Related papers: Beyond real: Investigating the role of complex num…
Contrary to Bell scenario, quantum nonlocality can be exploited even when all the parties do not have freedom to select inputs randomly. Such manifestation of nonlocality is possible in networks involving independent sources. One can…
The axioms of quantum mechanics provide limited information regarding the structure of the Hilbert space, such as the underlying number system. The latter is generally regarded as complex, but generalizations of complex numbers, so-called…
In a recent paper \cite{mySEPvsLOCC}, we showed how to construct a quantum protocol for implementing a bipartite, separable quantum measurement using only local operations on subsystems and classical communication between parties (LOCC)…
The assumption of measurement independence is required for a local deterministic model to conduct a Bell test. The violation of a Bell inequality by such a model implies that this assumption must be relaxed. The degree to which the…
In this paper we propose a measure of clustering quality or accuracy that is appropriate in situations where it is desirable to evaluate a clustering algorithm by somehow comparing the clusters it produces with ``ground truth' consisting of…
Quantum theory is commonly formulated in complex Hilbert spaces. However, the question of whether complex numbers need to be given a fundamental role in the theory has been debated since its pioneering days. Recently it has been shown that…
The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This…
Quantum nonlocality as a witness of entanglement plays a crucial role in various fields. Existing quantum monogamy relations rule out the possibility of simultaneous violations of any Bell inequalities with partial statistics generated from…
The experimental detection of multipartite entanglement usually requires a number of appropriately chosen local quantum measurements which are aligned with respect to a previously shared common reference frame. The latter, however, can be a…
We show that the use of probabilistic noiseless amplification in entangled coherent state-based schemes for the test of quantum non locality provides substantial advantages. The threshold amplitude to falsify a Bell-CHSH non locality test,…
A Bell test can rule out local realistic models, and has potential applications in communications and information tasks. For example, a Bell inequality violation can certify the presence of intrinsic randomness in measurement outcomes,…
The question of how Bell nonlocality behaves in bipartite systems of higher dimensions is addressed. By employing the probability of violation of local realism under random measurements as the figure of merit, we investigate the nonlocality…
We consider bipartite systems as versatile probes for the estimation of transformations acting locally on one of the subsystems. We investigate what resources are required for the probes to offer a guaranteed level of metrological…
Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to…
The structure of a local hidden variable model for experiments involving sequences of measurements rigorously is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are…
Given the importance of urban sustainability and resilience to the future of our planet, there is a need to better understand the interconnectedness between the social, economic, environmental, and governance outcomes that underline these…
In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…
Based on the new general framework for the probabilistic description of experiments, introduced in quant-ph/0305126, quant-ph/0312199, we analyze in mathematical terms the link between the validity of Bell-type inequalities under joint…
Bell nonlocality, the fact that local hidden variable models cannot reproduce the correlations obtained by measurements on entangled states, is a cornerstone in our modern understanding of quantum theory. Apart from its fundamental…
Standard quantum mechanics employs complex Hilbert spaces, but whether complex numbers are fundamental or merely convenient has long been debated. For decades, real-valued equivalents were considered mathematically possible but cumbersome.…