Nash equilibrium quantum states and optimal quantum data classification

Abstract

This letter reports a novel application of game theory to quantum informational processes which can be used to optimally classify data generated by these processes. To this end, the notion of simultaneously distinguishing a pure quantum state, generated by a quantum informational process, from its constituent observable states optimally - given the constraint of these observables being orthogonal to each other, is first introduced. This problem is solved via a non-cooperative game model and the affiliated solution concept of Nash equilibrium. The notion of Nash equilibrium quantum states is introduced and used to classify quantum data optimally.