论文标题
超越密度运算符和TR（ρa）：利用随机纯状态的高阶统计来进行量子信息处理
Beyond the density operator and Tr(ρA): Exploiting the higher-order statistics of random-coefficient pure states for quantum information processing
论文作者
论文摘要
两种类型的状态被广泛用于量子力学中，即（确定性）纯状态和统计混合物。密度运算符可以与每个密度相关联。我们在这里谈到了以前在更受限制的框架中引入的第三种状态。这些状态通过通过随机变量替换其确定性的KET系数来概括纯度。因此，我们称它们为随机纯状态或RCP。我们分析了它们的特性及其与两种常规状态的关系。我们表明，RCP所包含的信息比密度运算符和与它们相关联的可观察物的均值要丰富。之所以发生这种情况，是因为后一种操作员仅利用随机状态系数的二阶统计数据，而其高阶统计数据包含其他信息。通过使用二阶和高阶统计，可以通过我们为RCP提出的多重准备程序访问该信息，以测量结果的随机概率。利用这些高阶统计信息为执行高级量子信息处理任务的非常通用的方法开辟了道路。我们说明了这种方法与一个通用示例的相关性，即处理量子过程参数的估计，从而与量子过程断层扫描有关。此参数估计是在非盲（监督）或盲（即无监督的）模式下执行的。我们表明，仅通过仅使用与所考虑的物理量相对应的操作员A的RCPS和相关的平均值TR（ρA）来解决此问题。除了二阶统计外，我们还通过利用状态系数的四阶统计参数来成功解决此问题。数值测试验证了此结果。
Two types of states are widely used in quantum mechanics, namely (deterministic-coefficient) pure states and statistical mixtures. A density operator can be associated with each of them. We here address a third type of states, that we previously introduced in a more restricted framework. These states generalize pure ones by replacing each of their deterministic ket coefficients by a random variable. We therefore call them Random-Coefficient Pure States, or RCPS. We analyze their properties and their relationships with both types of usual states. We show that RCPS contain much richer information than the density operator and mean of observables that we associate with them. This occurs because the latter operator only exploits the second-order statistics of the random state coefficients, whereas their higher-order statistics contain additional information. That information can be accessed in practice with the multiple-preparation procedure that we propose for RCPS, by using second-order and higher-order statistics of associated random probabilities of measurement outcomes. Exploiting these higher-order statistics opens the way to a very general approach for performing advanced quantum information processing tasks. We illustrate the relevance of this approach with a generic example, dealing with the estimation of parameters of a quantum process and thus related to quantum process tomography. This parameter estimation is performed in the non-blind (i.e. supervised) or blind (i.e. unsupervised) mode. We show that this problem cannot be solved by using only the density operator ρof an RCPS and the associated mean value Tr(ρA) of the operator A that corresponds to the considered physical quantity. We succeed in solving this problem by exploiting a fourth-order statistical parameter of state coefficients, in addition to second-order statistics. Numerical tests validate this result.
