Resources needed for non-unitary quantum operations

TL;DR

This paper establishes lower bounds on the resources required for implementing non-unitary quantum operations, such as state preparation and discrimination, in non-Hermitian quantum systems, highlighting fundamental limits in resource efficiency.

Contribution

It provides a theoretical framework for quantifying the minimal resources needed for non-unitary quantum operations, with detailed analysis of passive systems and specific examples.

Findings

Lower bounds on resources for non-Hermitian state preparation

Lower bounds on resources for non-orthogonal state discrimination

Analytical examples illustrating resource constraints

Abstract

Non-unitary operations generated by an effective non-Hermitian Hamiltonian can be used to create quantum state manipulations which are impossible in Hermitian quantum mechanics. These operations include state preparation (or cooling) and non-orthogonal state discrimination. In this work we put a lower bound on the resources needed for the construction of some given non-unitary evolution. Passive systems are studied in detail and a general feature of such a system is derived. After interpreting our results using the singular value decomposition, several examples are studied analytically. In particular, we put a lower bound on the resources needed for non-Hermitian state preparation and non-orthogonal state discrimination.