Pearson correlation coefficient as a measure for certifying and quantifying high-dimensional entanglement

Abstract

A scheme for characterizing entanglement using the statistical measure of correlation given by the Pearson correlation coefficient (PCC) was recently suggested that has remained unexplored beyond the qubit case. Towards the application of this scheme for the high dimensional states, a key step has been taken in a very recent work by experimentally determining PCC and analytically relating it to Negativity for quantifying entanglement of the empirically produced bipartite pure state of spatially correlated photonic qutrits. Motivated by this work, we present here a comprehensive study of the efficacy of such an entanglement characterizing scheme for a range of bipartite qutrit states by considering suitable combinations of PCCs based on a limited number of measurements. For this purpose, we investigate the issue of necessary and sufficient certification together with quantification of entanglement for the two-qutrit states comprising maximally entangled state mixed with white noise and coloured noise in two different forms respectively. Further, by considering these classes of states for d = 4 and 5, extension of this PCC based approach for higher dimensions (d) is discussed.

Neural Network Model for Detecting Network Scanning Attacks

“…When processing data from the original set of "NSL-KDD", records that are not related to network scanning attacks were removed. Also, for processing the initial data, the method of calculating Pearson's correlation was used [18], which allows one's to reduce the dimension of the input feature space. As a result of preprocessing the data, the most significant input attributes that are involved in training the neural network were selected.…”

Relating an entanglement measure with statistical correlators for two-qudit mixed states using only a pair of complementary observables

“…Due to the U ⊗ U * symmetry of the isotropic noise, it is often used a test-bed for studying entanglement [31,32]. On the other hand, coloured noise A has a special property of being completely correlated in the computational basis whereas coloured noise B is completely anti-correlated [28]. The former is produced in the Hong-Ou-Mandel interferometers using polarisation flipper [33], and in the case of d = 2, coloured noise B occurs when one of the parties (of the bipartite system) goes through a local dephasing channel [34].…”

“…While the separability bounds for MP and MI were analytically proved for an arbitrary d for any bipartite state [12,13], the conjectured bound for PCC was proved analytically, restricted to any pure bipartite qubit state [13]. Later, it was proved for d = 3, 4, 5 for a certain class of mixed states [28]. For a pure bipartite qutrit state, the validity of Eq.…”

“…At this stage, a couple of points need to be noted: a) An earlier preliminary study had investigated the use of PCCs for determining N of a class of bipartite entangled states, but this study was restricted to dimensions 3, 4 and 5 [28]. b) A scheme was earlier proposed to relate the EMs like the Concurrence and Negativity of pure and isotropic mixed states to the values of the Bell-SLK function evaluated using a limited number of observables [29].…”

An Automated Statechart Diagram Assessment using Semantic and Structural Similarities

“…Moreover, based on the validity of using Pearson [42]- [44] and the reliability of using Cronbach's alpha, the answers from these experts were statistically tested [45], [46]. Fig.…”