如何使用任意测量设备实现几乎完美的测量
How to use arbitrary measuring devices to perform almost perfect measurements
AI总结：
本文提出利用任意不完美测量设备通过少量多次使用和经典克隆等协议实现目标量子测量的复现，证明渐近意义下所有非平凡量子测量等价，并给出有限次数最优协议及并行分组编码方案。
摘要：
我们考虑在具备执行另一种量子测量能力的条件下复现某一种量子测量的问题。我们为这一问题给出了一个一般性框架和具体协议。例如，我们展示了如何少量多次地使用可用的“不完美”设备来实现目标测量，其平均误差随所用不完美测量次数的增加呈指数下降。我们希望这能在近期应用中作为一种对测量设备的轻量级误差缓解手段发挥作用。除了面向实际应用的视角，我们还在最一般的设定下，即可用测量和目标测量均为任意广义量子测量的情形中，从一般理论角度考察了这一问题。我们证明，这一一般性问题实际上可以归结为复现（完备）冯·诺依曼测量统计量的能力，并且在可用测量被无限多次使用的渐近极限下，一个基于“经典克隆”的简单协议能够完美地完成这一任务。我们证明，在渐近意义下所有（非平凡的）量子测量都是等价的。我们还研究了在可用测量使用次数固定时的最优协议。这包括但不限于同时改善含噪声和有损耗的量子测量。此外，我们证明，在并行执行多次测量的设定下，通过使用经典信息论中的分组编码技术，我们可以实现有限速率的测量复现。最后，我们证明，利用概率性协议也可以获得优势。
英文摘要：
We consider the problem of reproducing one quantum measurement given the ability to perform another. We give a general framework and specific protocols for this problem. For example, we show how to use available "imperfect" devices a small number of times to implement a target measurement with average error that drops off exponentially with the number of imperfect measurements used. We hope that could be useful in near-term applications as a type of lightweight error mitigation of the measuring devices. As well as the view to practical applications, we consider the question from a general theoretical perspective in the most general setting where both the available and target measurements are arbitrary generalised quantum measurements. We show that this general problem in fact reduces to the ability to reproduce the statistics of (complete) von Neumann measurements, and that in the asymptotic limit of infinitely many uses of the available measurement, a simple protocol based upon `classical cloning' can perfectly achieve this task. We show that asymptotically all (non-trivial) quantum measurements are equivalent. We also study optimal protocols for a fixed number of uses of the available measurement. This includes, but is not limited to, improving both noisy and lossy quantum measurements. Furthermore, we show that, in a setting where we perform multiple measurements in parallel, we can achieve finite-rate measurement reproduction, by using block-coding techniques from classical information theory. Finally, we show that advantages can also be gained by making use of probabilistic protocols.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
