An explicit pretty-good-measurement protocol solves worst-case quantum state discrimination with O(log n) copies for low-fidelity mixed states and with a Gram-matrix-dependent copy count for pure states.
How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?
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abstract
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of approximate degree and bounded-error quantum query complexity. We show that for these measures the correct lower bound is Omega(log n / loglog n), and we exhibit quantum algorithms for two functions where this bound is achieved.
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quant-ph 1years
2019 1verdicts
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Pretty simple bounds on quantum state discrimination
An explicit pretty-good-measurement protocol solves worst-case quantum state discrimination with O(log n) copies for low-fidelity mixed states and with a Gram-matrix-dependent copy count for pure states.