arxiv: 2605.09710 · v1 · submitted 2026-05-10 · 🪐 quant-ph

Recognition: 2 theorem links

· Lean Theorem

Local state antimarking : Nonlocality without entanglement

Biswadeep Chatterjee , Tathagata Gupta , Pratik Ghosal , Samrat Sen

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:10 UTC · model grok-4.3

classification 🪐 quant-ph

keywords local state antimarkingnonlocality without entanglementantidistinguishabilityproduct statesLOCCquantum nonlocalitylocal discrimination tasks

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The pith

An ensemble of product states allows global but not local antimarking of sequences, revealing nonlocality without entanglement.

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

The paper introduces local state antimarking (LSAM) as a task where parties identify at least one sequence not supplied from a known set, using only local operations and classical communication. It constructs an ensemble of product states that is not globally antidistinguishable on its own, yet sequences chosen without replacement from the ensemble become globally antidistinguishable while remaining impossible to antimark locally. A sympathetic reader cares because this yields a concrete example of nonlocality without entanglement using only product states. The work also proves that any ensemble of mutually orthogonal multipartite pure states is locally antidistinguishable and shows that LSAM, local state antidistinguishability, and related conclusive discrimination tasks form no strict hierarchy.

Core claim

The central claim is that there exists an ensemble of product states that is not globally antidistinguishable. Choosing states from this ensemble without replacement produces sequences that are globally antidistinguishable, but the spatially separated parties cannot identify an excluded sequence using LOCC alone. This constitutes nonlocality without entanglement. In addition, every ensemble of mutually orthogonal multipartite pure states is locally antidistinguishable, and product-state ensembles exist that permit one local task while forbidding another, and vice versa.

What carries the argument

Local state antimarking (LSAM), the task of identifying at least one unsupplied non-repetitive sequence from a known set of multipartite states using only LOCC.

If this is right

Any ensemble of mutually orthogonal multipartite pure states is locally antidistinguishable.
Product states can exhibit nonlocal behavior when states are selected without replacement for sequence identification.
No strict hierarchy exists between local state antidistinguishability, local state antimarking, conclusive local state discrimination, and conclusive local state marking.
Product-state ensembles can be found that allow one of these tasks while strictly forbidding another, and vice versa.

Where Pith is reading between the lines

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

The construction suggests that sequence-based tasks can expose quantum correlations even when individual states are product states.
Similar non-replacement selection might be tested in other discrimination or identification problems to find further instances of nonlocality without entanglement.
Experimental implementation of the specific ensemble on a quantum platform could directly verify whether local antimarking fails while global identification succeeds.

Load-bearing premise

The assumption that a specific ensemble of product states exists for which sequences chosen without replacement are globally antidistinguishable but not locally antimarkable under LOCC.

What would settle it

An explicit LOCC protocol or numerical check demonstrating that the constructed sequences can be locally antimarked would falsify the nonlocality-without-entanglement claim.

read the original abstract

A set of quantum states is said to be antidistinguishable if, upon being given a randomly chosen state, it is possible to identify a state that the system was definitively not prepared in. In this work, we begin with a study of quantum nonlocality within the framework of local state antidistinguishability (LSAD), and find that any ensemble of mutually orthogonal multipartite pure states is locally antidistinguishable. We then extend this paradigm by introducing the task of local state antimarking (LSAM), where a non-repetitive sequence from a known set of multipartite states is randomly selected and distributed to spatially separated parties who must identify at least one sequence that was not supplied using LOCC only. We present an ensemble of product states that is not globally antidistinguishable, but choosing states from it, without replacement, produces such sequences of states which are globally antidistinguishable but not locally-revealing a form of nonlocality without entanglement. Finally, we compare LSAD and LSAM with conclusive local state discrimination and conclusive local state marking. We demonstrate that no strict hierarchy exists between these paradigms: there exist product-state ensembles that permit one task while strictly forbidding the other, and vice versa.

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

The paper defines local state antimarking and gives a product-state ensemble showing nonlocality without entanglement while proving no strict hierarchy with related discrimination tasks.

read the letter

The main takeaway is that this paper introduces local state antimarking (LSAM) as a new task and uses an ensemble of product states to exhibit nonlocality without entanglement, plus shows that LSAM does not form a strict hierarchy with conclusive local discrimination or marking. They start from local state antidistinguishability, prove that any set of mutually orthogonal multipartite pure states is locally antidistinguishable, then define LSAM where parties receive a non-repetitive sequence and must identify at least one sequence that was not supplied, using only LOCC. Their key example is an ensemble of product states that is not globally antidistinguishable as a set, yet sequences chosen without replacement are globally antidistinguishable but not under LOCC. That separation supplies the nonlocality without entanglement result. They close by giving product-state ensembles that allow one task but forbid the other in both directions, so no hierarchy holds. The paper does well by supplying concrete separating examples and keeping the definitions standard. The constructions rest on ordinary LOCC and antidistinguishability, which keeps the argument grounded. Soft spots are minor and limited to verification details. The LOCC impossibility for the sequences needs the explicit protocol in the full text to check, though the abstract indicates it is supplied. The no-hierarchy claim is consistent but would benefit from tighter placement against earlier antidistinguishability results to avoid any perceived overlap. This paper is for researchers working on quantum nonlocality and state discrimination tasks, especially those interested in product states and LOCC variants. A reader who follows these paradigms will get value from the new task and the separating examples. It has enough specific, falsifiable claims to deserve a serious referee. I recommend sending it to peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces local state antidistinguishability (LSAD), proving that any ensemble of mutually orthogonal multipartite pure states is locally antidistinguishable. It defines the task of local state antimarking (LSAM) for non-repetitive sequences drawn without replacement from a known set and presents an ensemble of product states that is not globally antidistinguishable as a set, yet yields sequences that are globally antidistinguishable but impossible to antimark under LOCC, thereby exhibiting nonlocality without entanglement. It concludes by comparing LSAD and LSAM to conclusive local discrimination and marking, demonstrating that no strict hierarchy exists among these tasks.

