bibkey: zhang2017subentropy
authors: Lin Zhang, Uttam Singh, Arun Kumar Pati
year: 2017
title: "Average subentropy, coherence and entanglement of random mixed quantum states"
doi: 10.1016/j.aop.2016.12.024
url: https://arxiv.org/abs/1510.08859
claim: "Section 7.1 asks whether subentropy satisfies strong subadditivity, Q(ρ_ABC) + Q(ρ_B) ≤ Q(ρ_AB) + Q(ρ_BC)."
strata_touched:
  - D5/S3/Quantum/Subentropy/StrongSubadditivityRefutation
  - D5/S3/Quantum/Subentropy/Subadditivity
license: citation-only
triage: anchor

Subentropy and the strong-subadditivity question

Locator

• URL: https://arxiv.org/abs/1510.08859
• DOI: 10.1016/j.aop.2016.12.024 — ASSUMED-UNVERIFIED; supplied citation, not checked against an original arXiv abstract page or publisher record.
• Question locator supplied with the quotation: arXiv:1510.08859v2, §7.1.

Question

A similarly question can be asked for the strong subadditivity of subentropy: Q(ρ ABC) + Q(ρ B) ⩽ Q(ρ AB) + Q(ρ BC).

The quantifiers range over finite-dimensional tripartite density operators, with the three displayed reduced states obtained by partial trace. The question concerns subentropy, not von Neumann entropy.

Attribution boundary

The quotation, arXiv identifier, version, section, author attribution and DOI are supplied source information. The expanded author names and bibliographic title are ASSUMED-UNVERIFIED. The source’s question label establishes neither present-day openness nor priority.

The determinant-integral construction and the Bell-state counterexample in the associated problem dossier are repository derivations; they are not attributed to this paper. This citation-only note incorporates no source software.

Literature-check result: searches of the arXiv identifiers, “subentropy subadditive”, “strong subadditivity” with subentropy, and the titles found no answer; citation indexes were not exhaustively checked.

Bipartite subadditivity restatement

The supplied quotation from arXiv:1510.08859v2, §7.1 is:

At present, we do not know wether the subadditivity inequality of subentropy is true or not

The spelling and locator are supplied source information, ASSUMED-UNVERIFIED against the original paper under the offline constraint. This historical statement is separate from the strong-subadditivity question and establishes no present-day literature-wide status.

The finite bipartite inequality is proved by the repository theorem Subadditivity.subentropy_subadditive. Its Gaussian and pinching argument is a repository derivation, distinct from the cited historical statement and from the strong-subadditivity refutation.