Fluctuation theorems for multipartite quantum coherence and correlation dynamics

TL;DR

This work addresses the problem of describing nonequilibrium quantum information dynamics beyond conventional thermodynamics by formulating fluctuation theorems for multipartite coherence and correlations. The authors develop a two-point measurement-based FT for total classical correlations, and extend to quantum correlations and coherence through a quasiprobability formalism, yielding integral and detailed fluctuation relations for $ΔI$, $ΔI_{ ext{cl}}$, $ΔC$, $Δι$, and $Δc$. The key contributions include a decomposition $ΔI=ΔI_{ ext{cl}}+ΔC$, exact FT relations in both classical and quantum regimes, and concrete three-qubit demonstrations that verify the predictions and outline experimental verification routes. This framework offers a rigorous statistical lens on information flow in open quantum systems and paves the way for analyzing information-driven protocols in quantum technologies, with potential extensions to other quantum resources such as discord, steering, and entanglement dynamics.

Abstract

Fluctuation theorems establish exact relations for nonequilibrium dynamics, profoundly advancing the field of stochastic thermodynamics. In this work, we extend quantum fluctuation theorems beyond the traditional thermodynamic framework to quantum multipartite information dynamics, where both the system and the environment are multipartite without assuming any thermodynamic constraints. Based on the two-point measurement scheme and the classical probability, we establish the fluctuation theorem for the dynamics of classical multipartite mutual information. By extending to quasiprobability, we derive quantum fluctuation theorems for multipartite coherence and quantum correlations, presenting them in both integral and detailed forms. Our theoretical results are illustrated and verified using three-qubit examples, and feasible experimental verification protocols are proposed. These findings uncover the statistical structure underlying the nonequilibrium quantum information dynamics, providing fundamental insights and alternative tools for advancing quantum technologies.

Figures (3)

• Figure 1: Schematic of the dynamics of an $N$-partite correlated state $\rho_S = \rho_{S_1S_2\cdots S_N}$ interacting with multipartite environments $\rho_E = \bigotimes_{j=1}^N\rho_{E_j}$. Initially, the subenvironments are uncorrelated. The interaction between the subsystem $S_j$ and the subenvironment $E_j$ is denoted as $U_{S_jE_j}$, where $j = 1,2,\cdots, N$.
• Figure 2: Verifications of the integral fluctuation relations (\ref{['eq:FT_i_cl']}), (\ref{['eq:FT_i_q']}), and (\ref{['eq:FT_c']}), through three-qubit examples. The initial states of the system, $\rho_S$ or $\tilde{\rho}_S$, and the environment qubits $\rho_{E_j}$ are randomly generated. For the total classical and quantum correlations, the dynamics $U_{SE}$ are randomly chosen. For the coherence change, the dynamics is set to the two-qubit swap gate, namely $U_{S_jE_j} = \text{SWAP}$.
• Figure 3: The relationship between the expectation value and the second moment distribution of the total classical and quantum correlations, as well as the coherence change. The red dashed line represents $\langle x^2\rangle = 2\langle x\rangle$. The results are obtained from the data in Fig. \ref{['fig_ft']}.

Theorems & Definitions (10)

• Theorem 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof
• Theorem 4
• proof
• Theorem 5
• proof