TY - JOUR
T1 - Pearson correlation coefficient as a measure for certifying and quantifying high-dimensional entanglement
AU - Jebarathinam, C.
AU - Home, Dipankar
AU - Sinha, Urbasi
N1 - Funding Information:
C.J. acknowledges S. N. Bose Centre, Kolkata for a postdoctoral fellowship and support from the Ministry of Science and Technology, Taiwan (Grants No. MOST 108-2811-M-006-501 and No. MOST 108-2811-M-006-516). The research of D.H. is supported by a NASI Senior Scientist Fellowship. Thanks are due to Surya Narayan Banerjee (IISER Pune) for help in numerical computations. D.H. thanks Som Kanjilal for useful discussions.
PY - 2020/2
Y1 - 2020/2
N2 - 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 colored 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.
AB - 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 colored 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.
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U2 - 10.1103/PhysRevA.101.022112
DO - 10.1103/PhysRevA.101.022112
M3 - Article
AN - SCOPUS:85082832708
VL - 101
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 2
M1 - 022112
ER -