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Gaussian states and operations -- a quick reference
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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.
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Cited by 7 Pith papers
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Formal Verification of Continuous-Variable Quantum Programs
A sound and relatively complete Hoare logic for continuous-variable quantum programs, with polynomial assertions and an automated weakest-precondition calculator.
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Higher-order covariance matrices for non-Gaussian quantum states
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Bosonic quantum error-correcting codes with finite stellar rank
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