Gaussian states and operations -- a quick reference

2021/02/10 by Jonatan Bohr Brask, Brask, Jonatan Bohr · 17 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.48550/arxiv.2102.05748

9 pages, no figures. Minor edits and corrections. Added reference to QuGIT

arxiv created 2022/03/30 · arxiv updated 2022/03/31

Abstract

Gaussian quantum states of bosonic systems are an important class of states. In particular, they play a key role in quantum optics as all processes generated by Hamiltonians up to second order in the field operators (i.e. linear optics and quadrature squeezing) preserve Gaussianity. A powerful approach to calculations and analysis of Gaussian states is using phase-space variables and symplectic transformations. The purpose of this note is to serve as a concise reference for performing phase-space calculations on Gaussian states. In particular, we list symplectic transformations for commonly used optical operations (displacements, beam splitters, squeezing), and formulae for tracing out modes, treating homodyne measurements, and computing fidelities.

Citations

• Gaussian quantum information

Cited by

• A Bogoliubov-ratio framework for quantum-information diagnostics of time-dependent two-mode Boson Hamiltonian
• Detecting Symmetrizability in Physical Systems
• Charge-Preserving Operations in Quantum Batteries
• Quantum advantage bounds for a multipartite Gaussian battery
• Explicitly Quantum-parallel Computation by Displacements
• Exploiting higher-order correlation functions for photon-statistics-based characterization and reconstruction of arbitrary Gaussian states
• Privacy in continuous-variable distributed quantum sensing
• Simultaneous generation and transfer of mechanical noise squeezing
• Unified boson sampling
• The loss tolerance of cat breeding for fault-tolerant grid state generation
• Fast simulations of continuous-variable circuits using the coherent state decomposition
• Relativistic implications of entropy and purity
• Noise-reduction of multimode Gaussian Boson Sampling circuits via Unitary Averaging
• Precision bounds for bosonic quantum batteries
• Information geometry and entanglement under phase-space deformation through nonsymplectic congruence transformation
• A Complete Characterization of Passive Unitary Normalizable (PUN) Gaussian States
• Gaussian states in quantum field theory: Exact representations of relative phase in superpositions of Gaussian states

Related

• Tutorial Notes on One-Party and Two-Party Gaussian States
• Properties and Application of Gaussian Quantum Processes
• On the covariance matrix for Gaussian states
• What's my phase again? Computing the vacuum-to-vacuum amplitude of quadratic bosonic evolution
• Symmetry and Asymmetry in Bosonic Gaussian Systems: A Resource-Theoretic Framework