Path-Phase Information Complementarity for Interfering Particles through State-Discrimination

TL;DR

This paper investigates the fundamental trade-off in extracting information about complementary properties of a qubit through repeated measurements, revealing a new aspect of quantum complementarity via a mutual information relation.

Contribution

It introduces a general complementarity relation for path-phase guesses in a state discrimination scenario, highlighting a novel aspect of quantum information trade-offs.

Findings

Derived a complementarity relation for path-phase guesses.

Revealed a new aspect of quantum complementarity.

Established a mutual information-based framework for state discrimination.

Abstract

We analyze the trade-off between the amounts of information obtainable on complementary properties of a qubit state by simultaneous measurements. We consider a "state discrimination" scenario wherein the same measurements are repeated, but the input states must be guessed in every run. We find a general complementarity relation for path-phase guesses by any generalized measurements in this scenario. The counterpart of this input-output mutual information (MI) reveals a hitherto unknown aspect of complementarity.