Resources needed for non-unitary quantum operations

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.

References in corpus (2)

• The Naimark dilated PT-symmetric brachistochrone
• Distance Bounds on Quantum Dynamics

Cited by in corpus (6)

• Quantum Equivalence and Quantum Signatures in Heat Engines
• Quantum speed limits on operator flows and correlation functions
• Response strengths of open systems at exceptional points
• Time-energy tradeoff in unambiguous state discrimination POVM
• Interaction without back-action in the context of quantum manipulation
• The role of singular values in entanglement distillation and unambiguous state discrimination