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arxiv: 2607.01320 · v1 · pith:USPBVNDZnew · submitted 2026-07-01 · 🪐 quant-ph · cond-mat.str-el· hep-th· math-ph· math.MP

Logarithmic negativity typically equals exact entanglement cost

Bowen Ouyang , Jonah Kudler-Flam This is my paper

Pith reviewed 2026-07-03 20:40 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-elhep-thmath-phmath.MP
keywords logarithmic negativityentanglement costrandom induced statesPPT operationsquantum entanglementmany-body systemsoperational interpretation
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The pith

For large random induced mixed states, logarithmic negativity equals the exact entanglement cost under PPT-preserving operations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that in the regime of large random induced mixed states, the logarithmic negativity coincides with the entanglement cost under positive partial transpose preserving operations. This equality is generic, meaning it holds for almost all such states. Because the logarithmic negativity can be computed efficiently while the entanglement cost is difficult to evaluate in general, this result provides an operational meaning to the negativity and a practical way to quantify entanglement in complex quantum systems. A reader would care as it bridges an efficiently computable quantity to a fundamental operational resource in quantum information.

Core claim

For large random induced mixed states the logarithmic negativity, an efficiently computable entanglement measure, generically coincides with the exact entanglement cost under positive-partial-transpose-preserving operations, thereby acquiring a precise operational interpretation. Our results establish logarithmic negativity as an exact characterization of entanglement in generic many-body states and provide a tractable route for quantifying entanglement in complex quantum systems.

What carries the argument

The generic equality between logarithmic negativity and the exact entanglement cost under PPT-preserving operations, for the ensemble of large random induced mixed states.

If this is right

  • Logarithmic negativity acquires a precise operational interpretation as the exact entanglement cost.
  • It serves as an exact characterization of entanglement in generic many-body states.
  • It offers a tractable computational method to quantify entanglement in complex quantum systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The result suggests that for typical states arising in physical many-body systems, an efficiently computable measure can replace harder operational costs.
  • It may be possible to verify the equality numerically on finite but large systems drawn from the induced ensemble to check the asymptotic claim.
  • Extensions could examine whether the same generic coincidence appears in other ensembles used to model realistic quantum states.

Load-bearing premise

The states belong to the ensemble of large random induced mixed states and the equality holds generically for that ensemble.

What would settle it

Constructing or identifying even one large random induced mixed state where the numerical value of the logarithmic negativity differs from the exact entanglement cost under PPT operations would falsify the generic equality.

Figures

Figures reproduced from arXiv: 2607.01320 by Bowen Ouyang, Jonah Kudler-Flam.

Figure 1
Figure 1. Figure 1: FIG. 1. Phase diagram of a random induced mixed state [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Entanglement-saturation-phase binegativity spec [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

Quantum entanglement plays a leading role in modern understanding of physical systems, from quantum phases of matter to quantum gravity. In quantum information theory, one seeks operationally meaningful quantifiers of entanglement, which for large quantum systems are notoriously difficult to evaluate due to the lack of computationally efficient algorithms. In this Letter, we show that for large random induced mixed states the logarithmic negativity, an efficiently computable entanglement measure, generically coincides with the exact entanglement cost under positive-partial-transpose-preserving operations, thereby acquiring a precise operational interpretation. Our results establish logarithmic negativity as an exact characterization of entanglement in generic many-body states and provide a tractable route for quantifying entanglement in complex quantum systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The paper claims that for large random induced mixed states, the logarithmic negativity (an efficiently computable entanglement measure) generically coincides with the exact entanglement cost under positive-partial-transpose-preserving operations, thereby acquiring a precise operational interpretation and establishing logarithmic negativity as an exact characterization of entanglement in generic many-body states.

Significance. If the result holds, it would provide a tractable route for quantifying entanglement in complex quantum systems where direct computation of entanglement cost is difficult, and give an operational meaning to logarithmic negativity for the ensemble of large random induced mixed states.

minor comments (1)
  1. The abstract refers to 'large random induced mixed states' and states that the equality holds 'generically,' but does not specify the precise ensemble definition or the measure of genericity used in the result.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their summary of the manuscript and for recognizing its potential significance. The recommendation is listed as uncertain, but the report contains no specific major comments or points of criticism to address. We stand by the results as presented and would welcome any detailed questions or concerns the referee may have.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract and context present a theorem establishing generic equality between logarithmic negativity and PPT entanglement cost on the ensemble of large random induced mixed states. No equations, self-definitions, fitted parameters renamed as predictions, or load-bearing self-citations are exhibited that reduce the claimed result to its inputs by construction. The derivation is described as independent of the target quantity, consistent with a standard mathematical result on random states rather than a tautology or ansatz smuggling. This is the expected non-finding for a paper whose central claim is an external equality on a defined ensemble.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated technical definition of the induced ensemble and the PPT cost.

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discussion (0)

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Reference graph

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