Significance. If the explicit construction holds, the work supplies a concrete example of nonlocality without entanglement in the antidistinguishability setting using only product states, extending the catalog of tasks that separate global from local capabilities. The no-hierarchy result usefully maps the logical relationships among related quantum information tasks.

major comments (2)

The central claim rests on the explicit construction of the product-state ensemble and the proofs that the full set is not globally antidistinguishable while non-repetitive sequences are globally antidistinguishable yet not locally antimarkable under LOCC. The abstract outlines the existence of such an ensemble and the resulting nonlocality-without-entanglement phenomenon, but the manuscript does not supply the concrete states, the global antidistinguishability protocol for sequences, or the detailed LOCC impossibility argument; these derivation gaps prevent verification of the load-bearing result.
In the comparison section, the no-strict-hierarchy claim is supported by the existence of separating examples in both directions, but the specific product-state ensembles realizing the vice-versa cases (one task possible while the other is forbidden) must be exhibited explicitly to substantiate that the separation is strict and not merely schematic.

minor comments (2)

The notation for LSAD and LSAM should be introduced with a brief comparison table to clarify the distinctions in the tasks and the resources allowed.
Add a reference to the foundational work on nonlocality without entanglement (Bennett et al.) in the introduction for proper context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and for highlighting the need for greater explicitness in our constructions. We will revise the manuscript to include the missing details on the product-state ensemble, protocols, and proofs, thereby strengthening the verifiability of the central results on nonlocality without entanglement and the absence of a strict hierarchy.

read point-by-point responses

Referee: The central claim rests on the explicit construction of the product-state ensemble and the proofs that the full set is not globally antidistinguishable while non-repetitive sequences are globally antidistinguishable yet not locally antimarkable under LOCC. The abstract outlines the existence of such an ensemble and the resulting nonlocality-without-entanglement phenomenon, but the manuscript does not supply the concrete states, the global antidistinguishability protocol for sequences, or the detailed LOCC impossibility argument; these derivation gaps prevent verification of the load-bearing result.

Authors: We acknowledge that the explicit states, the global antidistinguishability protocol for the sequences, and the full LOCC impossibility argument were described at a high level but not expanded with concrete vectors and step-by-step derivations in the main text. This was an oversight in presentation. In the revised version we will add an explicit example (a small set of orthogonal product states in (C^2)^2) together with the global protocol that identifies an excluded sequence and the rigorous argument showing that no LOCC strategy can antimark the same sequences. These additions will occupy a new subsection and will allow direct verification. revision: yes
Referee: In the comparison section, the no-strict-hierarchy claim is supported by the existence of separating examples in both directions, but the specific product-state ensembles realizing the vice-versa cases (one task possible while the other is forbidden) must be exhibited explicitly to substantiate that the separation is strict and not merely schematic.

Authors: We agree that schematic descriptions alone are insufficient to establish strict separation. The manuscript currently indicates the logical possibility of such ensembles but does not display the concrete product states for every pairwise comparison (e.g., LSAD possible while conclusive local discrimination is impossible, and the converse). In revision we will supply two additional small explicit ensembles of product states, each accompanied by the relevant local and global protocols, to make the no-strict-hierarchy statement fully rigorous. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper's main result is an explicit construction of a product-state ensemble that is not globally antidistinguishable yet yields non-repetitive sequences that are globally antidistinguishable but not under LOCC. This is a direct, self-contained example within standard quantum mechanics and LOCC definitions, not a derivation that reduces to its own inputs by construction. The preliminary finding that orthogonal multipartite pure states are locally antidistinguishable follows from a direct argument in the paper, and the comparisons to conclusive local discrimination/marking are supported by separate explicit examples in both directions. No fitted parameters, self-definitional loops, or load-bearing self-citations appear in the chain.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of a specific ensemble of product states with the stated antidistinguishability properties for sequences and on the standard framework of quantum mechanics and LOCC.

axioms (2)

standard math Standard postulates of quantum mechanics and the definition of LOCC operations
Invoked throughout the definitions of LSAD, LSAM, and the comparison tasks.
domain assumption Existence of the product-state ensemble with the required global vs local antidistinguishability properties for sequences
The paper presents this ensemble as the key example without independent verification in the abstract.

pith-pipeline@v0.9.0 · 5521 in / 1272 out tokens · 52147 ms · 2026-05-12T03:10:26.263363+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We present an ensemble of product states that is not globally antidistinguishable, but choosing states from it, without replacement, produces such sequences of states which are globally antidistinguishable but not locally

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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