Title:	Pearson correlation coefficient as a measure for certifying and quantifying high-dimensional entanglement
Authors:	Jebarathinam, C. Home, Dipankar Sinha, Urbasi
Issue Date:	24-Feb-2020
Publisher:	American Physical Society
Citation:	Physical Review A, 2020 ,Vol.101, p022112
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.
Description:	Open Access.
URI:	http://hdl.handle.net/2289/7443
ISSN:	2469-9926 2469-9934 (online)
Alternative Location:	https://ui.adsabs.harvard.edu/abs/2019arXiv190901372J/abstract https://arxiv.org/abs/1909.01372 https://doi.org/10.1103/PhysRevA.101.022112
Copyright:	2020 American Physical Society
Appears in Collections:	Research Papers (LAMP)

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