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Shor's Conjecture Is True: Projective Measurements Suffice for Binary Accessible Information

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Sunghyeon Jo

Quantum Physics · Submitted 4 Aug 2026

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove the conjecture constructively in arbitrary finite dimension.

how it is stated · asserted 1.00 read the record →

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arXiv ID2609.19003 (version 1)
Pith IDFDO3NICN, Pith's permanent record of this paper and its review
CitationSunghyeon Jo. "Shor's Conjecture Is True: Projective Measurements Suffice for Binary Accessible Information." arXiv:2609.19003 (2026). https://pith.science/paper/FDO3NICN
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,411 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.26 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.85 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Shor conjectured that a von Neumann measurement attains the accessible information of every binary quantum ensemble. We prove the conjecture constructively in arbitrary finite dimension. For every finite-outcome positive operator-valued measure (POVM) $M$, we form an operator $T_M$ from the posterior label probabilities and show that its spectral projection-valued measure (PVM) $\Pi_M$ satisfies $I_{\Pi_M}(X{:}Y)\ge I_M(X{:}Y)$; every rank-one refinement retains the inequality. Two applications of Jensen's operator inequality prove the comparison and yield an exact concave variational formula for the accessible information. The result is a special case of the general theorem of Fang, Fawzi, and Fawzi on measured $f$-divergences; the proof below isolates the binary argument and makes the replacement $M\mapsto T_M\mapsto\Pi_M$ explicit.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Shor conjectured that a von Neumann measurement attains the accessible information of every binary quantum ensemble. background 1.00 0.04 0.11 speculative 0.72
s1 We prove the conjecture constructively in arbitrary finite dimension. contribution 0.75 0.96 0.80 asserted 1.00
s2 For every finite-outcome positive operator-valued measure (POVM) $M$, we form an operator $T_M$ from the posterior label probabilities and show that its spectral projection-valued measure (PVM) $\Pi_M$ satisfies $I_{\Pi_M}(X{:}Y)\ge I_M(X{:}Y)$; every rank-one refinement retains the inequality. method 0.73 0.94 0.36 asserted 1.00
s3 Two applications of Jensen's operator inequality prove the comparison and yield an exact concave variational formula for the accessible information. method 0.94 0.90 0.08 asserted 1.00
s4 The result is a special case of the general theorem of Fang, Fawzi, and Fawzi on measured $f$-divergences; the proof below isolates the binary argument and makes the replacement $M\mapsto T_M\mapsto\Pi_M$ explicit. interpretation 0.64 0.68 0.06 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Shor conjectured that a von Neumann measurement attains the accessible information of every binary quantum ensemble. We prove the conjecture constructively in arbitrary finite dimension. For every finite-outcome positive operator-valued measure (POVM) $M$, we form an operator $T_M$ from the posterior label probabilities and show that its spectral projection-valued measure (PVM) $\Pi_M$ satisfies $I_{\Pi_M}(X{:}Y)\ge I_M(X{:}Y)$; every rank-one refinement retains the inequality. Two applications of Jensen's operator inequality prove the comparison and yield an exact concave variational formula for the accessible information. The result is a special case of the general theorem of Fang, Fawzi, and Fawzi on measured $f$-divergences; the proof below isolates the binary argument and makes the replacement $M\mapsto T_M\mapsto\Pi_M$ explicit.

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