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• W1929126829 abstract "We consider the problem of testing multiple quantum hypotheses ${rho_1^{otimes n},ldots,rho_r^{otimes n}}$, where an arbitrary prior distribution is given and each of the $r$ hypotheses is $n$ copies of a quantum state. It is known that the average error probability $P_e$ decays exponentially to zero, that is, $P_e=exp{-xi n+o(n)}$. However, this error exponent $xi$ is generally unknown, except for the case that $r=2$. In this paper, we solve the long-standing open problem of identifying the above error exponent, by proving Nussbaum and Szkol a's conjecture that $xi=min_{ineq j}C(rho_i,rho_j)$. The right-hand side of this equality is called the multiple quantum Chernoff distance, and $C(rho_i,rho_j):=max_{0leq sleq 1}{-logoperatorname{Tr}rho_i^srho_j^{1-s}}$ has been previously identified as the optimal error exponent for testing two hypotheses, $rho_i^{otimes n}$ versus $rho_j^{otimes n}$. The main ingredient of our proof is a new upper bound for the average error probability, for testing an ensemble of finite-dimensional, but otherwise general, quantum states. This upper bound, up to a states-dependent factor, matches the multiple-state generalization of Nussbaum and Szkol a's lower bound. Specialized to the case $r=2$, we give an alternative proof to the achievability of the binary-hypothesis Chernoff distance, which was originally proved by Audenaert et al." @default.
• W1929126829 created "2016-06-24" @default.
• W1929126829 creator A5017100408 @default.
• W1929126829 date "2016-08-01" @default.
• W1929126829 modified "2023-10-14" @default.
• W1929126829 title "Discriminating quantum states: The multiple Chernoff distance" @default.
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• W1929126829 doi "https://doi.org/10.1214/16-aos1436" @default.
• W1929126829 hasPublicationYear "2016" @default.
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