The problem of closing the detection loophole in Bell tests is studied in the presence of a limited number of efficient detectors using multipartite quantum states. It is found that most of the studied pure multipartite states can violate a family of multipartite Bell inequalities with only two efficient detectors, whereas the remaining detectors may have arbitrary small efficiencies.
The problem of closing the detection loophole in Bell tests is studied in the presence of a limited number of efficient detectors using multipartite quantum states. It is found that most of the studied pure multipartite states can violate a family of multipartite Bell inequalities with only two efficient detectors, whereas the remaining detectors may have arbitrary small efficiencies.
We investigate the problem of closing the detection loophole in multipartite Bell tests, and show that the required detection efficiencies can be significantly lowered compared to the bipartite case. In particular, we present Bell tests based on n-qubit Greenberger-Horne-Zeilinger states, which can tolerate efficiencies as low as 38 for a reasonable number of parties and measurements. Even in the presence of a significant amount of noise, efficiencies below 50 can be tolerated, which is encouraging given recent experimental progress. Finally, we give strong evidence that, for a sufficiently large number of parties and measurements, arbitrarily small efficiencies can be tolerated, even in the presence of an arbitrary large amount of noise.
We study the problem of closing the detection loophole in three-qubit Bell tests, the experimentally most relevant case beyond the usual bipartite scenario, and show that the minimal detection efficiencies required can be considerably lowered compared to the two-qubit case. The lowest reported detection efficiency thresholds for two and three qubits so far are $\ensuremath{\sim}66.7$ and 60, respectively. Using the three-qubit W state and a three-setting Bell inequality, we beat these thresholds and with an eight-setting Bell inequality we reach 50.13. We also investigate generic three-qubit states which allow us to attain a detection efficiency of 50 in a four-setting Bell test. We conjecture that the limit of 50 is unbeatable using three-qubit states and any number of measurements.
Let us imagine an experimentalist, who has maximally entangled photons and wants to violate Bell’s inequality in his laboratory. Among many obstacles he has to overcome, two of them are the most significant. Firstly, he has to avoid exchanging information about the measurement settings between the particles. Secondly, he has to detect particles with a high enough probability, because if the detection efficiency is too low, one can reproduce quantum correlations using a LHV (Local Hidden Variables) model. These two problems are known in the literature, respectively, as the locality loophole [1] and the detection loophole [2, 3]. Fortunately, it is possible to close the locality loophole using photons in the experiment [4, 5, 6, 7, 8]. However, closing the detection loophole is still an object of study. The authors of [9] showed that for the CHSH inequality, the lower bound for detector efficiency needed to close the loophole is 82.8% for maximally entangled states. This bound was lowered to 66.7% by Eberhard [10]. Furthermore, the detector efficiency has been studied for other Bell inequalities [11, 12, 13, 14, 15, 16]. In our research, we are trying to answer the following question: If we prepare a Bell experiment and we have two detectors, having different efficiencies both smaller than 100%, which detector should each party receive? And also: Which representation of the chosen Bell inequality should we consider? These are very crucial questions, which arise in laboratories. Hence, we hope that our results will be useful for experimentalists. We focus on the I3322 inequality [17], which is a natural candidate for testing, because of its asymmetry [14, 18]. We consider the case of a post-selection strategy, which consists in rejecting all the rounds in the Bell experiment when one of the detectors does not click. We used numerical optimisation methods to find both the best classical strategy for Alice and Bob and the best detector clicking strategy. Thus, we have found minimal efficiencies of the detectors of Alice and Bob needed to violate I3322. We made the same studies also for symmetric representations of I3322 [19]. Our results show that the minimal efficiencies of Alice and Bob’s detectors of the asymmetric representation of I3322 is lower than in case of the symmetric one [20]. It is work in progress, and we are examining other post-selection methods as well as other Bell inequalities. We want to consider also the case when non-maximally entangled states are used in Bell experiments.
In many quantum information applications, a minimum detection efficiency must be exceeded to ensure success. Protocols depending on the violation of a Bell inequality, for instance, may be subject to the so-called detection loophole: Imperfect detectors may yield spurious violations, which consequently cannot be used to ensure, say, quantum cryptographic security. Hence, we investigate the possibility of giving lower bounds on detector efficiency even if an adversary has full control over both the source and the detectors. To this end, we present a technique to systematically derive Bell inequalities free from the detection loophole using only the observed measurements statistics. The violation of these inequalities certifies that the detectors used exceed a certain minimal efficiency.
We show that the detection efficiencies required for closing the detection loophole in Bell tests can be significantly lowered using quantum systems of dimension larger than two. We introduce a series of asymmetric Bell tests for which an efficiency arbitrarily close to 1/N can be tolerated using N-dimensional systems, and a symmetric Bell test for which the efficiency can be lowered down to 61.8% using four-dimensional systems. Experimental perspectives for our schemes look promising considering recent progress in atom-photon entanglement and in photon hyperentanglement.