Universality in distribution of monogamy scores for random multiqubit pure states

Soorya Rethinasamy, Saptarshi Roy, Titas Chanda, Aditi Sen(De), and Ujjwal Sen
Phys. Rev. A 99, 042302 – Published 1 April 2019

Abstract

Monogamy of quantum correlations provides a way to study restrictions on their sharability in multiparty systems. We find the critical exponent of these measures, above which randomly generated multiparty pure states satisfy the usual monogamy relation, and show that the critical power decreases with the increase in the number of parties. For three-qubit pure states, we detect that W-class states are more prone to being nonmonogamous as compared to the GHZ-class states. We also observe a different criticality in monogamy power up to which random pure states remain nonmonogamous. We prove that the “average monogamy” score asymptotically approaches its maximal value on increasing the number of parties. Analyzing the monogamy scores of random three-, four-, five-, and six-qubit pure states, we also report that almost all random pure six-qubit states possess maximal monogamy score, which we confirm by evaluating statistical quantities like mean, variance, and skewness of the distributions. In particular, with the variation of number of qubits, means of the distributions of monogamy scores for random pure states approach to unity—which is the algebraic maximum—thereby conforming to the known results of random states having maximal multipartite entanglement in terms of geometric measures.

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  • Received 17 January 2019

DOI:https://doi.org/10.1103/PhysRevA.99.042302

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Soorya Rethinasamy1,2, Saptarshi Roy1, Titas Chanda1,3, Aditi Sen(De)1, and Ujjwal Sen1

  • 1Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211 019, India
  • 2Birla Institute of Technology and Science, Pilani, Rajasthan 333031, India
  • 3Instytut Fizyki im. Mariana Smoluchowskiego, Uniwersytet Jagielloński, Łojasiewicza 11, PL-30-348 Kraków, Poland

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Issue

Vol. 99, Iss. 4 — April 2019

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