Ancilla models for quantum operations: For what unitaries does the ancilla state have to be physical?

TL;DR

This paper investigates the conditions under which the unitary interactions in quantum operations ensure that the ancilla's initial state remains physically valid, i.e., positive, to produce a valid quantum evolution.

Contribution

It characterizes the properties of unitary operators that guarantee the ancilla state must be positive for the overall quantum evolution to be physically valid.

Findings

Identifies conditions on unitaries for physical ancilla states

Links unitary properties to complete positivity of quantum maps

Provides criteria for physical ancilla in quantum operations

Abstract

Any evolution described by a completely positive trace-preserving linear map can be imagined as arising from the interaction of the evolving system with an initially uncorrelated ancilla. The interaction is given by a joint unitary operator, acting on the system and the ancilla. Here we study the properties such a unitary operator must have in order to force the choice of a physical- that is, positive-state for the ancilla if the end result is to be a physical-that is, completely positive-evolution of the system.