Analytical calculation of optimal POVM for unambiguous discrimination of quantum states using KKT method

TL;DR

This paper derives an exact analytical formula for the optimal unambiguous discrimination of multiple quantum states using convex optimization techniques, advancing the theoretical understanding of quantum measurement strategies.

Contribution

It provides a novel analytical solution for the optimal POVM in unambiguous quantum state discrimination involving multiple states, utilizing KKT and semidefinite programming.

Findings

Derived an explicit formula for optimal POVM in unambiguous discrimination

Established the relation between optimal measurement and quantum states

Extended the solution to states with real and complex inner products

Abstract

In the present paper, an exact analytic solution for the optimal unambiguous state discrimination (OPUSD) problem involving an arbitrary number of pure linearly independent quantum states with real and complex inner product is presented. Using semidefinite programming and Karush-Kuhn-Tucker convex optimization method, we derive an analytical formula which shows the relation between optimal solution of unambiguous state discrimination problem and an arbitrary number of pure linearly independent quantum states.