Bounded-error quantum state identification and exponential separations in communication complexity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The minimum-error discrimination via Helstrom family of ensembles and convex optimization
Quantum Information Processing
Ancilla-assisted discrimination of quantum gates
Quantum Information & Computation
Upper bounds on the performance of differential-phase-shift quantum key distribution
Quantum Information & Computation
On the maximal singularity-free ellipse of planar 3-RP R parallel mechanisms via convex optimization
Robotics and Computer-Integrated Manufacturing
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We consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can be formulated as a semidefinite programming problem. Based on this formulation, we develop a set of necessary and sufficient conditions for an optimal quantum measurement. We show that the optimal measurement can be computed very efficiently in polynomial time by exploiting the many well-known algorithms for solving semidefinite programs, which are guaranteed to converge to the global optimum. Using the general conditions for optimality, we derive necessary and sufficient conditions so that the measurement that results in an equal probability of an inconclusive result for each one of the quantum states is optimal. We refer to this measurement as the equal-probability measurement (EPM). We then show that for any state set, the prior probabilities of the states can be chosen such that the EPM is optimal. Finally, we consider state sets with strong symmetry properties and equal prior probabilities for which the EPM is optimal. We first consider geometrically uniform (GU) state sets that are defined over a group of unitary matrices and are generated by a single generating vector. We then consider compound GU state sets which are generated by a group of unitary matrices using multiple generating vectors, where the generating vectors satisfy a certain (weighted) norm constraint.