinear and dissipative effects. In particular, using the method of quantum states presentation in a quantum phase space via quasiprobability functions (namely, a P-function and a Wigner function), we study the effect of the laser and the exciton-photon detuning on the second order correlation function of the emitted photons. We determine the conditions for the phenomena of bunching, giant bunching, and antibunching of the emitted light. In particular, we predict the effect of a giant bunching for the case of a large exciton to photon population ratio. Within the domain of parameters supporting a bistability regime we demonstrate the effect of bunching of photons.

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