Multi-copy programmable discrimination of general qubit states

TL;DR

This paper develops optimal programmable discrimination machines for general qubit states, analyzing their performance with multiple copies and different levels of prior knowledge, including asymptotic limits and special cases.

Contribution

It provides analytical solutions for optimal discrimination strategies for general qubit states with multiple copies, covering both known and unknown purity scenarios.

Findings

Derived analytical formulas for unambiguous discrimination

Calculated minimum error discrimination performance

Analyzed asymptotic behavior with many copies

Abstract

Quantum state discrimination is a fundamental primitive in quantum statistics where one has to correctly identify the state of a system that is in one of two possible known states. A programmable discrimination machine performs this task when the pair of possible states is not a priori known, but instead the two possible states are provided through two respective program ports. We study optimal programmable discrimination machines for general qubit states when several copies of states are available in the data or program ports. Two scenarios are considered: one in which the purity of the possible states is a priori known, and the fully universal one where the machine operates over generic mixed states of unknown purity. We find analytical results for both, the unambiguous and minimum error, discrimination strategies. This allows us to calculate the asymptotic performance of programmable discrimination machines when a large number of copies is provided, and to recover the standard state discrimination and state comparison values as different limiting cases.