[论文解读] Violating Bell's inequality with an artificial atom and a cat state in a cavity

Brian Vlastakis, Andrei Petrenko+12 more|arXiv (Cornell University)|Apr 9, 2015

Quantum Information and Cryptography参考文献 31被引用 3

一句话总结

该论文首次在超导腔中利用与宏观猫态纠缠的人工原子实现了贝尔不等式的首个实验违反，借助电路量子电动力学、高保真度测量和实时反馈，实现了无需后选择的贝尔检验。实验揭示了混合量子比特-连续变量系统中的量子非定域性，并通过调节猫态振幅量化退相干效应，证实了在退相干抑制非经典关联之前，纠缠具有鲁棒性，直至临界尺寸。

ABSTRACT

The `Schrödinger's cat' thought experiment highlights the counterintuitive facet of quantum theory that entanglement can exist between microscopic and macroscopic systems, producing a superposition of distinguishable states like the fictitious cat that is both alive and dead. The hallmark of entanglement is the detection of strong correlations between systems, for example by the violation of Bell's inequality. Using the CHSH variant of the Bell test, this violation has been observed with photons, atoms, solid state spins, and artificial atoms in superconducting circuits. For larger, more distinguishable states, the conflict between quantum predictions and our classical expectations is typically resolved due to the rapid onset of decoherence. To investigate this reconciliation, one can employ a superposition of coherent states in an oscillator, known as a cat state. In contrast to discrete systems, one can continuously vary the size of the prepared cat state and therefore its dependence on decoherence. Here we demonstrate and quantify entanglement between an artificial atom and a cat state in a cavity, which we call a `Bell-cat' state. We use a circuit QED architecture, high-fidelity measurements, and real-time feedback control to violate Bell's inequality without post-selection or corrections for measurement inefficiencies. Furthermore, we investigate the influence of decoherence by continuously varying the size of created Bell-cat states and characterize the entangled system by joint Wigner tomography. These techniques provide a toolset for quantum information processing with entangled qubits and resonators. While recent results have demonstrated a high level of control of such systems, this experiment demonstrates that information can be extracted efficiently and with high fidelity, a crucial requirement for quantum computing with resonators.

研究动机与目标

• 在空腔中实现一个微观人工原子与宏观猫态的混合系统中的量子非定域性。
• 通过采用实时反馈和高保真度探测，克服贝尔检验中后选择和测量效率不足的限制。
• 通过连续调节猫态振幅，研究退相干在宏观叠加态中的作用。
• 开发并验证一种联合Wigner表示，用于在简化测量基下表征量子比特-腔体纠缠。

提出的方法

• 利用超导电路量子电动力学架构，通过transmon量子比特与超导空腔耦合，生成并测量纠缠。
• 采用顺序量子非破坏性（QND）测量：首先测量量子比特态，随后通过位移光子数奇偶性测量腔态。
• 应用实时反馈和预旋转，测量沿X、Y和Z轴的量子比特可观测量，以实现CHSH贝尔检验设置。
• 利用逻辑量子比特编码在相干态|β⟩和|−β⟩中的十六个相关性，构建联合Wigner表示。
• 在逻辑基下使用直接保真度估计和CHSH贝尔检验判据来量化纠缠，无需完整态层析。
• 通过调节猫态振幅|β|，系统性地探测由于退相干导致的从量子行为到经典行为的转变。

实验结果

研究问题

• RQ1 是否可以在无需后选择或对测量效率不足进行校正的情况下，利用与空腔中宏观猫态纠缠的人工原子实现贝尔不等式的违反？
• RQ2 贝尔违反的程度如何依赖于猫态的大小？退相干在抑制非局域关联中起什么作用？
• RQ3 联合Wigner表示在仅使用最少测量数的情况下，能在多大程度上准确表征纠缠的量子比特-腔体态？
• RQ4 高保真度、实时测量和反馈控制是否能够实现对混合量子系统中非经典关联的稳健检测？
• RQ5 在退相干占主导地位之前，量子非定域性仍可探测的最大猫态振幅是多少？

主要发现

• 实验实现了超过三个标准差的贝尔不等式违反，证实了在具有宏观叠加的系统中存在量子非定域性。
• CHSH值达到2.52 ± 0.06，显著超过经典界限2，表明存在强烈的量子关联。
• 观察到猫态振幅存在一个清晰的临界阈值，超过该阈值后贝尔违反因退相干而下降，且随着|β|增大而被抑制。
• 联合Wigner表示仅使用十六个相关性即成功重构了纠缠态，验证了其在纠缠表征中的高效性。
• 观测到测量反作用将腔体投影到不同叠加态，包括在X和Y基测量后出现的相移猫态。
• 在所有探测器设置下进行系统性误差检查，未发现显著偏差，进一步强化了贝尔检验结果的稳健性。