<i>s</i>-order nondiagonal quasiprobabilities

Fa, de Oliveira

doi:10.1103/physreva.45.5104

Cited by 9 publications

(6 citation statements)

References 37 publications

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“…The s-ordered representations were first generalised to doubled phase space by de Oliveira [31]. Later studies [35,71,116] used a different normalisation that is closer to the original single-phase space formulation (52) of Cahill and Glauber [19].…”

Section: Doubled Phase Space S-ordered Representationsmentioning

confidence: 99%

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Deuar

2021

Quantum

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A number of physically intuitive results for the calculation of multi-time correlations in phase-space representations of quantum mechanics are obtained. They relate time-dependent stochastic samples to multi-time observables, and rely on the presence of derivative-free operator identities. In particular, expressions for time-ordered normal-ordered observables in the positive-P distribution are derived which replace Heisenberg operators with the bare time-dependent stochastic variables, confirming extension of earlier such results for the Glauber-Sudarshan P. Analogous expressions are found for the anti-normal-ordered case of the doubled phase-space Q representation, along with conversion rules among doubled phase-space s-ordered representations. The latter are then shown to be readily exploited to further calculate anti-normal and mixed-ordered multi-time observables in the positive-P, Wigner, and doubled-Wigner representations. Which mixed-order observables are amenable and which are not is indicated, and explicit tallies are given up to 4th order. Overall, the theory of quantum multi-time observables in phase-space representations is extended, allowing non-perturbative treatment of many cases. The accuracy, usability, and scalability of the results to large systems is demonstrated using stochastic simulations of the unconventional photon blockade system and a related Bose-Hubbard chain. In addition, a robust but simple algorithm for integration of stochastic equations for phase-space samples is provided.

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Section: Doubled Phase Space S-ordered Representationsmentioning

confidence: 99%

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Deuar

2021

Quantum

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“…Of these, only the Q-function is positive-definite. Subsequently, positive-definite extensions of these were developed that use complex instead of real phase-spaces, including the positive P-representation [16], the positive Wigner representation [59,60] and the Gaussian representation [61]. The positive P-representation is useful, as it combines stochastic time-evolution with simple observables.…”

Section: A Phase-space Methodsmentioning

confidence: 99%

Quantum probabilistic sampling of multipartite 60-qubit Bell-inequality violations

et al. 2014

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We show that violation of genuine multipartite Bell inequalities can be obtained with sampled, probabilistic phase space methods. These genuine Bell violations cannot be replicated if any part of the system is described by a local hidden variable theory. The Bell violations are simulated probabilistically using quantum phase-space representations. We treat mesoscopically large Greenberger-Horne-Zeilinger (GHZ) states having up to 60 qubits, using both a multipartite SU(2) Q-representation and the positive P-representation. Surprisingly, we find that sampling with phase-space distributions can be exponentially faster than experiment. This is due to the classical parallelism inherent in the simulation of quantum measurements using phase-space methods. Our probabilistic sampling method predicts a contradiction with local realism of "Schrödinger-cat" states that can be realized as a GHZ spin state, either in ion traps or with photonic qubits. We also present a quantum simulation of the observed super-decoherence of the ion-trap "cat" state, using a phenomenological noise model.

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“…The s-ordered representations were first generalised to doubled phase space by de Oliveira [76]. Later studies [70,71,77] used a different normalisation that is closer to the original single-phase space formulation (52) of Cahill and Glauber [74].…”

Section: A Doubled Phase Space S-ordered Representationsmentioning

confidence: 99%

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Deuar

2020

Preprint

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A number of physically intuitive results for the calculation of multi-time correlations in phasespace representations of quantum mechanics are obtained. They relate time-dependent stochastic samples to multi-time observables, and rely on the presence of derivative-free operator identities. In particular, expressions for time-and normal-ordered observables in the positive-P distribution are derived which replace Heisenberg operators with the bare time-dependent stochastic variables, confirming extension of earlier such results for the Glauber-Sudarshan P. Analogous expressions are found for the anti-normal-ordered case in the Q and doubled phase-space Q representations, along with conversion rules among doubled phase-space s-ordered representations. The latter are then shown to be readily exploited to further calculate anti-normal and mixed-ordered observables in the positive-P, Wigner, and doubled-Wigner representations. Which mixed-order observables are amenable and which not is indicated, and explicit tallies are given up to 4th order. Overall then, the theory of quantum multi-time observables in phase-space representations is extended, allowing non-perturbative treatment of many cases. The accuracy, usability, and scalability of the results to large systems is demonstrated using stochastic simulations of the unconventional photon blockade system, and a related Bose-Hubbard chain.

show abstract

s-order nondiagonal quasiprobabilities

Cited by 9 publications

References 37 publications

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Quantum probabilistic sampling of multipartite 60-qubit Bell-inequality violations

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

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