Detecting Non-Commutativity of Unknown Hamiltonians via Extreme Gain of Correlations

Tanjung Krisnanda, Ray Ganardi, Su‐Yong Lee, Jaewan Kim, Tomasz Paterek

Published Apr 26, 2018• 0 citations

Abstract

Non-commutativity is one of the most elementary non-classical features of quantum observables. Here we present a method to detect non-commutativity of Hamiltonians, which is applicable even if these Hamiltonians are completely unknown. We consider two probe objects individually interacting with the third object (mediator) but not with each other. If the probe-mediator Hamiltonians commute, we derive upper bounds on correlations between the probes that depend on the dimension of the mediator. We then demonstrate that these bounds can be violated with correlation dynamics generated by non-commuting Hamiltonians. 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, to detect non-classicality in the form of non-commutativity.

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