将量子比特正算符值测量分解为连续破坏性弱测量
Decomposing qubit positive-operator valued measurements into continuous destructive weak measurements
摘要：
已经证明，任何广义测量都可以分解为一个随机过程对应的弱测量序列。然而，弱测量可能需要几乎任意的幺正，这是不可能实现的任何真正的测量设备。此外，许多测量过程是破坏性的，如光子计数过程，一旦所有光子消耗完毕就终止。在这种破坏性的测量下，人们不能期望完全控制状态的演化，而可能的幺正也只允许有限的弱测量。在本文中，我们考虑了一个破坏性弱测量的量子比特模型，它是一个玩具版的光学腔，其中腔中的电磁场模式的状态泄漏出来，并被破坏性地测量，而真空状态|0>泄漏到腔中。在很长一段时间里，量子比特的状态不可避免地演变为|0>，唯一可用的控制是选择外部辅助系统上的测量。令人惊讶的是，这个非常有限的模型仍然可以在任何基础上对量子比特进行任意投影测量，其中得到结果的概率满足通常的玻恩规则。将该方法与概率后处理相结合，其结果可以推广到任何具有可交换POVM元素的广义测量。这意味着，在其他结果中，量子比特上的任何两个结果POVM都可以通过这种受限的测量设备分解为一系列破坏性的弱测量。
英文摘要：
It has been shown that any generalized measurement can be decomposed into a sequence of weak measurements corresponding to a stochastic process. However, the weak measurements may require almost arbitrary unitaries, which are unlikely to be realized by any real measurement device. Furthermore, many measurement processes are destructive, like photon counting procedures that terminate once all photons are consumed. One cannot expect to have full control of the evolution of a state under such destructive measurements, and the possible unitaries allow only a limited set of weak measurements. In this paper, we consider a qubit model of destructive weak measurements, which is a toy version of an optical cavity, in which the state of an electromagnetic field mode inside the cavity leaks out and is measured destructively while the vacuum state |0> leaks in to the cavity. At long times, the state of the qubit inevitably evolves to be |0>, and the only available control is the choice of measurement on the external ancilla system. Surprisingly, this very limited model can still perform an arbitrary projective measurement on the qubit in any basis, where the probability of getting an outcome satisfies the usual Born rule. Combining this method with probabilistic post processing, the result can be extended to any generalized measurement with commuting POVM elements. This implies, among other results, that any two-outcome POVM on a qubit can be decomposed into a sequence of destructive weak measurements by this restricted measurement device.
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