Analytical Bounds for Nonasymptotic Asymmetric State Discrimination

Two types of errors can occur when discriminating pairs quantum states. Asymmetric state discrimination involves minimizing the probability one type error, subject to a constraint on other. We give explicit expressions bounding set achievable errors, using trace norm, fidelity, and Chernoff bound. The upper bound is asymptotically tight lower exact for pure Unlike asymptotic bounds, our bounds error values instead exponents, so more precise results applied finite-copy problems.