Intrinsic Quantum Mpemba Effect in Markovian Systems and Quantum Circuits

TL;DR

This paper introduces the intrinsic quantum Mpemba effect (IQME), a new way to understand counterintuitive quantum state dynamics using trajectory length in Riemannian space, applicable to Markovian systems and quantum circuits.

Contribution

It defines IQME using trajectory length as a distance measure, unifying the concept across open and closed quantum systems and providing new insights into quantum thermalization.

Findings

IQME exists in Markovian systems.

IQME observed in U(1)-symmetric quantum circuits.

Trajectory length offers a natural measure for quantum state evolution.

Abstract

The quantum Mpemba effect (QME) describes the counterintuitive phenomenon in which a system farther from equilibrium reaches steady state faster than one closer to equilibrium. However, ambiguity in defining a suitable distance measure between quantum states has led to varied interpretations across different contexts. Here we propose the intrinsic quantum Mpemba effect (IQME), defined using the trajectory length traced by the quantum state as a more appropriate measure of distance--distinct from previous trajectory-independent metrics. By treating quantum states as points in a Riemannian space defined by statistical distance, the trajectory length emerges as a more natural and accurate characterization of the counterintuitive dynamics, drawing an analogy to the classical Brachistochrone problem. We demonstrate the existence of IQME in Markovian systems and extend its definition to quantum circuits, thereby establishing a unified framework applicable to both open and closed systems. Notably, we observe an IQME in a $U(1)$-symmetric circuit, offering new insights into the rates of quantum thermalization for different initial states. This work deepens our understanding of quantum state evolution and lays the foundation for accurately capturing novel quantum dynamical behaviour.