Quantum correlations in the context of space-time physics

纠缠，或爱因斯坦称之为“幽灵般的远距离作用”，是量子力学的一个违反直觉的性质，说一个粒子可以与另一个遥远的粒子有比经典物理学所允许的更强的相关性。在过去的几年里，量子信息理论已经将纠缠从好奇心提升为具有深远理论影响和实际应用的重要资源。 这个研究计划的目标是重新审视量子相关性及其一些应用的研究，但结合一个强大而未被重视的事实：即携带相关性的物理系统必然嵌入在某些时空结构中。也就是说，相关性不仅仅是抽象的概率表，而且它们必须在测量设备可以旋转或移位，粒子可以离域的空间背景下工作。 这包括三个密切相关的主要目标和应用： 1.量子关联的表征 虽然量子理论允许比经典物理学更强的相关性，但它并不允许所有可能的相关性，即使我们强加“无信号”原则（没有超光速信息传输）。用简单的物理原理对量子关联进行分类是一个重要的开放性问题。在这里，我们将提出一个可能的解决方案，通过研究如何进一步方面的空间-时间（除了无信号）约束的容许相关性。 2.改进量子力学实验测试 最近有几个实验的建议，用更一般的可能的替代品来检验量子理论。这包括对可能更普遍的干涉图样的基本搜索，或量子非定域性的精确测试。几乎所有这类实验都涉及几何自由度，如极化或自旋。然而，我们相信这本身就已经迫使探测器的点击行为接近量子预测，强制产生负面结果。我们将分析在多大程度上是这种情况，并提出新的实验设置，避免这个问题。 3.量子引力：一种互补的操作方法 量子力学和广义相对论在“量子引力”理论中的统一可能是理论物理学中最重要的开放问题。我们的研究将揭示时空和量子理论结构之间的操作关系，为我们将与量子引力合作者一起利用的这个问题提供见解。特别是，我们将研究这样一个事实，即所有的测量设备，包括那些测量持续时间、距离或角度的设备，都必须由量子粒子构建。这意味着量子理论本身限制了我们对时空的了解或测量。

Entanglement, or "spooky action at a distance" as Einstein called it, is a counterintuitive property of quantum mechanics, saying that one particle can have stronger correlations with another distant particle than classical physics would allow. In the last few years, quantum information theory has lifted entanglement from a curiosity to an important resource with far-reaching theoretical consequences and practical applications. The goal of this research program is to revisit the study of quantum correlations and some of its applications, but in combination with a powerful and underappreciated fact: namely, that the physical systems which carry the correlations are necessarily embedded in some space-time structure. That is, correlations are not just abstract tables of probabilities, but they must work in a spatial context where measurement devices can be rotated or displaced, and particles can be delocalized. This comprises three closely related main objectives and applications: 1. Characterization of quantum correlations While quantum theory allows for stronger correlations than classical physics, it does not allow for all conceivable correlations, even if we impose the "no-signalling" principle (no superluminal information transfer). It is a major open problem to classify the set of quantum correlations in terms of simple physical principles. Here, we will propose a possible solution by studying how further aspects of space-time (in addition to no-signalling) constrain the admissible correlations. 2. Improving experimental tests of quantum mechanics There have been several recent proposals of experiments which test quantum theory against more general conceivable alternatives. This includes fundamental searches for possibly more general interference patterns, or precision tests of quantum non-locality. Almost all experiments of this kind involve geometric degrees of freedom, like polarization or spin. However, we believe that this in itself already enforces the detector clicks to behave close to the quantum predictions, enforcing a negative result. We will analyze to what extent this is the case, and propose novel experimental setups that avoid this problem.? 3. Quantum gravity: a complementary operational approach The unification of quantum mechanics and general relativity in some theory of „quantum gravity“ is perhaps the most important open problem of theoretical physics. Our research will shed light on the operational relation between space-time and the structure of quantum theory, contributing insights into this problem which we will exploit with collaborators in quantum gravity. In particular, we will examine the fact that all measurement devices, including those that measure time durations, distances, or angles, must be built from quantum particles. This implies that quantum theory itself constrains what we can know or measure about spacetime.