On errors generated by unitary dynamics of bipartite quantum systems

TL;DR

This paper explores how to define quantum errors associated with graphs generated by unitary dynamics in bipartite quantum systems, using POVMs and Naimark dilatation, with applications to quantum oscillators.

Contribution

It provides a novel method to associate errors with graphs from unitary dynamics via POVMs and Naimark dilatation, expanding understanding of quantum error structures.

Findings

Constructed errors for graphs from bipartite unitary dynamics.

Analyzed POVMs on ${f Z}_n$ and ${f R}$ groups.

Presented an example with two-mode quantum oscillator.

Abstract

Given a quantum channel it is possible to define the non-commutative operator graph whose properties determine a possibility of error-free transmission of information via this channel. The corresponding graph has a straight definition through Kraus operators determining quantum errors. We are discussing the opposite problem of a proper definition of errors that some graph corresponds to. Taking into account that any graph is generated by some POVM we give a solution to such a problem by means of the Naimark dilatation theorem. Using our approach we construct errors corresponding to the graphs generated by unitary dynamics of bipartite quantum systems. The cases of POVMs on the circle group ${\mathbb Z}_n$ and the additive group $\mathbb R$ are discussed. As an example we construct the graph corresponding to the errors generated by dynamics of two mode quantum oscillator.