Qudits for witnessing quantum-gravity-induced entanglement of masses under decoherence
Qudits for witnessing quantum-gravity-induced entanglement of masses under decoherence
复制标题
用于见证退相干下量子引力引起的质量纠缠的 Qudits
作者：
J. Tilly;Ryan J. Marshman;A. Mazumdar;S. Bose
最近，一个理论和实验协议被称为量子引力诱导的质量纠缠（QGEM）已经提出了使用两个介观质量，每个放置在两个位置的叠加来测试引力的量子性质。如果在消除它们之间的所有非引力相互作用后，粒子变得纠缠，我们可以得出结论，引力势是通过量子介体（即虚引力子）诱导的。在本文中，我们研究了一系列不同的实验装置，考虑到不同的几何形状和空间叠加态的数量，以确定哪一种会更快地产生纠缠。我们的结论是，在没有退相干的情况下，并且给定叠加的任何两个空间状态之间的最大距离λ x，一组相互平行的空间叠加的两个量子比特将优于给定现实实验参数的所有其他模型。此外，当引入足够高的退相干率时，多分量叠加可以胜过两量子比特设置。通过实验模拟进一步验证了这一点，表明在99.9%的置信水平下，在没有退相干的情况下，需要O（10）测量来拒绝无纠缠假设。当引入退相干时，测量的数量增加。当退相干率达到0.125 Hz时，两量子比特系统的纠缠不再存在，需要6维量子比特。但是，在这种情况下，需要O（10）测量。可以将见证操作员分组进行测量，以减少测量次数（最多十倍）。然而，这在实验上实现可能具有挑战性。
Recently a theoretical and an experimental protocol known as quantum gravity induced entanglement of masses (QGEM) has been proposed to test the quantum nature of gravity using two mesoscopic masses each placed in a superposition of two locations. If, after eliminating all nongravitational interactions between them, the particles become entangled, one can conclude that the gravitational potential is induced via a quantum mediator, i.e. a virtual graviton. In this paper, we examine a range of different experimental set-ups, considering different geometries and the number of spatially superposed states taken, in order to determine which would generate entanglement faster. We conclude that without decoherence, and given a maximum distance ∆x between any two spatial states of a superposition, a set of two qubits placed in spatial superposition parallel to one another will outperform all other models given realistic experimental parameters. Furthermore, when a sufficiently high decoherence rate is introduced, multi-component superpositions can outperform the two-qubit set-up. This is further verified with an experimental simulation, showing that O(10) measurements are required to reject the no entanglement hypothesis with a parallel qubits set-up without decoherence at a 99.9% confidence level. The number of measurements increases when decoherence is introduced. When the decoherence rate reaches 0.125 Hz, 6-dimensional qudits are required as the two-qubit system entanglement cannot be witnessed anymore. However, in this case, O(10) measurements will be required. One can group the witness operators to measure in order to reduce the number of measurements (up to ten-fold). However, this may be challenging to implement experimentally.
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