Coherent control and distinguishability of quantum channels via PBS-diagrams

TL;DR

This paper introduces a graphical language inspired by quantum optics for coherently controlling quantum channels, using purified channels to accurately represent their behavior under such control.

Contribution

It proposes a new graphical framework based on purified channels for representing coherently controlled quantum channels, addressing limitations of standard CP maps.

Findings

Characterizes observational equivalence of purified channels in coherent-control scenarios

Provides a faithful representation of quantum channels under coherent control

Extends Stinespring's dilation for practical quantum optical setups

Abstract

We introduce a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS). As standard completely positive trace preserving maps are known not to be appropriate to represent coherently controlled quantum channels, we propose to instead use purified channels, an extension of Stinespring's dilation. We characterise the observational equivalence of purified channels in various coherent-control contexts, paving the way towards a faithful representation of quantum channels under coherent control.