Derives QSLs based on square roots of Jensen-Shannon and Jeffreys divergences, expressed via Schatten speed and eigenvalue cost functions, for general quantum processes including unitary evolution and specific open channels.
Lower bounds on the quantum Fisher information based on the variance and various types of entropies
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abstract
We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., $(\Delta A)^2-F_{\rm Q}[\varrho,A]/4.$ We find that it is equal to a generalized variance defined in Petz [J. Phys. A 35, 929 (2002)] and Gibilisco, Hiai, and Petz [IEEE Trans. Inf. Theory 55, 439 (2009)]. We present an upper bound on this quantity that is proportional to the linear entropy. As expected, our relation shows that for states that are close to being pure, the quantum Fisher information over four is close to the variance. We also obtain the variance and the quantum Fisher information averaged over all Hermitian operators, and examine its relation to the von Neumann entropy. Apart from the usual quantum Fisher information, we also consider the Kubo-Mori-Bogoliubov quantum Fisher information.
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An iterative semidefinite programming method maximizes quantum Fisher information over local Hamiltonians to optimize metrological performance of quantum states and solves related entanglement problems.
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Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes
Derives QSLs based on square roots of Jensen-Shannon and Jeffreys divergences, expressed via Schatten speed and eigenvalue cost functions, for general quantum processes including unitary evolution and specific open channels.
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Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
An iterative semidefinite programming method maximizes quantum Fisher information over local Hamiltonians to optimize metrological performance of quantum states and solves related entanglement problems.