Loophole-Free Bell Test for Continuous Variables via Wave and Particle Correlations

Abstract

We derive two classes of multimode Bell inequalities under local realistic assumptions, which are violated only by the entangled states negative under partial transposition in accordance with the Peres conjecture. Remarkably, the failure of local realism can be manifested by exploiting wave and particle correlations of readily accessible continuous-variable states, with very large violation of inequalities insensitive to detector efficiency, which makes a strong case for a loophole-free test.

Feasibility of loophole-free nonlocality tests with a single photon

“…In the case N = 3, the threshold for violation agrees with Eq. (14), obtained from the inequality (10), but higher N allows for better tolerance than this inequality predicts. Another case is the approximate implementation of σ x given in Sec.…”

“…To achieve efficiency thresholds compatible with those of laboratory detectors, various approaches have been considered, e.g., changing the number of settings, outcomes, and parties [7][8][9][10][11][12] as well as the detection schemes and types of states [12][13][14][15][16][17]. Interestingly, as first noted by Eberhard [18], the state providing better robustness against losses is not necessarily the most entangled.…”

Large violation of Bell inequalities using both particle andwave measurements

“…This state can be created by having two heralded single photons from down-conversion sources bunch on a beam splitter, in a Hong-Ou-Mandel setup [22]. Our scheme was motivated by a recent result by Ji and coworkers in the tentative finding of Bell tests for easy-toprepare quantum states [23]. However, the inequalities they used are not Bell inequalities in the most general sense since they rule out only a particular class of local models.…”

Hyper- and hybrid nonlocality

“…For example, so-called hyperentanglement, i.e., entanglement in multiple DOF [4], can improve the capacity of dense coding in linear optics [7], or enhance the performance of quantum teleportation [6]. Similarly, architectures using hybrid entanglement, i.e., entanglement across discrete and continuous variables [5,13], have been suggested as a promising platform for quantum information, being able to overcome the limitations posed by the finite detection efficiencies of traditional approaches to quantum cryptography and computing [8,12].…”