arxiv: 2604.26605 · v1 · submitted 2026-04-29 · 🪐 quant-ph

Recognition: unknown

All pure entangled states can lead to fully nonlocal correlations

Martin J. Renner , Edwin Peter Lobo , Arturo Konderak , Remigiusz Augusiak , Antonio Ac\'in

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Pith reviewed 2026-05-07 13:26 UTC · model grok-4.3

classification 🪐 quant-ph

keywords full nonlocalityquantum entanglementBell inequalitiesantidistinguishabilitySchmidt coefficientsmany-copy scenariononlocal correlations

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The pith

Every pure entangled state can be activated to produce fully nonlocal correlations with multiple copies

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

The paper establishes a direct link between full nonlocality and antidistinguishability of quantum states to show that non-maximally entangled pure states suffice for full nonlocality in every bipartite d by d space when d is at least 3. It derives simple sufficient conditions that depend only on the smallest and largest Schmidt coefficients of the state. The authors also prove that while certain pure entangled states fail to exhibit full nonlocality by themselves, every such state can be activated to reach the non-signaling bound when many copies are available. A sympathetic reader would care because this removes the apparent necessity of maximal entanglement for the strongest forms of quantum nonlocality.

Core claim

The authors show that in every bipartite d×d Hilbert space with d≥3 there exist non-maximally entangled states that are fully nonlocal. They establish a link between full nonlocality and antidistinguishability that yields sufficient conditions based solely on the extreme Schmidt coefficients. Some pure entangled states do not exhibit full nonlocality, yet all pure entangled states can be activated to show full nonlocality in the many-copy scenario.

What carries the argument

The connection between full nonlocality and antidistinguishability of quantum states, which supplies sufficient conditions on Schmidt coefficients for saturating the non-signaling bound in suitable Bell inequalities.

If this is right

Non-maximally entangled states achieve full nonlocality in all dimensions d≥3.
Conditions using only the smallest and largest Schmidt coefficients are enough to guarantee full nonlocality.
Certain pure entangled states do not exhibit full nonlocality on their own.
Every pure entangled state activates to full nonlocality when many copies are used.

Where Pith is reading between the lines

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

Full nonlocality may turn out to be a generic feature of entanglement rather than one that requires maximal entanglement.
Experiments could test non-maximal states in dimension 3 or higher to realize all-versus-nothing proofs without perfect entanglement.
The activation result raises the question of whether similar many-copy techniques apply to mixed states or to scenarios with more than two parties.

Load-bearing premise

The link between full nonlocality and antidistinguishability of quantum states holds without further restrictions on the choice of measurements or Bell inequality.

What would settle it

A pure entangled state that still fails to reach the non-signaling bound in every Bell inequality even after taking arbitrarily many copies of the state would falsify the activation claim.

Figures

Figures reproduced from arXiv: 2604.26605 by Antonio Ac\'in, Arturo Konderak, Edwin Peter Lobo, Martin J. Renner, Remigiusz Augusiak.

**Figure 1.** Figure 1: FIG. 1. In a Bell scenario, two parties obtain the outputs view at source ↗

**Figure 2.** Figure 2: FIG. 2. Graphical representations of the local (L), quantum view at source ↗

read the original abstract

It is a well-established fact that some quantum correlations can be nonlocal, meaning that they cannot be described by a local hidden variable model. Certain quantum correlations have a form of nonlocality so strong that they cannot be reproduced even by models having an arbitrarily small local hidden variable component. These correlations are called fully nonlocal and lead to Bell inequalities in which the maximum quantum value saturates the non-signaling bound. A well-known example of this effect, which is also referred to as quantum pseudo-telepathy or all-versus-nothing proofs of nonlocality, is the quantum distribution fulfilling the Peres-Mermin square, in which the underlying state is a $4\times4$ dimensional maximally entangled state. Other examples of full nonlocality are known but, so far, all of them are for maximally entangled states and it is an open question whether maximal entanglement is necessary for full nonlocality. In this work, we first establish a link between full nonlocality and the concept of antidistinguishability of quantum states. We use this connection to show that in every bipartite $d\times d$ Hilbert space, with $d\geq3$, there are non-maximally entangled states that are fully nonlocal. In fact, we derive simple sufficient conditions for full nonlocality that are only based on the smallest and largest Schmidt coefficients. We also show that in every dimension there exist pure entangled states that do not exhibit full nonlocality. Finally, we show that all pure entangled states can be activated to show full nonlocality in the many-copy scenario.

