Asymptotic Properties for Markovian Dynamics in Quantum Theory and General Probabilistic Theories

Abstract

We address asymptotic decoupling in the context of Markovian quantum dynamics. Asymptotic decoupling is an asymptotic property on a bipartite quantum system, and asserts that the correlation between two quantum systems is broken after a sufficiently long time passes. The first goal of this paper is to show that asymptotic decoupling is equivalent to local mixing which asserts the convergence to a unique stationary state on at least one quantum system. In the study of Markovian dynamics, mixing and ergodicity are fundamental properties which assert the convergence and the convergence of the long-time average, respectively. The second goal of this paper is to show that mixing for dynamics is equivalent to ergodicity for the two-fold tensor product of dynamics. This equivalence gives us a criterion of mixing that is a system of linear equations. All results in this paper are proved in the framework of general probabilistic theories (GPTs), but we also summarize them in quantum theory.

42 pages, 5 figures

References in corpus (10)

• Improved transfer of quantum information using a local memory
• Fisher information and asymptotic normality in system identification for quantum Markov chains
• The Generalized Lyapunov Theorem and its Application to Quantum Channels
• Tensor power of dynamical maps and P- vs. CP-divisibility
• When Do Composed Maps Become Entanglement Breaking?
• Eventually Entanglement Breaking Maps
• The positive partial transpose conjecture for n=3
• Eventually entanglement breaking Markovian dynamics: structure and characteristic times
• Spectral Properties of Tensor Products of Channels
• Asymptotic and Non-Asymptotic Analysis for Hidden Markovian Process with Quantum Hidden System

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• Quantum theory in finite dimension cannot explain every general process with finite memory
• Probing the limits of quantum theory with quantum information at subnuclear scales
• Maximum Dimension of Subspaces with No Product Basis