Universal quantum uncertainty relations between non-ergodicity and loss of information

TL;DR

This paper derives universal quantum uncertainty relations linking information loss and non-ergodicity in open quantum systems, showing that increased non-ergodicity can help preserve quantum information during lossy evolution.

Contribution

It establishes the first general uncertainty relations between information loss and non-ergodicity applicable to any quantum system and environment, using distance measures on quantum states.

Findings

Uncertainty relations hold for arbitrary distance measures satisfying axioms.

Higher non-ergodicity correlates with lower information loss bounds.

Model analysis confirms the theoretical relations in a qubit-bath system.

Abstract

We establish uncertainty relations between information loss in general open quantum systems and the amount of non-ergodicity of the corresponding dynamics. The relations hold for arbitrary quantum systems interacting with an arbitrary quantum environment. The elements of the uncertainty relations are quantified via distance measures on the space of quantum density matrices. The relations hold for arbitrary distance measures satisfying a set of intuitively satisfactory axioms. The relations show that as the non-ergodicity of the dynamics increases, the lower bound on information loss decreases, which validates the belief that non-ergodicity plays an important role in preserving information of quantum states undergoing lossy evolution. We also consider a model of a central qubit interacting with a fermionic thermal bath and derive its reduced dynamics, to subsequently investigate the information loss and nonergodicity in such dynamics. We comment on the minimal situations that saturate the uncertainty relations.