Linear entropy in quantum phase space

Abstract

We calculate the quantum Renyi entropy in a phase space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner product divergences. The preferred method is to use generalized Gaussian phase space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.

12 pages, 3 figures. To be published in Phys. Rev. A

References in corpus (12)

• Optomechanical Crystals
• Dynamics of Loschmidt echoes and fidelity decay
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Measurement of the Entropy and Critical Temperature of a Strongly Interacting Fermi Gas
• Atom-atom correlations in colliding Bose-Einstein condensates
• Gaussian-Basis Monte Carlo Method for Numerical Study on Ground States of Itinerant and Strongly Correlated Electron Systems
• Quantum Pumping with Ultracold Atoms on Microchips: Fermions versus Bosons
• Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
• Gaussian phase-space representation of Fermion dynamics; Beyond the time-dependent-Hartree-Fock approximation
• First-principles quantum dynamics for fermions: Application to molecular dissociation
• Stochastic simulations of fermionic dynamics with phase-space representations
• Directional spatial structure of dissociated elongated molecular condensates

Cited by in corpus (7)

• Quantum fidelity measures for mixed states
• Probabilistic quantum phase-space simulation of Bell violations and their dynamical evolution
• Probabilistic Q-function distributions in fermionic phase-space
• Quantum dynamics in ultra-cold atomic physics
• Resolution of unity for fermionic Gaussian operators
• Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors
• On the Dynamics of the Fermi-Bose Model