Estimation of Gaussian quantum states
Abstract
We derive several expressions for the quantum Fisher information matrix (QFIM) for the multiparameter estimation of multimode Gaussian quantum states, the corresponding symmetric logarithmic derivatives, and conditions for saturability of the quantum CramérRao 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.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 January 2019
 DOI:
 10.1088/17518121/aaf068
 arXiv:
 arXiv:1801.00299
 Bibcode:
 2019JPhA...52c5304S
 Keywords:

 quantum metrology;
 quantum parameter estimation;
 Gaussian quantum states;
 phasespace formalism;
 Quantum Physics
 EPrint:
 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 Cram\'erRao bound, v4: Added an appendix of the real and the complex phasespace representations of common Gaussian unitaries and states