Abstract
In this article, we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.
Highlights
Quantum metrology or quantum parameter estimation is the theory that studies the accuracy by which a physical parameter of a quantum system can be estimated through measurements and statistical inference
We derived a general expression for the symmetric logarithmic derivative of an arbitrary Fermionic Gaussian state
We obtained a compact expression in terms of a correlation matrix of a Fermionic Gaussian states (FGSs), which allows for the calculation of the quantum Fisher information
Summary
Quantum metrology or quantum parameter estimation is the theory that studies the accuracy by which a physical parameter of a quantum system can be estimated through measurements and statistical inference. Deriving closed form expressions of quantities involved in parameter estimation problems for many-body quantum systems is a major challenge. This work addresses this task in the special, yet relevant, case of arbitrary Fermionic Gaussian states. Since asymptotically the CR bound is saturable, it implies that the equivalence between the simultaneous and separate scheme in the limit of a large number of experiment repetitions can only hold if F is a diagonal matrix, and there are no statistical correlations between the estimators [56]. We derive a closed form expression of the SLD of Fermionic Gaussian states, which are of fundamental importance in the analysis of steady-states of both equilibrium and non-equilibrium quantum many-body systems, and their applications to quantum metrology.
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