Orthogonal and projected orthogonal matched filter detection
Signal Processing
Performance of quantum data transmission systems in the presence of thermal noise
IEEE Transactions on Communications
Theory of quantum pulse position modulation and related numerical problems
IEEE Transactions on Communications
Ancilla-assisted discrimination of quantum gates
Quantum Information & Computation
For distinguishing conjugate hidden subgroups, the pretty good measurement is as good as it gets
Quantum Information & Computation
Minimum-error discrimination among three pure linearly independent symmetric qutrit states
Quantum Information Processing
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We develop a sufficient condition for the least-squares measurement (LSM), or the square-root measurement, to minimize the probability of a detection error when distinguishing between a collection of mixed quantum states. Using this condition we derive the optimal measurement for state sets with a broad class of symmetries. We first consider geometrically uniform (GU) state sets with a possibly non-Abelian generating group, and show that if the generator satisfies a weighted norm constraint, then the LSM is optimal. In particular, for pure-state GU ensembles, the LSM is shown to be optimal. For arbitrary GU state sets we show that the optimal measurement operators are GU with generator that can be computed very efficiently in polynomial time, within any desired accuracy. We then consider compound GU (CGU) state sets which consist of subsets that are GU. When the generators satisfy a certain constraint, the LSM is again optimal. For arbitrary CGU state sets, the optimal measurement operators are shown to be CGU with generators that can be computed efficiently in polynomial time.