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arxiv: 2604.13169 · v1 · submitted 2026-04-14 · 🪐 quant-ph

Threshold entanglement sharing: quantum states with absolutely separable marginals

Albert Rico , Jofre Abellanet-Vidal , Naga Bhavya Teja Kothakonda , Anna Sanpera , Gerard Angl\`es Munn\'e This is my paper

Pith reviewed 2026-05-10 14:43 UTC · model grok-4.3

classification 🪐 quant-ph
keywords statesentanglementquantumboundsabsolutelymarginalsqubitsseparable
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The pith

Threshold entanglement states exist for 4 and 7 qubits but not 8, with SDP-derived bounds showing they must carry substantial average entanglement and magic.

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

Quantum networks need ways to share entanglement resources without letting small groups of parties access too much information on their own. The authors define threshold entanglement states as those where any entanglement present across a cut forces all marginals involving half or fewer qubits to be separable, meaning they contain no entanglement at all. They prove such states exist for four qubits and for seven qubits. Using two families of semidefinite programming relaxations, they place lower bounds on how pure the marginals of any pure state must be and upper bounds on how pure a mixed absolutely separable state can be. These bounds together show that no such threshold state can exist for eight qubits. The same calculations also improve the best previously known limits on both purity problems independently of the threshold-entanglement question. Numerical checks suggest that when these states do exist they contain useful amounts of entanglement and magic, two resources thought to be necessary for quantum computational advantage.

Core claim

TE states exist for four and seven qubits; TE states of eight qubits cannot exist; the SDP relaxations improve the best known bounds on minimal purity of pure-state marginals and maximal purity of mixed absolutely separable states.

Load-bearing premise

The SDP relaxations used to bound purity are sufficiently tight to decide existence or non-existence of TE states for the qubit numbers considered; the numerical evidence for significant entanglement and magic is representative of the actual states.

read the original abstract

Motivated to understand how entanglement resources can be distributed in quantum networks, we introduce threshold entanglement (TE) states. These are multipartite quantum states whose entanglement across bipartitions forces all marginals of half or less local systems to be (absolutely) separable. First, in contrast to states used for quantum secret sharing, we demonstrate that TE states exist for four and seven qubits. Second, between four and nine qubits, we delimit the average entanglement that TE states must have by combining two semidefinite programming relaxations: (i) lower bounds on the minimal purity of pure state marginals, and (ii) upper bounds on the maximal purity of mixed absolutely separable states. Besides delimiting the existence regions of TE states, our approach independently improves the best known bounds on both of the above problems. Moreover, these improved bounds show that TE states of eight qubits cannot exist. Numerical evidence suggests that TE states accommodate significant amounts of entanglement and magic, which are resources needed for quantum advantage in quantum computing.

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.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only; the claims rest on the standard assumption that SDP relaxations provide valid bounds on purity and on the definition of absolute separability; no free parameters or invented physical entities are visible.

axioms (1)
  • domain assumption Semidefinite programming relaxations yield valid lower/upper bounds on the purity quantities considered
    Invoked when combining the two SDP families to delimit TE-state existence regions

pith-pipeline@v0.9.0 · 5495 in / 1271 out tokens · 32773 ms · 2026-05-10T14:43:13.627807+00:00 · methodology

discussion (0)

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