A variational framework yields closed-form Bayesian estimators for Gaussian quantum states via polynomial quadrature operators and a global optimality condition.
Phase space formalism for quantum estimation of Gaussian states
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abstract
We formulate, with full generality, the asymptotic estimation theory for Gaussian states in terms of their first and second moments. By expressing the quantum Fisher information (QFI) and the elusive symmetric logarithmic derivative (SLD) in terms of the state's moments (and their derivatives) we are able to obtain the noncommutative extension of the well known expression for the Fisher information of a Gaussian probability distribution. Focusing on models with fixed first moments and identical Williamson 'diagonal' states --which include pure state models--, we obtain their SLD and QFI, and elucidate what features of the Wigner function are fundamentally accessible, and at what rates. In addition, we find the optimal homodyne detection scheme for all such models, and show that for pure state models they attain the fundamental limit.
fields
quant-ph 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
Embedding squeezing in the system Hamiltonian and leveraging environmental memory induces higher-order QFI time dependence and information backflow that can restore or exceed unitary precision in noisy frequency estimation.
Derives SBS input-output model and shows quantum-limited detection outperforms classical and photon-counting methods for eavesdropper localization in optical fibers via hypothesis testing and metrology.
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Closed-form Bayesian quantum estimation of Gaussian states
A variational framework yields closed-form Bayesian estimators for Gaussian quantum states via polynomial quadrature operators and a global optimality condition.
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Beating noise in frequency estimation with squeezing and memory in continuous-variable systems
Embedding squeezing in the system Hamiltonian and leveraging environmental memory induces higher-order QFI time dependence and information backflow that can restore or exceed unitary precision in noisy frequency estimation.
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Fundamental Limits of Eavesdropper Detection and Localization in Optical Fiber via Stimulated Brillouin Scattering
Derives SBS input-output model and shows quantum-limited detection outperforms classical and photon-counting methods for eavesdropper localization in optical fibers via hypothesis testing and metrology.