It is generally assumed that sources randomly sending two particles to one or two different observers, random destination sources (RDSs), cannot be used for genuine quantum nonlocality tests because of the postselection loophole. We demonstrate that Bell experiments not affected by the postselection loophole may be performed with (i) an RDS and local postselection using perfect detectors, (ii) an RDS, local postselection, and fair sampling assumption with any detection efficiency, and (iii) an RDS and a threshold detection efficiency required to avoid the detection loophole. These results allow the adoption of RDS setups which are simpler and more efficient for long-distance free-space Bell tests, and extend the range of physical systems which can be used for loophole-free Bell tests.
It is generally assumed that sources randomly sending two particles to one or two different observers, random destination sources (RDSs), cannot be used for genuine quantum nonlocality tests because of the postselection loophole. We demonstrate that Bell experiments not affected by the postselection loophole may be performed with (i) an RDS and local postselection using perfect detectors, (ii) an RDS, local postselection, and fair sampling assumption with any detection efficiency, and (iii) an RDS and a threshold detection efficiency required to avoid the detection loophole. These results allow the adoption of RDS setups which are simpler and more efficient for long-distance free-space Bell tests, and extend the range of physical systems which can be used for loophole-free Bell tests.
We discuss Bell nonlocality in quantum networks with unreliable sources. Our main result is a condition on the observed data that ensures that inconclusive events can be safely discarded, without introducing any loophole. More formally, we characterize the fair-sampling property for measurements in a network. When all measurements are fair-sampling, we show that the postselection of conclusive outcomes does not compromise the assumption of source independence, hence avoiding the detection loophole. Furthermore, we show that in some cases, the fair-sampling property can in fact be certified directly from observed data. To show this, we prove that saturation of the Finner inequality provides a self-test of the underlying quantum model. We illustrate the relevance of our results by demonstrating an improvement in device-independent randomness generation for a photonic Bell test with a probabilistic source and for the triangle network.
Discarding undesirable measurement results in Bell experiments opens the detection loophole that prevents a conclusive demonstration of nonlocality. As closing the detection loophole represents a major technical challenge for many practical Bell experiments, it is customary to assume the so-called fair sampling assumption (FSA) that, in its original form, states that the collectively postselected statistics are a fair sample of the ideal statistics. Here, we analyze the FSA from the viewpoint of causal inference: We derive a causal structure that must be present in any causal model that faithfully encapsulates the FSA. This provides an easy, intuitive, and unifying approach that includes different accepted forms of the FSA and underlines what is really assumed when using the FSA. We then show that the FSA can not only be applied in scenarios with non-ideal detectors or transmission losses, but also in ideal experiments where only parts of the correlations are postselected, e.g., when the particles' destinations are in a superposition state. Finally, we demonstrate that the FSA is also applicable in multipartite scenarios that test for (genuine) multipartite nonlocality.
There are bipartite quantum nonlocal correlations requiring very low detection efficiency to reach the loophole-free regime but that need too many measurement settings to be practical for actual experiments. This leads to the general problem of what can be concluded about loophole-free Bell nonlocality if only a random subset of these settings is tested. Here we develop a method to address this problem. We show that, in some cases, it is possible to detect loophole-free Bell nonlocality by testing only a small random fraction of the settings. The consequence is a higher detection efficiency. The method allows for the design of loophole-free Bell tests in which, given a quantum correlation that violates a Bell inequality, one can calculate the minimum fraction of contexts needed to reach the detection-loophole-free regime. The results also enforce a different way of thinking about how local realistic models or classical communication can be used to simulate quantum nonlocal correlations, as it shows that the amount of resources that are needed can be made arbitrarily large simply by considering more contexts.
Summary form only given. In a Bell experiment, one prepares pairs of entangled particles and sends them to two observers, Alice and Bob, for measurement and detection [1]. For some choices of their measurement settings, Alice and Bob may observe strong correlations between their results in accordance with the predictions of quantum mechanical theory. Conversely, any physical theory that assumes no physical influence can be faster than the speed of light and that properties of physical systems are elements of reality [2] - a local realistic theory - can predict only a limited amount of correlation between Alice's and Bob's measurement outcomes. Upon observing correlations sufficient to violate Bell's inequality, Alice and Bob must abandon local realism.It is common that in an experiment, some particles emitted by the source will not be detected. Then the subset of detected particles might display correlations that violate the Bell inequality although the entire ensemble can be described by a local realistic theory [3]. To achieve a conclusive Bell violation without assuming that the detected particles are a “fair” sample, a highly efficient setup is necessary. Due to experimental limitations, fair sampling has been assumed in most Bell experiments performed to date, and it has never been possible to avoid this assumption with photons due to the absence of efficient sources and detectors. Here we report the first Bell experiment with photons that does not rely on any fair-sampling assumption. In our experiment we employ the Eberhard inequality, a Bell inequality that by construction does not rely on the fair-sampling assumption [4]. Our source of entangled photon pairs utilizes bulk-crystal spontaneous parametric downconversion in a Sagnac configuration, which has shown to be very efficient [5, 6]. For photon detection, we employ superconducting transition-edge sensors, which not only offer high efficiency but also are intrinsically free of dark counts [7]. This combination of features is imperative for an experiment in which no correction of count rates can be tolerated. We achieve uncorrected coupling efficiencies over 73% in each arm of our source, facilitating a violation of the inequality by nearly 70 standard deviations after five minutes of measurement. Since the first experimental Bell test, a satisfactory laboratory realization of the motivating gedankenexperiment has remained an outstanding challenge. The two other main assumptions include “locality” [8, 9] and “freedom of choice” [10]. Invoking any of these renders an experiment vulnerable to explanation by a local realistic theory. The realization of an experiment that is free of all three assumptions-a so-called loopholefree Bell test-remains an important outstanding goal for the physics community with strong implications for quantum technologies. We note that with our experiment, photons are the first physical system for which each of these three assumptions has been successfully addressed, albeit in different experiments. This represents promise for practical applications like one-sided device-independent quantum key distribution [11], and in an additional test, we also demonstrate that our experimental apparatus is capable of implementing this protocol on both sides.
We present a source of entangled photons that violates a Bell inequality free of the "fair-sampling" assumption, by over 7 standard deviations. This violation is the first reported experiment with photons to close the detection loophole, and we demonstrate enough "efficiency" overhead to eventually perform a fully loophole-free test of local realism. The entanglement quality is verified by maximally violating additional Bell tests, testing the upper limit of quantum correlations. Finally, we use the source to generate "device-independent" private quantum random numbers at rates over 4 orders of magnitude beyond previous experiments.
A common problem in Bell-type experiments is the well-known detection loophole: if the detection efficiencies are not perfect and if one simply postselects the conclusive events, one might observe a violation of a Bell inequality, even though a local model could have explained the experimental results. In this paper, we analyze the set of all postselected correlations that can be explained by a local model, and show that it forms a polytope, larger than the Bell local polytope. We characterize the facets of this postselected local polytope in the Clauser-Horne-Shimony-Holt scenario, where two parties have binary inputs and outcomes. Our approach gives interesting insights on the detection loophole problem.