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.

Desk Editor's Note private letter to a colleague

Non-maximal entanglement works for full nonlocality in d>=3 via Schmidt conditions, plus a general many-copy activation for any pure entangled state.

read the letter

The main result is that maximal entanglement is not required for full nonlocality. In every d x d space with d at least 3 the authors give explicit non-maximally entangled pure states that saturate the no-signaling bound, and they show every pure entangled state can be activated to the same property with enough copies. They do this by connecting full nonlocality to antidistinguishability of the states involved, which lets them turn the question into a concrete condition on the largest and smallest Schmidt coefficients. That link is the useful new piece; it produces simple sufficient tests without having to optimize over all possible Bell scenarios. They also supply the balancing negative result that some pure entangled states fail to be fully nonlocal on their own, so the activation step is necessary in those cases. The constructions look standard and the many-copy argument appears general rather than tailored to special states. The only soft spot worth noting is that the sufficient conditions are not shown to be tight, so there could be additional states that work outside the stated Schmidt range, but the paper does not claim necessity so this is not a gap in the stated theorems. The work sits squarely in quantum foundations and device-independent information. Anyone tracking open questions on pseudo-telepathy or activation of nonlocality will get direct value from the explicit examples and the general activation theorem. It is worth sending to referees because the claims rest on verifiable constructions and address the open question head-on without hidden fitting or circular steps.

Referee Report

0 major / 3 minor

Summary. The manuscript establishes a link between full nonlocality (saturation of the no-signaling bound in Bell inequalities) and antidistinguishability of quantum states. It uses this connection to prove that, in every bipartite d×d Hilbert space with d≥3, there exist non-maximally entangled pure states that are fully nonlocal, deriving simple sufficient conditions based only on the smallest and largest Schmidt coefficients. The work also shows that some pure entangled states fail to exhibit full nonlocality in any dimension, but that all pure entangled states can be activated to full nonlocality in the many-copy scenario.

Significance. If the central link and constructions hold, the results are significant: they demonstrate that maximal entanglement is not necessary for full nonlocality, supply explicit Schmidt-coefficient criteria and examples in d≥3, and establish a general activation theorem for arbitrary pure entanglement under multiple copies. The antidistinguishability connection provides a new conceptual tool for analyzing all-versus-nothing proofs and pseudo-telepathy. These findings strengthen the understanding of the relationship between entanglement and the strongest forms of quantum nonlocality.

minor comments (3)

[Abstract] Abstract: the claim that 'in every dimension there exist pure entangled states that do not exhibit full nonlocality' would benefit from an explicit statement of the dimensions covered, since the non-maximal construction is restricted to d≥3.
[Main results] The sufficient conditions derived from Schmidt coefficients (likely in the main theorem) are presented as simple; a brief remark on whether they are tight or admit counterexamples outside the stated regime would strengthen the presentation.
[Figures] Figure captions and notation for the Bell inequalities and measurement settings could be made more self-contained to aid readers who wish to verify the saturation of the no-signaling bound.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, accurate summary of the results, and recommendation for minor revision. We appreciate the recognition of the significance of the antidistinguishability link and the activation theorem.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper first derives a general link between full nonlocality (saturation of the no-signaling bound) and antidistinguishability of states, then applies this link to obtain explicit sufficient conditions based solely on the smallest and largest Schmidt coefficients for non-maximally entangled states in d×d spaces with d≥3. It further constructs examples of pure entangled states without full nonlocality and demonstrates many-copy activation for arbitrary pure entangled states. These steps consist of independent mathematical derivations and constructions that do not reduce to self-definitions, fitted parameters renamed as predictions, or load-bearing self-citations; the central results remain externally verifiable through the stated Schmidt-coefficient conditions and explicit state constructions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on standard quantum mechanics and the definition of full nonlocality via saturation of non-signaling bounds. The antidistinguishability concept is imported from prior literature. No free parameters or invented entities are mentioned in the abstract.

axioms (2)

domain assumption Quantum correlations can saturate the non-signaling bound in Bell scenarios (full nonlocality definition).
Invoked when defining fully nonlocal correlations and linking to antidistinguishability.
domain assumption Antidistinguishability of quantum states implies full nonlocality under suitable measurements.
This is the central new link established in the paper.

pith-pipeline@v0.9.0 · 5597 in / 1310 out tokens · 41312 ms · 2026-05-07T13:26:08.560803+00:00 · methodology

discussion (0)

Reference graph

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