Abstract
We consider optimal state discrimination in a general convex operational framework, so-called generalized probabilistic theories (GPTs), and present a general method of optimal discrimination by applying the complementarity problem from convex optimization. The method exploits the convex geometry of states but not other detailed conditions or relations of states and effects. We also show that properties in optimal quantum state discrimination are shared in GPTs in general: (i) no measurement sometimes gives optimal discrimination, and (ii) optimal measurement is not unique.
Highlights
Suppose that there is a party, say Alice, who prepares her system in a particular state
We investigate general properties of optimal state discrimination in generalized probabilistic theories (GPTs) and present a method of optimal state discrimination based on the convex geometry of a state space
In quantum cases it is the operational task that corresponds to the information-theoretic measure, the min-entropy [21]
Summary
Suppose that there is a party, say Alice, who prepares her system in a particular state. In a GPT where ensemble steering is possible, the no-signaling principle can determine optimal state discrimination This holds true in quantum theory, where the no-signaling principle elucidates the relation between optimal state discrimination and quantum cloning [10]. We show that primal and dual problems return the idential result, and formulate the problem in the form of the complementarity problem that gives a generalization of the optimization problems This allows us to derive a geometric method of state discrimination. We consider an example of GPTs, the polygon states, and apply the geometric formulation to optimal discrimination We identify those properties that optimal quantum state discrimination shares with GPTs: (i) optimal measurement is not unique in general, and (ii) no measurement can sometimes give optimal state discrimination. The polygon system is considered as examples of GPTs, and we apply the method to optimal discrimination of polygon states
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