Related papers: Semi-classical geometric tensor in multiparameter quantum information

Semi-classical geometric tensor in multiparameter quantum information

URL: http://arxiv.org/abs/2504.06812v1
Date: Wed, 09 Apr 2025 12:06:57 GMT
Title: Semi-classical geometric tensor in multiparameter quantum information
Authors: Satoya Imai, Jing Yang, Luca Pezzè,
Abstract summary: We introduce a counterpart to the quantum geometric tensor (QGT) that includes measurement operators.<n>We show that the SCGT provides a lower bound to the QGT that is tight for pure states.
Score: 2.624076371876711
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The quantum geometric tensor (QGT) captures the variations of quantum states with parameters, serving as a central concept in modern quantum physics. Its real part, the quantum Fisher information matrix (QFIM), has a measurement-dependent counterpart that links statistics to distinguishability. However, an analogous extension for the QGT is hindered by the fundamental inaccessibility of its imaginary part through measurement probabilities. Here we introduce a counterpart to the QGT that includes measurement operators, termed the \textit{semi-classical} geometric tensor (SCGT). We show that the SCGT provides a lower bound to the QGT that is tight for pure states. Moreover, we use the SCGT to derive sharp multiparameter information bounds and discuss extensions of the Berry phase.

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