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arXiv:1602.04905

Strong Bell violations in N level systems

V. Ravishankar, Radha Pyari Sandhir

Published Feb 16, 2016• 0 citations
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Abstract

We study the variety of ways in which nonlocality can be experimentally detected in N level systems, with conventional Bell inequality violation. By simple constructions, show that there are an exponentially large number of correlations that violate the inequality strongly, which remain robust at any N. We further formulate the concept of weak classical limit to get a better insight to the so called classical behaviour that quantum systems are expected to exhibit when N->infinity.

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We study the variety of ways in which nonlocality can be experimentally detected in N level systems, with conventional Bell inequality violation. By simple constructions, show that there are an exponentially large number of correlations that violate the inequality strongly, which remain robust at any N. We further formulate the concept of weak classical limit to get a better insight to the so called classical behaviour that quantum systems are expected to exhibit when N->infinity.
Intensive studies of entanglement properties have proven essential for our understanding of quantum many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems because the available multipartite Bell inequalities involve correlations among many particles, which are difficult to access experimentally. We constructed multipartite Bell inequalities that involve only two-body correlations and show how they reveal the nonlocality in many-body systems relevant for nuclear and atomic physics. Our inequalities are violated by any number of parties and can be tested by measuring total spin components, opening the way to the experimental detection of many-body nonlocality, for instance with atomic ensembles.
Quantum correlations between spatially separated parts of a d-dimensional bipartite system (d ≥ 2) have no classical analog. Such correlations, also called entanglements, are not only conceptually important, but also have a profound impact on information science. In theory the violation of Bell inequalities based on local realistic theories for d-dimensional systems provides evidence of quantum nonlocality. Experimental verification is required to confirm whether a quantum system of extremely large dimension can possess this feature, however it has never been performed for large dimension. Here, we report that Bell inequalities are experimentally violated for bipartite quantum systems of dimensionality d = 16 with the usual ensembles of polarization-entangled photon pairs. We also estimate that our entanglement source violates Bell inequalities for extremely high dimensionality of d > 4000. The designed scenario offers a possible new method to investigate the entanglement of multipartite systems of large dimensionality and their application in quantum information processing.
Nonlocality is one of the main characteristic features of quantum systems involving more than one spatially separated subsystem. It is manifested theoretically as well as experimentally through violation of some local realistic inequality. On the other hand, classical behavior of all physical phenomena in the macroscopic limit gives a general intuition that any physical theory for describing microscopic phenomena should resemble classical physics in the macroscopic regime, the so-called macrorealism. In the 2-2-2 scenario (two parties, with each performing two measurements and each measurement having two outcomes), contemplating all the no-signaling correlations, we characterize which of them would exhibit classical (local realistic) behavior in the macroscopic limit. Interestingly, we find correlations which at the single-copy level violate the Bell-Clauser-Horne-Shimony-Holt inequality by an amount less than the optimal quantum violation (i.e., Cirel'son bound 222\sqrt{2}22​), but in the macroscopic limit gives rise to a value which is higher than 222\sqrt{2}22​. Such correlations are therefore not considered physical. Our study thus provides a sufficient criterion to identify some of unphysical correlations.
We address the problem of detecting non-locality in coupled N level systems in the language of spin. Through a number of examples, we show that non-locality can be detected via a violation of the standard Bell inequality, irrespective of what N is, with correlations from observables of order k ~ 2s in the fundamental spin operators. We further show that, contrarily, if the order k is frozen, then non-locality eludes a detection when s >> k, leading to a weak classical limit. Armed with these results, we proceed to characterize observables that 'genuinely' reflect non-locality in higher dimensions, and demonstrate that one needs to go beyond the standard set-ups such as Stern-Gerlach and those with correlations involving measurement of spin projections along quantization axes.
Multipartite Bell nonlocality provides a device-independent probe of many-body quantum correlations, but its characterization is limited by the rapid growth of the underlying classical and quantum optimization problems. We develop a scalable method for constructing and certifying permutationally invariant Bell inequalities using only one- and two-body correlators. The construction gives families of inequalities with robust quantum violations for general mmm measurements as the number of parties NNN becomes large. To improve robustness against noise, we optimize the ratio of the quantum value to the classical bound for these families in the large-NNN limit. We then certify the resulting quantum violation using semidefinite programming. For the broad class of Bell inequalities studied here, the infinite-NNN ratios take simple rational values for finite mmm and converge to coth⁡(1)\coth(1)coth(1) as m→∞m\to\inftym→∞. The optimized inequalities efficiently detect many-body Bell nonlocality with collective measurements, with more measurement settings leading to stronger violations.
The demonstration and use of nonlocality, as defined by Bell's theorem, rely strongly on dealing with nondetection events due to losses and detectors'inefficiencies. Otherwise, the so-called detection loophole could be exploited. The only way to avoid this is to have detection efficiencies that are above a certain threshold. We introduce the intermediate assumption of limited detection efficiency, that is, in each run of the experiment, the overall detection efficiency is lower bounded by η(min)>0. Hence, in an adversarial scenario, the adversaries have arbitrary large but not full control over the inefficiencies. We analyze the set of possible correlations that satisfy limited detection locality and show that they necessarily satisfy some linear Bell-like inequalities. We prove that quantum theory predicts the violation of one of these inequalities for all η(min)>0. Hence, nonlocality can be demonstrated with arbitrarily small limited detection efficiencies. We validate this assumption experimentally via a twin-photon implementation in which two users are provided with one photon each out of a partially entangled pair. We exploit on each side a passive switch followed by two measurement devices with fixed settings. Assuming the switches are not fully controlled by an adversary, nor by hypothetical local variables, we reveal the nonlocality of the established correlations despite a low overall detection efficiency.