论文标题
关于量子假设检验的猜想
On a conjecture regarding quantum hypothesis testing
论文作者
论文摘要
在本MSC论文中，我考虑复合假设检验中对称误差的渐近行为。在经典情况下，当零假设和替代假设是有限状态时，最佳可实现的对称误差指数只是与“最坏情况”对相对应的最佳可实现的对称误差指数。猜想 - 几年前提出的 - 在量子案例中也是如此。在某些特殊情况下，这是正确的。但是，在某种意义上，所有已知的特殊情况都“太好”，例如，具有某些对称性。 希望在我的论文中找到一个反示例，我考虑了一种新的特殊情况，一方面，它尽可能“不对称”，但仍可以在分析上进行计算。但是，由于从某些涉及的计算中，在这种情况下，猜想也是正确的，因此为该猜想提供了进一步的证据。
In this MSc thesis I consider the asymptotic behaviour of the symmetric error in composite hypothesis testing. In the classical case, when the null and alternative hypothesis are finite sets of states, the best achievable symmetric error exponent is simply the the best achievable symmetric error exponent corresponding to the "worst case pair". The conjecture -- raised several years ago -- is that this remains true in the quantum case, too. This is known to be true in some special case. However, all of the known special cases are in some sense "too nice", e.g., have certain symmetries. Hoping to find a counter-example, in my thesis I consider a new special case, which on one hand is as "asymmetrical" as possible, yet still analytically computable. However, as it turns out from some involved computation, the conjecture is also true in this case, and thus gives further evidence to this conjecture.
