Quantum correlations in the context of space-time physics

量子纠缠，或爱因斯坦所说的“幽灵般的超距作用”，是量子力学的一种违反直觉的特性，即一个粒子与另一个遥远粒子的相关性可能比经典物理学所允许的更强。在过去的几年里，量子信息理论已经将纠缠从一个好奇的事物提升到一个具有深远理论影响和实际应用的重要资源。

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.