给定量子仪器保守的最少信息量观测量的构造
Construction of the least informative observable conserved by a given quantum instrument
摘要：
对于由量子仪器$\mathcal{I}$和对应于正算符值测度（POVM）的系统观测量描述的量子测量过程，如果对$\mathcal{I}$和$E$的联合连续测量等价于对$E .$的单次测量，则称$\mathcal{I}$ $\mathcal{I}$守恒于$E$的信息。我们证明了对于任何量子仪器$\mathcal{I}$，我们都可以构造出由$\mathcal{I}$守恒的POVM。直观地，该构造给出了$\mathcal{I}.$的无限联合连续测量。我们还表明，所构造的POVM是$\mathcal{I}$所守恒的POVM中信息量最少的可观测POVM，即所构造的POVM可以通过对$\mathcal{I} .$所守恒的任何POVM的经典后处理来实现。我们明确评估光子计数和量子计数器仪器的无限连续测量的POVM。
英文摘要：
For a quantum measurement process described by a quantum instrument $\mathcal{I}$ and a system observable corresponding to a positive-operator valued measure (POVM) $E ,$ $\mathcal{I}$ is said to conserve the information of $E$ if the joint successive measurement of $\mathcal{I}$ followed by $E$ is equivalent to a single measurement of $E .$ We show that for any quantum instrument $\mathcal{I}$ we can construct a POVM conserved by $\mathcal{I}$. Intuitively the construction gives the infinite joint successive measurement of $\mathcal{I}.$ We also show that the constructed POVM is the least informative observable among POVMs conserved by $\mathcal{I}$, i.e. the constructed POVM can be realized by a classical post-processing of any POVM conserved by $\mathcal{I} .$ As typical examples of quantum instruments, we explicitly evaluate POVMs of infinite successive measurements for photon counting and quantum counter instruments.
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