Quantum State Discrimination and Quantum Cloning: Optimization and Implementation

In our work we explore the field of quantum state discrimination and quantum cloning. Recently the problem of optimal state discrimination with a Fixed Rate of Inconclusive Outcomes (FRIO strategy) has been solved for two pure quantum states and a few other highly symmetric cases. An optical implementation to FRIO for pure states is provided. The physical implementation can be carried out with the use of a six-port interferometer constructed with optical fibers beam splitters, phase shifters and mirrors. The input states are composed of qubits which are realized as photons in the dual-rail representation. The non-unitary measurements are carried out at the output for the presence or absence of a photon. The setup optimally interpolates between minimum error and unambiguous state discrimination. We also extend the FRIO strategy to two mixed states, whose eigenvectors in their spectral representation form a Jordan basis. We derive the minimum error rate PE for a fixed inconclusive rate Q and, in particular, the optimal distribution of the total Q over the Jordan subspaces. As Q is varied between the two limits, 0 \u3c Q \u3c Qc, a structure with multiple thresholds, Q1(th) (=0) \u3c Q2(th) \u3c . . . \u3c QN(th) \u3c Qc, emerges. We also solve the problem of state separation of two known pure states in the general case where the known states have arbitrary prior probabilities. The solution emerges from a geometric formulation of the problem. This formulation also reveals a deeper connection between cloning and state discrimination. The results are then applied in designing a scheme for hybrid cloning which interpolates between approximate and probabilistic exact cloning. It is shown that state separation and hybrid cloning are generalized schemes to well established state discrimination and cloning strategies. The connection between cloning and state separation is derived in the asymptotic limit