[论文解读] Quantum state reconstruction made easy: a direct method for tomography

R. P. Rundle, Todd Tilma+2 more|arXiv (Cornell University)|May 28, 2016

Quantum Information and Cryptography被引用 9

一句话总结

本文提出了一种直接的量子态层析方法，通过实验测量和重建量子自旋态的Wigner函数，适用于任何量子系统。该方法成功地在IBM的Quantum Experience上直接检测并区分了两个Bell态以及五量子比特的GHZ态，证明了其在量子信息系统的可行性。

ABSTRACT

In quantum mechanics, the state of the system, or set of systems, is encoded as a vector in a state space. While this sounds simple, it has several implications that are not limited to the more well known and spooky consequences of quantum physics, such as entanglement. One of these is that we can never directly observe the state of the system itself; we are only able to measure its observable properties, such as position and momentum, that are affected by the system's state. By making many measurements of this set of observables of the state, we can generate marginal distributions of each. From these distributions, we can reconstruct the original state vector from its associated phase-space Wigner function. It has been shown that such a measurement of the Wigner function is possible for light. Here we give a procedure for the direct measurement and reconstruction of the Wigner function for a series of quantum spin states that should be applicable to any quantum system. We have applied our procedure to IBM's Quantum Experience five qubit quantum processor to demonstrate that we can directly measure and distinguish two different Bell states - states central to understanding entanglement - via this method. We have also performed direct measurements of the five qubit Greenberger-Horne-Zeilinger (GHZ) state Wigner function.

研究动机与目标

• 开发一种基于Wigner函数的直接、实验上可行的量子态重建方法。
• 实现实验测量和重建量子自旋态，而无需完整态层析或复杂的逆运算过程。
• 在真实量子处理器上展示该方法在纠缠态（如Bell态和GHZ态）中的适用性。
• 在真实世界量子计算平台（特别是IBM的五量子比特量子处理器）上验证该方法。

提出的方法

• 通过重复测量获得可观测量（如位置和动量）的边缘分布，直接测量量子态的Wigner函数。
• 利用相空间重建技术，从测量得到的Wigner函数重建原始量子态矢量。
• 该方法可推广至任意量子系统，包括自旋系统和量子比特寄存器。
• 该方法利用了Wigner函数可通过可观测量（如位置和动量）的边缘分布获得的特性。
• 该方法在IBM的Quantum Experience上实现，利用其五量子比特处理器制备并测量Bell态和GHZ态。

实验结果

研究问题

• RQ1 是否可在实际量子系统中直接测量并重建量子自旋态的Wigner函数？
• RQ2 所提出的方法是否能够通过直接测量Wigner函数来区分纠缠的Bell态？
• RQ3 该方法是否可应用于多量子比特纠缠态（如五量子比特GHZ态）？
• RQ4 直接测量方法是否可避免对完整态层析或复杂态逆运算的需求？

主要发现

• 该方法成功地在IBM的五量子比特量子处理器上直接测量并重建了两个不同Bell态的Wigner函数。
• 该方法基于其独特的Wigner函数特征，清晰地区分了两个Bell态。
• 五量子比特Greenberger-Horne-Zeilinger（GHZ）态被直接测量，其Wigner函数成功重建，证实了该方法在多量子比特系统中的可扩展性。
• 结果表明，Wigner函数测量为量子态层析提供了一条切实可行的直接路径，而无需完整态重建。