Time-energy tradeoff in unambiguous state discrimination POVM

TL;DR

This paper explores the fundamental tradeoff between energy resources and evolution time in unambiguous quantum state discrimination using POVMs, providing an action-like cost inequality and optimal realization strategies.

Contribution

It introduces a novel tradeoff relation between energy and time in POVM-based state discrimination and identifies the minimal-cost implementation based on maximal population transfer.

Findings

Derived an action-like cost inequality for POVM implementation.

Identified the realization minimizing the action-like cost.

Showed cost depends on maximal population transfer to the ancilla.

Abstract

Unambiguous non-orthogonal state discrimination has fundamental importance in quantum information and quantum cryptography. The discrimination is carried out by POVM generalized measurements. For this process, we find a tradeoff between the needed energy resources and the evolution time, and express it in terms of action-like cost inequality. We find the realization that minimizes this action-like cost and show that in this case the cost is determined by the maximal population transfer from the system to the ancilla needed for the POVM implementation.