Multiparty quantum mutual information: An alternative definition

Asutosh Kumar
Phys. Rev. A 96, 012332 – Published 27 July 2017

Abstract

Mutual information is the reciprocal information that is common to or shared by two or more parties. Quantum mutual information for bipartite quantum systems is non-negative, and bears the interpretation of total correlation between the two subsystems. This may, however, no longer be true for three or more party quantum systems. In this paper, we propose an alternative definition of multipartite information, taking into account the shared information between two and more parties. It is non-negative, observes monotonicity under partial trace as well as completely positive maps, and equals the multipartite information measure in literature for pure states. We then define multiparty quantum discord, and give some examples. Interestingly, we observe that quantum discord increases when a measurement is performed on a large number of subsystems. Consequently, the symmetric quantum discord, which involves a measurement on all parties, reveals the maximal quantumness. This raises a question on the interpretation of measured mutual information as a classical correlation.

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  • Received 8 June 2017

DOI:https://doi.org/10.1103/PhysRevA.96.012332

©2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Asutosh Kumar*

  • Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019, India; The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India; and Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India

  • *asutoshk@imsc.res.in

Comments & Replies

Reply to “Comment on ‘Multiparty quantum mutual information: An alternative definition' ”

Asutosh Kumar
Phys. Rev. A 108, 066402 (2023)

Comment on “Multiparty quantum mutual information: An alternative definition”

Jaehak Lee, Gibeom Noh, Changsuk Noh, and Jiyong Park
Phys. Rev. A 108, 066401 (2023)

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Vol. 96, Iss. 1 — July 2017

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