Multi-time correlations in the positive-P, Q, and doubled phase-space representations
arXiv:2011.10107 · doi:10.22331/q-2021-05-10-455
Abstract
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.
arXiv comment20 pages+refs, 6 figures. Added an extensive appendix that describes in detail a robust algorithm for integrating stochastic trajectories generated by quantum phase-space methods. Introduction reworked and extended to connect to quantum information topics. Plus some other minor edits and additional connections to earlier work. Accepted version
References in corpus (97)
- A bound on chaos
- Observation of a Discrete Time Crystal
- Floquet Time Crystals
- Quantum Time Crystals
- Light-cone-like spreading of correlations in a quantum many-body system
- Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
- Phase space representation of quantum dynamics
- Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
- Measuring the scrambling of quantum information
- Single photons from coupled quantum modes
- Dynamical quantum noise in Bose-Einstein condensates
- On the origin of strong photon antibunching in weakly nonlinear photonic molecules
- Negative Quasi-Probability as a Resource for Quantum Computation
- The truncated Wigner method for Bose condensed gases: limits of validity and applications
- Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
- Circuit QED lattices: towards quantum simulation with superconducting circuits
- Negativity and contextuality are equivalent notions of nonclassicality
- Out-of-Time-Order Correlation for Many-Body Localization
- Resource theory of quantum non-Gaussianity and Wigner negativity
- Scrambling and thermalization in a diffusive quantum many-body system
- XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations
- Quasi-probability representations of quantum theory with applications to quantum information science
- The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
- Relating out-of-time-order correlations to entanglement via multiple-quantum coherences
- Out-of-Time-Order Correlation at a Quantum Phase Transition
- Stochastic classical field model for polariton condensates
- Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
- Correlations in a BEC collision: First-principles quantum dynamics with 150 000 atoms
- Corner space renormalization method for driven-dissipative 2D correlated systems
- Does Simple Two-Dimensional Hubbard Model Account for High-Tc Superconductivity in Copper Oxides?
- Experimental determination of a nonclassical Glauber-Sudarshan P function
- Gaussian quantum Monte Carlo methods for fermions
- Quantum turbulence in condensate collisions: an application of the classical field method
- Quantum dynamics of evaporatively cooled Bose-Einstein Condensates
- Split-step Fourier methods for the Gross-Pitaevskii equation
- Gauge P-representations for quantum-dynamical problems: Removal of boundary terms
- Nonclassical correlation properties of radiation fields
- Violation of the Cauchy-Schwarz inequality with matter waves
- Critical fluctuations and entanglement in the nondegenerate parametric oscillator
- Simulations and Experiments on Polarisation Squeezing in Optical Fibre
- Many-body quantum dynamics of polarisation squeezing in optical fibre
- Scalable quantum simulation of pulsed entanglement and Einstein-Podolsky-Rosen steering in optomechanics
- Non-local pair correlations in the 1D Bose gas at finite temperature
- Nonlinear Polariton Fluids in a Flatband Reveal Discrete Gap Solitons
- Time crystal behavior of excited eigenstates
- Proposal for demonstrating the Hong-Ou-Mandel effect with matter waves
- Temporal coherence of one-dimensional non-equilibrium quantum fluids
- Wigner phase space distribution as a wave function
- First-principles quantum dynamics in interacting Bose gases I: The positive P representation
- A quantum Langevin model for non-equilibrium condensation
- Decay of a superfluid current of ultra-cold atoms in a toroidal trap
- Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation
- Controlling spontaneous-emission noise in measurement-based feedback cooling of a Bose-Einstein Condensate
- Hilbert's 17th problem and the quantumness of states
- Quantum simulations of the early universe
- Quasiprobability distributions in open quantum systems: spin-qubit systems
- Quasiprobability distributions for quantum-optical coherence and beyond
- Proposal for a motional-state Bell inequality test with ultracold atoms
- Beyond the Fokker-Planck equation: Stochastic Simulation of Complete Wigner representation for the Optical Parametric Oscillator
- Characterizing maximally singular phase-space distributions
- Phase-Space Methods for Simulating the Dissipative Many-Body Dynamics of Collective Spin Systems
- Fully quantum scalable description of driven dissipative lattice models
- Strain tunable single-photon source based on a quantum dot-micropillar system
- Gaussian-Basis Monte Carlo Method for Numerical Study on Ground States of Itinerant and Strongly Correlated Electron Systems
- An exact stochastic field method for the interacting Bose gas at thermal equilibrium
- Probing photon correlations in the dark sites of geometrically frustrated cavity lattices
- Matrix product state of multi-time correlations
- Quantum Time: experimental multi-time correlations
- Bogoliubov dynamics of condensate collisions using the positive-P representation
- Hybrid phase-space simulation method for interacting Bose fields
- Quantum software for linear photonic simulations
- Qubit phase-space: SU(n) coherent state P-representations
- Simulating and assessing boson sampling experiments with phase-space representations
- Exact Real Time Dynamics of Quantum Spin Systems Using the Positive-P Representation
- Stochastic Differential Equations for Quantum Dynamics of Spin-Boson Networks
- The time-reversal test for stochastic quantum dynamics
- Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space Techniques
- Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function
- Exciton-Polariton Trapping and Potential Landscape Engineering
- Multi-time correlators in continuous measurement of qubit observables
- Simulation of complete many-body quantum dynamics using controlled quantum-semiclassical hybrids
- The scaling of boson sampling experiments
- Multitime correlation functions in nonclassical stochastic processes
- Tradeoffs for number-squeezing in collisions of Bose-Einstein condensates
- A comparative study of dynamical simulation methods for the dissociation of molecular Bose-Einstein condensates
- Quantum fluctuation effects on the quench dynamics of thermal quasicondensates
- Quantum dynamics of long-range interacting systems using the positive-P and gauge-P representations
- Robustness of quantum Fourier transform interferometry
- Quantum phase-space analysis of the pendular cavity
- Initial states and apodisation for quantum field simulations in phase-space
- Correlation evolution in dilute Bose-Einstein condensates after quantum quenches
- Anisotropy in s-wave Bose-Einstein condensate collisions and its relationship to superradiance
- On the survival of the quantum depletion of a condensate after release from a magnetic trap
- A tractable prescription for large-scale free flight expansion of wavefunctions
- Exact reformulation of the bosonic many-body problem in terms of stochastic wave functions: convergence issues
- Quantum-field-theoretical approach to phase-space techniques: Symmetric Wick theorem and multitime Wigner representation
- A semiclassical field theory that is freed of the ultraviolet catastrophe
Cited by in corpus (7)
- Realistic simulations of spin squeezing and cooperative coupling effects in large ensembles of interacting two-level systems
- On the survival of the quantum depletion of a condensate after release from a magnetic trap
- Self-organized cavity bosons beyond the adiabatic elimination approximation
- Discrete-phase-space method for driven-dissipative dynamics of strongly interacting bosons in optical lattices
- Two-dimensional correlation propagation dynamics with a cluster discrete phase-space method
- Path-Integral Formulation of Bosonic Markovian Open Quantum Dynamics with Monte Carlo stochastic trajectories using the Glauber-Sudarshan P, Wigner, and Husimi Q Functions and Hybrids
- Coherent pair injection as a route towards the enhancement of supersolid order in many-body bosonic models