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Register a new userA New Loophole in Recent Bell Test Experiments
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Peter Bierhorst
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Recent experiments have reached detection efficiencies sufficient to close the detection loophole with photons. Both experiments ran multiple successive trials in fixed measurement configurations, rather than randomly re-setting the measurement configurations before each measurement trial. This opens a new potential loophole for a local hidden variable theory. The loophole invalidates one proposed method of statistical analysis of the experimental results, as demonstrated in this note. Therefore a different analysis will be necessary to definitively assert that these experiments are subject only to the locality loophole.
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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.
We discuss the problem of finding the most favorable conditions for closing the detection loophole in a test of local realism with a Bell inequality. For a generic non-maximally entangled two-qubit state and two alternative measurement bases we apply Hardys proof of non-locality without inequality and derive an Eberhard-like inequality. For an infinity of non-maximally entangled states we find that it is possible to refute local realism by requiring perfect detection efficiency for only one of the two measurements: the test is free from the detection loophole for any value of the detection efficiency corresponding to the other measurement. The maximum tolerable noise in a loophole-free test is also evaluated.
We propose a feasible optical setup allowing for a loophole-free Bell test with efficient homodyne detection. A non-gaussian entangled state is generated from a two-mode squeezed vacuum by subtracting a single photon from each mode, using beamsplitters and standard low-efficiency single-photon detectors. A Bell violation exceeding 1% is achievable with 6-dB squeezed light and an homodyne efficiency around 95%. A detailed feasibility analysis, based upon the recent generation of single-mode non-gaussian states, confirms that this method opens a promising avenue towards a complete experimental Bell test.
Bells theorem is based on three assumptions: realism, locality, and measurement independence. The third assumption is identified by Bell as linked to the freedom of choice hypothesis. He holds that ultimately the human free will can ensure the measurement independence assumption. The incomplete experimental conditions for supporting this third assumption are known in the literature as freedom-of-choice loophole (FOCL). In a recent publication, Abellan et al [2018] address this problem and follow this same strategy embraced by Bell [2004]. Nevertheless, the possibility of human freedom of choice has been a matter of philosophical debate for more than 2000 years, and there is no consensus among philosophers on this topic. If human choice is not free, Bells solution would not be sufficient to close FOCL. Therefore, in order to support the basic assumption of this experiment, it is necessary to argue that human choice is indeed free. In this paper, we present a Kantian position on this topic and defend the view that this philosophical position is the best way to ensure that BigBell Test (Abellan et al. [2018]) can in fact close the loophole.
So far, all experimental tests of Bell inequalities which must be satisfied by all local realistic hidden-variable theories and are violated by quantum mechanical predictions have left at least one loophole open. We propose a feasible setup allowing for a loophole-free test of the Bell inequalities. Two electron spin qubits of phosphorus donors in semiconductors in different cavities 300 m apart are entangled through a bright coherent light and postselections using homodyne measurements. The electron spins are then read out randomly and independently by Alice and Bob, respectively, with unity efficiency in less than 0.7$mu$s by using optically induced spin to charge transduction detected by radio-frequency single electron transistor. A violation of Bell inequality larger than 37% and 18% is achievable provided that the detection accuracy is 0.99 and 0.95, respectively.
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