Coexistence of quantum operations

TL;DR

This paper investigates the conditions under which different quantum operations can be jointly measured, providing criteria for coexistence and analyzing common classes like Luders operations.

Contribution

It derives two equivalent criteria for the coexistence of quantum operations and analyzes the coexistence conditions for Luders operations and conditional state preparators.

Findings

Luders operations are coexistent only under restrictive conditions

Derived two equivalent criteria for joint measurability of quantum operations

Identified limitations for coexistence of common quantum operation classes

Abstract

Quantum operations are used to describe the observed probability distributions and conditional states of the measured system. In this paper, we address the problem of their joint measurability (coexistence). We derive two equivalent coexistence criteria. The two most common classes of operations - Luders operations and conditional state preparators - are analyzed. It is shown that Luders operations are coexistent only under very restrictive conditions, when the associated effects are either proportional to each other, or disjoint.