论文标题
从量子数据中构造量子POVM
Constructing a qubit POVM from quantum data
论文作者
论文摘要
给定一个Qubits的合奏，我们被告知由两个纯状态组成，一个均具有$η_{0} $的混合物，一个带有概率$η_{1} $的混合物，我们希望找到一个可以通过测量量子来区分两个状态的POVM。我们不知道状态，对于任何给定的量子，我们都不知道它所在的两个状态中的哪一个。这可以看作是从量子数据中学习POVM。一旦找到，POVM可用于将合奏中的其余量子位分为两组，与集合中存在的两个状态相对应。为了找到POVM，我们需要有关可能状态的更多信息。我们检查了几种情况。首先，我们假设我们知道状态的Bloch向量位于X-Z平面，其\ Emph {先验}概率相等。接下来，我们将限制限制到X-Z平面，但允许\ emph {先验}概率不同。最后，我们考虑了状态的Bloch向量具有相同Z分量的情况。
Given an ensemble of qubits, which we are told consists of a mixture of two pure states, one with probability $η_{0}$ and one with probability $η_{1}$, we want to find a POVM that will discriminate between the two states by measuring the qubits. We do not know the states, and for any given qubit, we do not know which of the two states it is in. This can be viewed as learning a POVM from quantum data. Once found, the POVM can be used to separate the remaining qubits in the ensemble into two groups, corresponding to the two states present in the ensemble. In order to find the POVM, we need more information about the possible states. We examine several cases. First, we suppose that we know that the Bloch vectors of the states lie in the x-z plane and their \emph{a priori} probabilities are equal. We next keep the restriction to the x-z plane, but allow the \emph{a priori} probabilities to be different. Finally, we consider the case in which the Bloch vectors of the states have the same z component.
