Given a unitary evolution $U$ on a multipartite quantum system and an ensemble of initial states, how well can $U$ be simulated by local operations and classical communication (LOCC) on that ensemble? We answer this question by establishing a general, efficiently computable upper bound on the maximal LOCC simulation fidelity—what we call an “LOCC inequality.” We then apply our findings to the fundamental setting where $U$ implements a quantum Newtonian Hamiltonian over a gravitationally interacting system. Violation of our LOCC inequality can rule out the LOCCness of the underlying evolution, thereby establishing the nonclassicality of the gravitational dynamics, which can no longer be explained by a local classical field. As a prominent application of this scheme we study systems of quantum harmonic oscillators initialized in coherent states following a normal distribution and interacting via Newtonian gravity, and discuss a possible physical implementation with torsion pendula. One of our main technical contributions is the analytical calculation of the above LOCC inequality for this family of systems. As opposed to existing tests based on the detection of gravitationally mediated entanglement, our proposal works with coherent states alone, and thus it does not require the generation of largely delocalized states of motion nor the detection of entanglement, which is never created at any point in the process.

中文翻译：

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在没有纠缠的情况下测试重力的量子性

给定单一演化$U$在多部分量子系统和初始态系综上，如何能够$U$通过该集合上的本地操作和经典通信（LOCC）进行模拟？我们通过建立一个通用的、可有效计算的最大 LOCC 模拟保真度上限（我们称之为“LOCC 不等式”）来回答这个问题。然后我们将我们的发现应用到基本环境中$U$在引力相互作用系统上实现量子牛顿哈密顿量。违反我们的 LOCC 不等式可以排除潜在演化的 LOCC 性，从而建立引力动力学的非经典性，它不再可以用局部经典场来解释。作为该方案的一个突出应用，我们研究了遵循正态分布并以相干态初始化并通过牛顿引力相互作用的量子谐振子系统，并讨论了扭转摆的可能物理实现。我们的主要技术贡献之一是对该系统系列的上述 LOCC 不等式进行分析计算。与基于检测引力介导的纠缠的现有测试相反，我们的建议仅适用于相干态，因此它不需要生成很大程度上离域的运动状态，也不需要检测纠缠，而纠缠在任何时候都不会创建。的过程。