Estimation of Gaussian quantum states
arXiv:1801.00299 · doi:10.1088/1751-8121/aaf068
Abstract
We derive several expressions for the quantum Fisher information matrix (QFIM) for the multi-parameter estimation of multi-mode Gaussian quantum states, the corresponding symmetric logarithmic derivatives, and conditions for saturability of the quantum Cramér-Rao bound. This bound determines the ultimate precision with which parameters encoded into quantum states can be estimated. We include expressions for mixed states, for the case when the Williamson decomposition of the covariance matrix is known, expressions in terms of infinite series, and expressions for pure states. We also discuss problematic behavior when some modes are pure, and present a method that allows the use of expressions that are defined only for mixed states, to compute QFIM for states with any number of pure modes.
8+9 pages, v2: introduction extended, examples added, v3(published version): Title changed, introduction extended, significantly extended results: added expressions for the symmetric logarithmic derivatives, and expressions for saturability of the quantum Cramér-Rao bound, v4: Added an appendix of the real and the complex phase-space representations of common Gaussian unitaries and states
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