Detecting nondecomposability of time evolution via extreme gain of correlations

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.

Hierarchy of correlation quantifiers comparable to negativity

“…Ref. [55] shows the gain in correlations between A and B under decomposable dynamics is bounded above. Thus a gain above this bound detects the non-decomposability.…”

“…where â and b are the annihilation operators for the fields A and B, respectively, and σ ± are the raising and lowering operators for the atom, which we will denote as object C. Theorem 1 in Ref. [55] applied to the partial transpose distance shows the following bound which holds for decomposable dynamics independently of the initial state:…”

Hierarchy of correlation quantifiers comparable to negativity

“…Ref. [51] shows the gain in correlations between A and B under decomposable dynamics is bounded above. Thus a gain above this bound detects the non-decomposability.…”

“…where â and b are the annihilation operators for the fields A and B, respectively, and σ ± are the raising and lowering operators for the atom, which we will denote as object C. Theorem 1 in Ref. [51] applied to the partial transpose distance shows the following bound which holds for decomposable dynamics independently of the initial state:…”

Distribution of quantum entanglement : principles and applications

“…Parts of this chapter are reproduced from our published articles of Refs [45,55],. c [2019] American Physical Society.…”