Belavkin加权量子测量的误差率和Holevo渐近最优性定理的逆定理
Error rates of Belavkin weighted quantum measurements and a converse to Holevo's asymptotic optimality theorem
摘要：
我们从量子态的最小误差判别的角度比较了几个纯态Belavkin加权平方根测量的例子。二次加权测量在许多方面被证明优于所谓的“相当好的测量”（PGM）：（1）Holevo的二次加权无条件地优于PGM的情况下，两个状态系综，只有在平凡的情况下相等。(2)证明了Holevo定理的一个逆定理，证明了加权测量只有当它是二次加权时才是渐近最优的。三个国家的反例构造。还考虑了Ballester、Wehner和Winter的立方加权测量。各种权重的充分最优性条件进行了比较。
英文摘要：
We compare several instances of pure-state Belavkin weighted square-root measurements from the standpoint of minimum-error discrimination of quantum states. The quadratically weighted measurement is proven superior to the so-called "pretty good measurement" (PGM) in a number of respects: (1) Holevo's quadratic weighting unconditionally outperforms the PGM in the case of two-state ensembles, with equality only in trivial cases. (2) A converse of a theorem of Holevo is proven, showing that a weighted measurement is asymptotically optimal only if it is quadratically weighted. Counterexamples for three states are constructed. The cube-weighted measurement of Ballester, Wehner, and Winter is also considered. Sufficient optimality conditions for various weights are compared.
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