Abstract

The non-local nature of the correlations possessed by quantum systems may be revealed by experimental demonstrations of the violation of Bell-type inequalities. Recent work has placed bounds on the correlations that quantum systems can possess in an actual experiment. These bounds were limited to a composite quantum system comprising of a few lower-dimensional subsystems. In a more general approach, it has been shown that fewer body correlations can reveal the non-local nature of the correlations arising from a quantum mechanical description of nature. Such tests on the correlations can be transformed to a semi-definite program (SDP). This study reports the experimental implementation of a local measurement-based hierarchy on the nuclear magnetic resonance (NMR) hardware utilizing three nuclear spins as qubits. The protocol has been experimentally tested on tripartite pseudo-entangled states such as W state, GHZ state and a few graph states. In all the cases, the experimentally measured correlations were used to formulate the SDP, using linear constraints on the entries of the moment matrix. We observed that for each entangled state, the SDP failed to find a semi-definite positive moment matrix consistent with the experimental data. This implies that the observed correlations can not arise from local measurements on a separable state and are hence non-local in nature, and also confirms that the states being tested are indeed entangled.

Graphical abstract

中文翻译：

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在NMR量子处理器上使用基于局部测量的层次结构进行非局部相关性的实验检测

摘要

量子系统所具有的相关性的非局部性质可以通过违反贝尔型不等式的实验证明来揭示。最近的工作已经限制了量子系统在实际实验中可以拥有的相关性。这些界限仅限于由几个低维子系统组成的复合量子系统。在更一般的方法中，已经表明，较少的身体相关性可以揭示由于对自然的量子力学描述而引起的相关性的非局部性质。可以将这种对相关性的测试转换为半定程序（SDP）。这项研究报告了利用三个核自旋作为量子位在核磁共振（NMR）硬件上基于局部测量的层次结构的实验实现。该协议已在三重伪纠缠状态（例如W状态，GHZ状态和一些图状态）上进行了实验测试。在所有情况下，通过对矩矩矩阵的条目进行线性约束，使用实验测量的相关性来制定SDP。我们观察到，对于每个纠缠态，SDP都无法找到与实验数据一致的半确定正矩矩阵。这意味着观察到的相关性不能从对可分离状态的局部测量中得出，因此本质上是非局部的，并且还确认了被测试的状态确实是纠缠的。在力矩矩阵的项上使用线性约束。我们观察到，对于每个纠缠态，SDP都无法找到与实验数据一致的半确定正矩矩阵。这意味着观察到的相关性不能从可分离状态的局部测量中得出，因此本质上是非局部的，并且还确认了被测试的状态确实是纠缠的。在力矩矩阵的项上使用线性约束。我们观察到，对于每个纠缠态，SDP都无法找到与实验数据一致的半确定正矩矩阵。这意味着观察到的相关性不能从可分离状态的局部测量中得出，因此本质上是非局部的，并且还确认了被测试的状态确实是纠缠的。

图形概要