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Register a new userEffects of white noise on Bell theorem for qudits
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We introduce two types of statistical quasi-separation between local observables to construct two-party Bell-type inequalities for an arbitrary dimensional systems and arbitrary number of measurement settings per site. Note that, the main difference between statistical quasi-separations and the usual statistical separations is that the former are not symmetric under exchange of the two local observables, whereas latter preserve the symmetry. We show that a variety of Bell inequalities can be derived by sequentially applying triangle inequalities which statistical quasi-separations satisfy. A sufficient condition is presented to show quantum violations of the Bell-type inequalities with infinitesimal values of critical visibility $v_c$.
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Generalizations of the classic Bell inequality to higher dimensional quantum systems known as qudits are reputed to exhibit a higher degree of robustness to noise, but such claims are based on one particular noise model. We analyze the violation of the Collins-Gisin-Linden-Massar-Popescu inequality subject to more realistic noise sources and their scaling with dimension. This analysis is inspired by potential Bell inequality experiments with superconducting resonator-based qudits. We find that the robustness of the inequality to noise generally decreases with increasing qudit dimension.
Greenberger-Horne-Zeilinger states are intuitively known to be the most non-classical ones. They lead to the most radically nonclassical behavior of three or more entangled quantum subsystems. However, in case of two-dimensional systems, it has been shown that GHZ states lead to more robustness of Bell nonclassicality in case of geometrical inequalities than in case of Mermin inequalities. We investigate various strategies of constructing geometrical Bell inequalities (BIs) for GHZ states for any dimensionality of subsystems.
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.
Bounds, expressed in terms of d and N, on full Bell locality of a quantum state for $Ngeq 3$ nonlocally entangled qudits (of a dimension $dgeq 2$) mixed with white noise are known, to our knowledge, only within full separability of this noisy N-qudit state. For the maximal violation of general Bell inequalities by an N-partite quantum state, we specify the analytical upper bound expressed in terms of dilation characteristics of this state, and this allows us to find new general bounds in $d, N$, valid for all $dgeq 2$ and all $Ngeq 3$, on full Bell locality under generalized quantum measurements of (i) the N-qudit GHZ state mixed with white noise and (ii) an arbitrary N-qudit state mixed with white noise. The new full Bell locality bounds are beyond the known ranges for full separability of these noisy N-qudit states.
We propose an operational quasiprobability function for qudits, enabling a comparison between quantum and hidden-variable theories. We show that the quasiprobability function becomes positive semidefinite if consecutive measurement results are described by a hidden-variable model with locality and noninvasive measurability assumed. Otherwise, it is negative valued. The negativity depends on the observables to be measured as well as a given state, as the quasiprobability function is operationally defined. We also propose a marginal quasiprobability function and show that it plays the role of an entanglement witness for two qudits. In addition, we discuss an optical experiment of a polarization qubit to demonstrate its nonclassicality in terms of the quasiprobability function.
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