Related papers: High-dimensional Bell test for a continuous variab…
We present a prescription for obtaining Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give examples of some families of such inequalities. The inequalities are violated by certain classes…
On one side, so far a great part of the evidence accepted as proof of the alleged quantum non-locality relied on inhomogeneous Bell inequalities involving an additional assumption (no-enhancement) whose role had not been sufficiently…
When applying multivariate extreme value statistics to analyze tail risk in compound events defined by a multivariate random vector, one often assumes that all dimensions share the same extreme value index. While such an assumption can be…
Quantum nonlocality is tested for an entangled coherent state, interacting with a dissipative environment. A pure entangled coherent state violates Bell's inequality regardless of its coherent amplitude. The higher the initial nonlocality,…
High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional…
We combine the concept of Bell measurements, in which two systems are projected into a maximally entangled state, with the concept of continuous measurements, which concerns the evolution of a continuously monitored quantum system. For such…
Quantum Bell nonlocality is an important quantum phenomenon. Recently, the shareability of Bell nonlocality under unilateral measurements has been widely studied. In this study, we consider the shareability of quantum Bell nonlocality under…
Quantum correlations may violate the Bell inequalities. Most of the experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiment which closes this loophole…
After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…
Bell inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description.…
The main result of this paper states that phase retrieval in infinite-dimensional Hilbert spaces is never uniformly stable, in sharp contrast to the finite dimensional setting in which phase retrieval is always stable. This leads us to…
We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…
We propose a variation of Bell inequalities for continuous variables that employs the Wigner function and Weyl symbols of operators in phase space. We present examples of Bell inequality violation which beat Cirel'son's bound.
I propose two U-statistics to test coefficients in generalized linear models. One of them is used to deal with global hypothesis and the other one to test with the nuisance parameter. Both the statistics proposed are within high-dimensional…
In this paper, we investigate the critical efficiency of detectors to observe Bell nonlocality using multiple copies of the maximally entangled two-qubit state carried by a single pair of particles, such as hyperentangled states, and the…
We consider testing regression coefficients in high dimensional generalized linear models. An investigation of the test of Goeman et al. (2011) is conducted, which reveals that if the inverse of the link function is unbounded, the high…
We propose an enhanced discrimination measurement for tripartite 3-dimensional entangled states in order to improve the discernible number of orthogonal entangled states. The scheme suggests 3-dimensional Bell state measurement by…
The Hardy test of nonlocality can be seen as a particular case of the Bell tests based on the Clauser-Horne (CH) inequality. Here we stress this connection when we analyze the relation between the CH-inequality violation, its threshold…
Bell non-locality represents the ultimate consequence of quantum entanglement, fundamentally undermining the classical tenet that spatially-separated degrees of freedom possess objective attributes independently of the act of their…
In high-dimensional data analysis, bi-level sparsity is often assumed when covariates function group-wisely and sparsity can appear either at the group level or within certain groups. In such cases, an ideal model should be able to…