Detecting non-decomposability of time evolution via extreme gain of correlations

TL;DR

This paper introduces a method to detect non-commutativity in quantum interactions by observing extreme correlation gains between probes, even when the mediating Hamiltonians are unknown, revealing non-decomposable evolution.

Contribution

The authors propose a novel correlation-based technique to identify non-commuting Hamiltonians without prior knowledge of their form or operations on the mediator.

Findings

Correlation bounds are violated by non-commuting Hamiltonians.

Excessive correlations indicate non-decomposable evolution.

Method applies to various correlation measures like entanglement and discord.

Abstract

Non-commutativity is one of the most elementary non-classical features of quantum observables. Here we propose a method to detect non-commutativity of interaction Hamiltonians of two probe objects coupled via a mediator. If these objects are open to their local environments, our method reveals non-decomposability of temporal evolution into a sequence of interactions between each probe and the mediator. The Hamiltonians or Lindblad operators can remain unknown throughout the assessment, we only require knowledge of the dimension of the mediator. Furthermore, no operations on the mediator are necessary. Technically, under the assumption of decomposable evolution, we derive upper bounds on correlations between the probes and then demonstrate that these bounds can be violated with correlation dynamics generated by non-commuting Hamiltonians, e.g., Jaynes-Cummings coupling. An intuitive explanation is provided in terms of multiple exchanges of a virtual particle which lead to the excessive accumulation of correlations. A plethora of correlation quantifiers are helpful in our method, e.g., quantum entanglement, discord, mutual information, and even classical correlation. Finally, we discuss exemplary applications of the method in quantum information: the distribution of correlations and witnessing dimension of an object.