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arxiv: 2605.29197 · v1 · pith:ZT4BR63Lnew · submitted 2026-05-28 · 🪐 quant-ph

Fundamental limitations on entanglement extraction from purity

Tulja Varun Kondra , Pedro Barrios Hita , Justus Neumann , Hermann Kampermann , Dagmar Bru{\ss} This is my paper

Pith reviewed 2026-06-29 07:28 UTC · model grok-4.3

classification 🪐 quant-ph
keywords absolutely separable statescompletely absolutely separableunital operationsprobabilistic protocolsentanglement generationspectral separability criteriapurity preservation
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The pith

Some absolutely separable states can generate entanglement via probabilistic unital protocols, but completely absolutely separable states cannot.

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

The paper shows that absolutely separable states, which remain separable under all deterministic unital operations, can still generate entanglement with positive probability using probabilistic unital protocols that preserve purity. This leads to the definition of completely absolutely separable states that cannot produce entanglement under any such probabilistic protocol, and the authors supply a complete characterization of this class. They also derive a new sufficient condition for separability that uses only the largest and smallest eigenvalues along with the smallest local dimension. A sympathetic reader cares because it sharpens the boundary on what entanglement can be extracted from low-purity states without experimentally costly purity increases.

Core claim

Absolutely separable states remain separable under all deterministic unital channels and thus cannot deterministically generate entanglement. However, some of them can generate entanglement via probabilistic protocols that preserve the unital property. This motivates the class of completely absolutely separable states, which fail to generate entanglement with any non-zero probability under any such protocol. The paper provides a full characterization of this class and a novel sufficient condition for separability that depends only on the largest and smallest eigenvalues, the smallest local dimension, and is independent of all previously known spectral separability criteria.

What carries the argument

The novel sufficient condition for separability depending only on the largest and smallest eigenvalues and the smallest local dimension, which enables the full characterization of completely absolutely separable states.

Load-bearing premise

The allowed operations are restricted to unital channels that do not increase purity.

What would settle it

A concrete counterexample would be any state that the derived characterization labels as completely absolutely separable yet produces entanglement with positive probability under some probabilistic unital protocol.

Figures

Figures reproduced from arXiv: 2605.29197 by Dagmar Bru{\ss}, Hermann Kampermann, Justus Neumann, Pedro Barrios Hita, Tulja Varun Kondra.

Figure 1
Figure 1. Figure 1: FIG. 1. Graphical representation of the absolutely separable set (AS), [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
read the original abstract

States of sufficiently low purity are separable and cannot be entangled by unital (purity-non-generating) operations. Since high-purity states are experimentally demanding, it is natural to ask how much purity a state must possess to enable entanglement generation. Absolutely separable states remain separable under all deterministic unital channels, and so cannot deterministically generate entanglement in this setting. We show, however, that some absolutely separable states can generate entanglement via probabilistic protocols that do not produce purity. This motivates the study of states that fail to generate entanglement with any non-zero probability, which we call completely absolutely separable; we give a full characterization of this class. Along the way, we derive a novel sufficient condition for separability that depends only on the largest and smallest eigenvalues, along with the smallest local dimension and is independent of all previously known spectral separability criteria.

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 / 2 minor

Summary. The manuscript claims that some absolutely separable states remain separable under all deterministic unital channels but can generate entanglement via probabilistic unital protocols that preserve purity. It defines the subclass of completely absolutely separable states (those that cannot generate entanglement with nonzero probability under any such protocol), provides a full characterization of this class, and derives a novel sufficient condition for separability depending only on the largest and smallest eigenvalues together with the smallest local dimension; this criterion is stated to be independent of all previously known spectral separability criteria.

Significance. If the characterization and independence claim hold, the work supplies a complete delineation, within the unital probabilistic setting, of states from which entanglement cannot be extracted without purity increase. This sharpens the resource-theoretic understanding of purity as a prerequisite for entanglement generation and supplies a simple, low-parameter separability test that may be useful in both theoretical analysis and experimental design. The explicit separation between deterministic and probabilistic unital protocols is a useful conceptual clarification.

minor comments (2)
  1. [Abstract / Introduction] The abstract and introduction should explicitly state the precise definition of the probabilistic protocols considered (e.g., whether they are required to be trace-preserving on average or only on the support of the input) to avoid ambiguity for readers unfamiliar with the unital setting.
  2. [Section introducing the new criterion] The independence of the new spectral criterion from prior tests (e.g., those based on the PPT criterion or other eigenvalue bounds) is asserted but would benefit from a short explicit comparison table or paragraph listing the functional forms of the earlier criteria.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment, the clear summary of our results, and the recommendation of minor revision. No specific major comments or concerns were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper's central results—a full characterization of completely absolutely separable states under unital probabilistic protocols and a novel sufficient separability condition depending only on λ_max, λ_min and local dimension—are presented as direct mathematical derivations from the definitions of absolute separability, unital channels, and probabilistic maps. The abstract explicitly states independence from prior spectral criteria. No self-citations, fitted parameters renamed as predictions, ansatzes smuggled via citation, or renamings of known results appear in the provided claims or abstract. The derivation chain remains independent of the paper's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper operates entirely within standard quantum mechanics and quantum information theory; no free parameters, new entities, or ad-hoc axioms beyond domain assumptions are indicated in the abstract.

axioms (2)
  • domain assumption Quantum states are represented by density operators on finite-dimensional Hilbert spaces; separability means the state is a convex combination of product states.
    Invoked throughout the definitions of absolutely separable and completely absolutely separable states.
  • domain assumption Unital channels are completely positive trace-preserving maps that fix the maximally mixed state and therefore cannot increase purity.
    Central to the distinction between deterministic and probabilistic protocols that do not produce purity.

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Reference graph

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44 extracted references · 6 canonical work pages · 1 internal anchor

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