Operational Resource Theory of Imaginarity
Operational Resource Theory of Imaginarity
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想象的作战资源理论
DOI：
10.1103/physrevlett.126.090401
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发表时间：
2021
影响因子：
8.6
通讯作者：
er
中科院分区：
文献类型：
--
作者：
Wu Kang-Da;Kondra Tulja Varun;Rana Swapan;Sc;olo Carlo Maria;Xiang Guo-Yong;Li Chuan-Feng;Guo Guang-Can;Streltsov Alex;er
波粒二象性是量子力学的基本特征之一，导致使用复数来描述量子系统的状态及其动力学和相互作用。自量子理论诞生以来，人们一直在争论复数是否必要，或者仅使用实数是否可以使用替代的一致公式。在这里，我们利用量子资源理论的强大工具，从理论上和实验上解决了这个长期存在的问题。我们证明，在合理的假设下，如果量子态只有实数元素，则更容易创建和操纵。这赋予了想象力的资源理论以可操作的意义。我们确定并回答了几个重要问题，其中包括所有量子位态和任何维度的所有纯态的状态转换问题以及所有量子态的近似虚数蒸馏。作为一种应用，我们证明了虚数在状态辨别中起着至关重要的作用，也就是说，存在可以通过局部操作和经典通信完美区分的真实量子态，但如果其中一方无法获得虚数，则无法以任何非零概率区分。我们通过线性光学实验证实了这种现象，通过局部投影测量来区分不同的双光子量子态。我们的结果证明复数是量子力学不可或缺的一部分。
Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems and their dynamics and interaction. Since the inception of quantum theory, it has been debated whether complex numbers are essential or whether an alternative consistent formulation is possible using real numbers only. Here, we attack this long-standing problem theoretically and experimentally, using the powerful tools of quantum resource theories. We show that, under reasonable assumptions, quantum states are easier to create and manipulate if they only have real elements. This gives an operational meaning to the resource theory of imaginarity. We identify and answer several important questions, which include the state-conversion problem for all qubit states and all pure states of any dimension and the approximate imaginarity distillation for all quantum states. As an application, we show that imaginarity plays a crucial role in state discrimination, that is, there exist real quantum states that can be perfectly distinguished via local operations and classical communication but that cannot be distinguished with any nonzero probability if one of the parties has no access to imaginarity. We confirm this phenomenon experimentally with linear optics, discriminating different two-photon quantum states by local projective measurements. Our results prove that complex numbers are an indispensable part of quantum mechanics.