Quantum nonlocality without entanglement and state discrimination measures

Shayeef Murshid; Tathagata Gupta; Vincent Russo; Somshubhro Bandyopadhyay

doi:10.22331/q-2026-07-23-2174

Quantum nonlocality without entanglement and state discrimination measures

Shayeef Murshid¹, Tathagata Gupta², Vincent Russo³, and Somshubhro Bandyopadhyay⁴

¹Electronics and Communication Sciences Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
²Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
³Unitary Foundation, 315 Montogomery St, Fl 10 San Francisco, California 94104, USA
⁴Department of Physical Sciences, Bose Institute, EN 80, Bidhannagar, Kolkata 700091, India

Published:	2026-07-23, volume 10, page 2174
Editor:	Paul Skrzypczyk
Eprint:	arXiv:2506.20560v2
Doi:	https://doi.org/10.22331/q-2026-07-23-2174
Citation:	Quantum 10, 2174 (2026).

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Updated version: The authors have uploaded version v3 of this work to the arXiv which may contain updates or corrections not contained in the published version v2. The authors left the following comment on the arXiv:

v3 - updated abstract

Abstract

An ensemble of product states is said to exhibit “quantum nonlocality without entanglement” if it cannot be optimally discriminated using local operations and classical communication (LOCC). We show that this property can depend on the chosen discrimination measure. Specifically, we construct a family of ensembles, each consisting of six linearly independent, equally probable bipartite product states, for which LOCC fails to achieve optimal minimum-error discrimination but succeeds in achieving optimal unambiguous discrimination. We further extend our construction to multipartite systems and provide strong numerical evidence that a similar separation between local and global optima is present for minimum-error discrimination, but not for unambiguous discrimination.

► BibTeX data

@article{Murshid2026quantumnonlocality,
  doi = {10.22331/q-2026-07-23-2174},
  url = {https://doi.org/10.22331/q-2026-07-23-2174},
  title = {Quantum nonlocality without entanglement and state discrimination measures},
  author = {Murshid, Shayeef and Gupta, Tathagata and Russo, Vincent and Bandyopadhyay, Somshubhro},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2174},
  month = jul,
  year = {2026}
}

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Cited by

[1] Jia-Xin Ma, Chen-Ming Bai, Su-Juan Zhang, and Lu Liu, "Genuine Activation of Hidden Nonlocality in Multipartite Quantum Systems", International Journal of Theoretical Physics 65 6, 155 (2026).

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