Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed

Abstract

We analyze families of measures for the quantum statistical speed which include as special cases the quantum Fisher information, the trace speed, i.e., the quantum statistical speed obtained from the trace distance, and more general quantifiers obtained from the family of Schatten norms. These measures quantify the statistical speed under generic quantum evolutions and are obtained by maximizing classical measures over all possible quantum measurements. We discuss general properties, optimal measurements, and upper bounds on the speed of separable states. We further provide a physical interpretation for the trace speed by linking it to an analog of the quantum Cramér-Rao bound for median-unbiased quantum phase estimation.

19 pages, 1 figure

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• Witnessing non-Markovian effects of quantum processes through Hilbert-Schmidt speed
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• Estimates of the Quantum Fisher Information in the $S=1$ Anti-Ferromagnetic Heisenberg Spin Chain with Uniaxial Anisotropy
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• Optimal quantum speed for mixed states
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• Witnessing global memory effects of multiqubit correlated noisy channels by Hilbert-Schmidt speed
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• Witnessing criticality in non-Hermitian systems via entropic uncertainty relation
• Excessive precision compromises accuracy even with unlimited resources due to the trade-off in quantum metrology
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• Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes
• Estimation precision of parameter associated with Unruh-like effect
• Implementation of multiparticle quantum speed limits on observables
• Bounds on quantum Fisher information and uncertainty relations for thermodynamically conjugate variables
• Approaching the Quantum Speed Limit in Quantum Gates with Geometric Control
• The temporal resolution limit in quantum sensing