Measure of quantum Fisher information flow in multi-parameter scenario

TL;DR

This paper extends the concept of quantum Fisher information flow to multi-parameter systems using information geometry, introducing the intrinsic density flow (IDF) to analyze quantum state distinguishability and non-Markovian dynamics.

Contribution

It generalizes quantum Fisher information flow to multi-parameter scenarios and defines the intrinsic density flow (IDF) from an information geometry perspective.

Findings

IDF vanishes under parameter-independent unitary evolution

IDF exhibits outward flow (negativity) under completely positive-divisible maps

Temporary backflow of IDF indicates non-Markovian dynamics

Abstract

We generalize the quantum Fisher information flow proposed by Lu \textit{et al}. [Phys. Rev. A \textbf{82}, 042103 (2010)] to the multi-parameter scenario from the information geometry perspective. A measure named the \textit{intrinsic density flow} (IDF) is defined with the time-variation of the intrinsic density of quantum states (IDQS). IDQS measures the local distinguishability of quantum states in state manifolds. The validity of IDF is clarified with its vanishing under the parameter-independent unitary evolution and outward-flow (negativity) under the completely positive-divisible map. The temporary backflow (positivity) of IDF is thus an essential signature of the non-Markovian dynamics. Specific for the time-local master equation, the IDF decomposes according to the channels, and the positive decay rate indicates the inwards flow of the sub-IDF. As time-dependent scalar fields equipped on the state space, the distribution of IDQS and IDF comprehensively illustrates the distortion of state space induced by its environment. As example, a typical qubit model is given.