Universal bound on the relaxation rates for quantum Markovian dynamics

TL;DR

This paper proves a universal, tight upper bound on quantum relaxation rates, linking them to the system's dimension, and highlights its significance as a fundamental constraint akin to Bell and Leggett-Garg inequalities.

Contribution

It establishes a universal, tight upper bound on quantum relaxation rates based on the system's dimension, a previously conjectured fundamental constraint.

Findings

The bound is valid for all finite-dimensional quantum systems.

Violations of the bound indicate non-CP-divisible evolution.

The bound is analogous to Bell and Leggett-Garg inequalities.

Abstract

Relaxation rates provide important characteristics both for classical and quantum processes. Essentially they control how fast the system thermalizes, equilibrates, {decoheres, and/or dissipates}. Moreover, very often they are directly accessible to be measured in the laboratory and hence they define key physical properties of the system. Experimentally measured relaxation rates can be used to test validity of a particular theoretical model. Here we analyze a fundamental question: {\em does quantum mechanics provide any nontrivial constraint for relaxation rates?} We prove the conjecture formulated a few years ago that any quantum channel implies that a maximal rate is bounded from above by the sum of all the relaxation rates divided by the dimension of the Hilbert space. It should be stressed that this constraint is universal (it is valid for all quantum systems with finite number of energy levels) and it is tight (cannot be improved). In addition, the constraint plays an analogous role to the seminal Bell inequalities and the well known Leggett-Garg inequalities (sometimes called temporal Bell inequalities). Violations of Bell inequalities rule out local hidden variable models, and violations of Leggett-Garg inequalities rule out macrorealism. Similarly, violations of the bound rule out completely positive-divisible evolution.