Quantum Correlations: Experiments

Armin Tavakoli

Abstract Bell experiments measure correlations between outcomes of a number of observers measuring on a shared physical state emitted from a single source. Quantum correlations arising in such Bell experiments have been intensively studied over the last decades. Much less is known about the nature of quantum correlations arising in network structures beyond Bell experiments. Such networks can involve many independent sources emitting states to observers in accordance with the network configuration. Here, we will study classical and quantum correlations in a family of networks which can be regarded as compositions of several independent multipartite Bell experiments connected together through a central node. For such networks we present tight Bell-type inequalities which are satisfied by all classical correlations. We study properties of the violations of our inequalities by probability distributions arising in quantum theory.

Miguel Orszag

Farid Shähandeh

Edwin Peter Lobo, Jef Pauwels, Stefano Pironio

Losses in the transmission channel, which increase with distance, pose a major obstacle to photonics demonstrations of quantum nonlocality and its applications. Recently, Chaturvedi, Viola, and Pawlowski (CVP) [arXiv:2211.14231] introduced a variation of standard Bell experiments with the goal of extending the range over which quantum nonlocality can be demonstrated. These experiments, which we call `routed Bell experiments', involve two distant parties, Alice and Bob, and allow Bob to route his quantum particle along two possible paths and measure it at two distinct locations – one near and another far from the source. The premise is that a high-quality Bell violation in the short-path should constrain the possible strategies underlying the experiment, thereby weakening the conditions required to detect nonlocal correlations in the long-path. Building on this idea, CVP showed that there are certain quantum correlations in routed Bell experiments such that the outcomes of the remote measurement device cannot be classically predetermined, even when its detection efficiency is arbitrarily low. In this paper, we show that the correlations considered by CVP, though they cannot be classically predetermined, do not require the transmission of quantum systems to the remote measurement device. This leads us to define and formalize the concept of `short-range' and `long-range' quantum correlations in routed Bell experiments. We show that these correlations can be characterized through standard semidefinite-programming hierarchies for non-commutative polynomial optimization. We then explore the conditions under which short-range quantum correlations can be ruled out and long-range quantum nonlocality can be certified in routed Bell experiments. We point out that there exist fundamental lower-bounds on the critical detection efficiency of the distant measurement device, implying that routed Bell experiments cannot demonstrate long-range quantum nonlocality at arbitrarily large distances. However, we do find that routed Bell experiments allow for reducing the detection efficiency threshold necessary to certify long-range quantum correlations. The improvements, though, are significantly smaller than those suggested by CVP's analysis.

Miguel Orszag

Armin Tavakoli, Roope Uola, Jef Pauwels

High-dimensional systems are an important frontier for photonic quantum correlation experiments. These correlation tests commonly prescribe measurements with many possible outcomes but they are often implemented through many individual binary-outcome measurements that use only a single-detector. Here, we discuss how this binarization procedure for multioutcome measurements can open a loophole, unless specific device-characterization assumptions are satisfied. We highlight that correlation tests designed for multioutcome measurements can be trivialized in binarized implementations and we then show how to accurately analyze binarized data to reveal their quantum features. For seminal types of correlation experiments, such as Bell inequality tests, steering tests and prepare-and-measure experiments, we find that binarization may incur a sizable cost in the magnitude of quantum advantages. This emphasizes the importance of both accurate data analysis and implementing genuinely multioutcome measurements in high-dimensional correlation experiments.