Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK.
Fondazione ISI, Via Chisola 5, Torino, 10126, Italy.
Nat Commun. 2019 Jan 14;10(1):182. doi: 10.1038/s41467-018-08100-1.
Closed timelike curves are striking predictions of general relativity allowing for time-travel. They are afflicted by notorious causality issues (e.g. grandfather's paradox). Quantum models where a qubit travels back in time solve these problems, at the cost of violating quantum theory's linearity-leading e.g. to universal quantum cloning. Interestingly, linearity is violated even by open timelike curves (OTCs), where the qubit does not interact with its past copy, but is initially entangled with another qubit. Non-linear dynamics is needed to avoid violating entanglement monogamy. Here we propose an alternative approach to OTCs, allowing for monogamy violations. Specifically, we describe the qubit in the OTC via a pseudo-density operator-a unified descriptor of both temporal and spatial correlations. We also simulate the monogamy violation with polarization-entangled photons, providing a pseudo-density operator quantum tomography. Remarkably, our proposal applies to any space-time correlations violating entanglement monogamy, such as those arising in black holes.
封闭类时曲线是广义相对论的惊人预测，允许时间旅行。它们受到著名的因果问题（例如祖父悖论）的困扰。量子模型中，一个量子位元回溯时间可以解决这些问题，但代价是违反量子理论的线性性——例如导致普遍的量子克隆。有趣的是，即使是开放类时曲线（OTCs）也违反了线性性，在 OTCs 中，量子位元不会与其过去的副本相互作用，而是与另一个量子位元初始纠缠。需要非线性动力学来避免违反纠缠单一性。在这里，我们提出了一种替代 OTC 的方法，允许违反单一性。具体来说，我们通过伪密度算子来描述 OTC 中的量子位元——这是时间和空间相关性的统一描述符。我们还使用偏振纠缠光子模拟了单一性违反，提供了伪密度算子量子层析成像。值得注意的是，我们的提议适用于任何违反纠缠单一性的时空相关性，例如黑洞中出现的那些相关性。
