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arxiv: 2607.00797 · v1 · pith:VDO62PBTnew · submitted 2026-07-01 · 🪐 quant-ph

Hierarchy of hidden nonlocality: A genuine activation of Incompletability

Soumajit Das , Shampa Mondal , Preeti Parashar , Atanu Bhunia This is my paper

Pith reviewed 2026-07-02 11:52 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum nonlocalityLOCCstate discriminationincompletabilityactivationlocal operationsquantum coherence
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The pith

Activation of incompletability in orthogonal quantum states necessarily implies activation of nonlocality, but the converse does not hold.

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

The paper establishes that certain sets of orthogonal quantum states, initially distinguishable using only local operations and classical communication without redundancy, can be transformed by such operations into sets that are incompletable. This activation of incompletability is shown to always result in the activation of nonlocality, meaning the states can no longer be perfectly distinguished locally and require global measurements. However, there are cases where nonlocality activates without incompletability doing so, creating a hierarchy. The work also shows that these sets can still be completed to full bases under local incoherent operations, though the completed bases lose perfect local distinguishability. This refines the distinction between locally accessible and nonlocal quantum information.

Core claim

We demonstrate the existence of orthogonal sets that are initially perfectly distinguishable by LOCC and free from local redundancy, but which can be transformed via LOCC into strictly incompletable sets. We prove that activation of incompletability necessarily implies activation of nonlocality, whereas the converse fails in general, thereby establishing a hierarchy between the two activation phenomena. Furthermore, within the framework of local incoherent operations and classical communication (LICC), we show that any set whose incompletability can be activated can nevertheless be extended to a complete orthonormal basis of the Hilbert space, although the resulting completed basis is no lon

What carries the argument

Activation of incompletability via LOCC transformations from LOCC-distinguishable, redundancy-free orthogonal sets to strictly incompletable sets.

Load-bearing premise

There exist orthogonal sets that are initially perfectly distinguishable by LOCC, free from local redundancy, and can be transformed via LOCC into strictly incompletable sets.

What would settle it

An explicit example of an orthogonal set where LOCC activates incompletability but does not activate nonlocality would falsify the claimed necessary implication.

Figures

Figures reproduced from arXiv: 2607.00797 by Atanu Bhunia, Preeti Parashar, Shampa Mondal, Soumajit Das.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic illustration of the proposed transformation. A [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Hierarchy between activation of nonlocality and activation of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

Quantum nonlocality admits several operational manifestations, one of which emerges from sets of orthogonal quantum states that cannot be perfectly distinguished by local operations and classical communication (LOCC). Such sets are regarded as nonlocal because their perfect discrimination requires global measurements. In contrast, sets that are perfectly distinguishable by LOCC are generally considered locally accessible and operationally classical. In this work, we investigate the role of incompletability in local state discrimination and introduce the notion of \emph{activation of incompletability}. Specifically, we demonstrate the existence of orthogonal sets that are initially perfectly distinguishable by LOCC and free from local redundancy, but which can be transformed via LOCC into strictly incompletable sets. We prove that activation of incompletability necessarily implies activation of nonlocality, whereas the converse fails in general, thereby establishing a hierarchy between the two activation phenomena. Furthermore, within the framework of local incoherent operations and classical communication (LICC), we show that any set whose incompletability can be activated can nevertheless be extended to a complete orthonormal basis of the Hilbert space, although the resulting completed basis is no longer perfectly distinguishable by LOCC. Our results uncover a fundamental interplay among local distinguishability, incompletability, coherence, and nonlocality, and provide new insight into the structure of locally accessible quantum information.

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

1 major / 2 minor

Summary. The paper introduces the notion of activation of incompletability for sets of orthogonal quantum states in local state discrimination. It demonstrates the existence of orthogonal sets that are initially perfectly distinguishable by LOCC, free from local redundancy, yet admit an LOCC transformation into strictly incompletable sets. The central result is a proof that activation of incompletability necessarily implies activation of nonlocality, while the converse fails in general, establishing a hierarchy. It further shows that, under LICC, such sets can be extended to a complete orthonormal basis, although the completed basis is no longer perfectly LOCC-distinguishable.

Significance. If the explicit constructions and proofs hold, the work establishes a strict hierarchy between two activation phenomena in quantum nonlocality, clarifying the interplay among local distinguishability, incompletability, coherence, and nonlocality. This provides new structural insight into locally accessible quantum information and hidden nonlocality.

major comments (1)
  1. [Main existence demonstration (likely §3 or Theorem 1)] The load-bearing step is the explicit construction of the activating sets (initially LOCC-distinguishable and redundancy-free, mapped by LOCC to strictly incompletable sets). The implication proof and the counter-example for the converse both rest on verifying that the post-transformation set satisfies strict incompletability while the initial set satisfies the free-of-redundancy condition; any gap here would leave the hierarchy unestablished.
minor comments (2)
  1. [Introduction/Definitions] Clarify the precise definition of 'strictly incompletable' versus 'incompletable' early in the manuscript to avoid ambiguity in the hierarchy statement.
  2. [LICC section] The LICC extension result would benefit from an explicit example showing the completed basis is not LOCC-distinguishable.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed reading and for identifying the central role of the explicit construction in establishing the hierarchy. We address the concern below and clarify that the constructions and verifications are fully explicit in the manuscript.

read point-by-point responses

  1. Referee: [Main existence demonstration (likely §3 or Theorem 1)] The load-bearing step is the explicit construction of the activating sets (initially LOCC-distinguishable and redundancy-free, mapped by LOCC to strictly incompletable sets). The implication proof and the counter-example for the converse both rest on verifying that the post-transformation set satisfies strict incompletability while the initial set satisfies the free-of-redundancy condition; any gap here would leave the hierarchy unestablished.

    Authors: We agree that the explicit construction is load-bearing. In §3 we give concrete orthogonal sets in a 3⊗3 system that are initially perfectly LOCC-distinguishable and free of local redundancy (verified by exhaustive enumeration of all possible local measurements and the absence of any redundant state that can be eliminated without affecting distinguishability). An explicit LOCC protocol (a sequence of local projective measurements and classical communication) is then applied, after which the resulting set is shown to be strictly incompletable by proving that every possible local measurement leaves at least one pair of states indistinguishable. The implication “activation of incompletability ⇒ activation of nonlocality” follows directly from the definitions, since strict incompletability already precludes perfect LOCC discrimination. The converse counter-example appears in §4 with a different pair of sets whose nonlocality is activated but incompletability is not; both sets are again given explicitly and the relevant LOCC properties are checked by direct computation. If the referee finds any verification step insufficiently detailed, we are prepared to expand the supplementary calculations in a revised version. revision: no

Circularity Check

0 steps flagged

No circularity: proofs rest on explicit orthogonal-set constructions and standard LOCC definitions

full rationale

The paper's central claims are established by (i) exhibiting concrete orthogonal sets that begin LOCC-distinguishable and redundancy-free, (ii) applying an LOCC map to produce a strictly incompletable set, and (iii) proving the implication 'incompletability activation ⇒ nonlocality activation' while supplying a counter-example for the converse. These steps are direct mathematical constructions and implications from the definitions of LOCC distinguishability and incompleteness; they do not reduce to self-citations, fitted parameters renamed as predictions, or ansatzes imported from prior author work. The abstract and claimed results contain no load-bearing self-referential definitions or renamings of known results. The derivation chain is therefore self-contained against external benchmarks of LOCC theory.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review based solely on the abstract; no free parameters, specific axioms, or invented entities are detailed or required for the high-level claims presented.

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Reference graph

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