Abstract
Loophole-free violations of Bell inequalities are crucial for fundamental tests of quantum nonlocality. They are also important for future applications in quantum information processing, such as device-independent quantum key distribution. Based on a detector model which includes detector inefficiencies and dark counts, we estimate the minimal requirements on detectors needed for performing loophole-free bipartite and tripartite Bell tests. Our numerical investigation is based on a hierarchy of semidefinite programs for characterizing possible quantum correlations. We find that for bipartite setups with two measurement choices and our detector model, the optimal inequality for a Bell test is equivalent to the Clauser–Horne inequality.
Highlights
Bell inequalities characterizing all possible classical correlations of local realistic theories and their violations by quantum theory have been an active field of research since Bell’s original paper published in 1964 [1]
If all possible quantum correlations can be obtained by using low-dimensional quantum systems, e.g., qubits distributed among some parties, a correspondingly low order semidefinite programs (SDP) is sufficient to obtain the possible quantum correlations, as proven in [13]
We found that a hierarchy of semidefinite programs can be used to retrieve exact minimal requirements on detector efficiencies for loophole-free Bell tests
Summary
Bell inequalities characterizing all possible classical correlations of local realistic theories and their violations by quantum theory have been an active field of research since Bell’s original paper published in 1964 [1]. Apart from revealing characteristic quantum properties, which could be demonstrated experimentally recently in loophole-free ways [2,3], violations of Bell inequalities are used in quantum physics as a measure for the secrecy of quantum key distribution schemes [4,5]. Such violations can only be achieved as long as losses and inefficiencies involved in an experimental setup under investigation are sufficiently small. We introduce an extension of these investigations to an error model which includes dark counts of the imperfect detectors involved
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