Related papers: Pair Correlations in Uniform Countable Sets
What is the communication cost of simulating the correlations produced by quantum theory? We generalize Bell inequalities to the setting of local realistic theories augmented by a fixed amount of classical communication. Suppose two parties…
We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the…
We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements,…
The pair correlations in mesoscopic systems such as $nm$-size superconducting clusters and nuclei are studied at finite temperature for the canonical ensemble of fermions in model spaces with a fixed particle number: i) a degenerate…
We show that sequences of the form $\alpha n^{\theta} \pmod{1}$ with $\alpha > 0$ and $0 < \theta < \tfrac{43}{117} = \tfrac{1}{3} + 0.0341 \ldots$ have Poissonian pair correlation. This improves upon the previous result by Lutsko,…
In this paper, we introduce the notion of a ``pairwise independent correlation gap'' for set functions with random elements. The pairwise independent correlation gap is defined as the ratio of the maximum expected value of a set function…
We show how the Bell correlations can be modelled locally by relaxing the joint probability relation for independent variables $P(a,b)=P(a)P(b)$ outside classical settings, with complex/quaternion generators for the measurement outcomes…
We quantify correlations (quantum and/or classical) between two continuous variable modes in terms of how many correlated bits can be extracted by measuring the sign of two local quadratures. On Gaussian states, such `bit quadrature…
We show that correlation functions have to satisfy contraint relations, owing to the non-negativity of the power spectrum of the underlying random process. Specifically, for any statistically homogeneous and (for more than one spatial…
The unitary correlation sets defined by the first author in conjunction with tensor products of $\mathcal{U}_{nc}(n)$ are further studied. We show that Connes' embedding problem is equivalent to deciding whether or not two smaller versions…
In the stable marriage problem N men and N women have to be matched by pairs under the constraint that the resulting matching is stable. We study the statistical properties of stable matchings in the large N limit using both numerical and…
We construct a set of 2^(2^n) independent Bell correlation inequalities for n-partite systems with two dichotomic observables each, which is complete in the sense that the inequalities are satisfied if and only if the correlations…
Calling the quantity; 2delta(A)delta(B)/|<[A, B]>|, with non-zero denominator, the uncertainty product ratio or UPR for the pair of observables, (A, B), it is shown that any non-zero correlation coefficient between two observables raises,…
In this article, we investigate the fine-scale statistics of real-valued arithmetic sequences. In particular, we focus on real-valued vector sequences and show the Poissonian behavior of the pair correlation function for certain classes of…
Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal…
We provide an interpretation of entanglement based on classical correlations between measurement outcomes of complementary properties: states that have correlations beyond a certain threshold are entangled. The reverse is not true, however.…
Complementary correlations can reveal the genuine quantum correlations present in a composite quantum system. Here we investigate the relation between complementary correlations and other aspects of genuine quantum correlations. We show…
With the help of the static and dynamic mean field spectroscopic amplitudes, taking into account successive and simultaneous transfer channels properly corrected because of non-orthogonality effects, as well as describing the associated…
A paired comparison analysis is the simplest way to make comparative judgments between objects where objects may be goods, services or skills. For a set of problems, this technique helps to choose the most important problem to solve first…
Quantum correlations arising in Bell experiments, involving a physical source that emits a quantum state to a number of observers, have been intensively studied over the last decades. Much less is known about the nature of quantum…