Detailed analysis of arbitrary measurement devices

测量设备通常被假设为是完美的并且使用投影算子来描述，然而更一般地，测量设备不是理想的并且由正算子值测量（POVM）来描述。在非理想情况下，测量结果从与理想情况下测量的状态的概率分布不一致的概率分布中采样。例如，当测量单个量子位时，存在非零概率，我们的测量设备可以在量子位实际上处于0状态时声明量子位处于1状态。在[1]中表明，给定任意测量设备，可以使用辅助量子比特和任意测量的多个副本来近似理想测量。我们可以通过将幺正门应用于我们想要测量的状态和辅助量子位，然后使用我们的任意测量设备测量所有量子位来做到这一点。协议将所有可能的结果分配给结果0或1。初始酉分配协议和结果分配协议都可以被优化以近似理想的测量设备。该建议围绕[1]的许多扩展，关于测量模拟的一般主题，将其转变为一个成熟的研究领域。这是建立在作为项目B的一部分开始的研究基础上的。

Measurement devices are often assumed to be perfect and are described using a projection operator, however more generally a measurement device is not ideal and is described by a positive operator valued measure (POVM). In the non-ideal case the measurement result is sampled from a probability distribution which is not consistent with the probability distribution of the state measured in the ideal case. For example, there is a non-zero probability when measuring a single qubit our measurement device may declare the qubit is in the 1 state when it is in fact in the 0 state. In [1] it was shown that given an arbitrary measurement device it is possible to approximate an ideal measurement using ancillary qubits and multiple copies of the arbitrary measurement. We can do this by applying a unitary gate to the state we want to measure and the ancillary qubits then measuring all of the qubits using our arbitrary measurement device. A protocol assigns all the possible outcomes to a result of either 0 or 1. Both the initial unitary and the outcome assignment protocol can be optimised to approximate an ideal measurement device. This proposal centres around numerous extensions of [1], on the general topic of measurement simulation, to turn this into a mature area of research. This builds upon the research started as part of Project B.