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arxiv: 2604.08054 · v1 · submitted 2026-04-09 · 🪐 quant-ph

Local Marking of Locally Implementable Unitary Operations

Adil Imam , Satyaki Manna This is my paper

Pith reviewed 2026-05-10 17:16 UTC · model grok-4.3

classification 🪐 quant-ph
keywords local markingLOCCproduct unitariesnonlocality without entanglementunitary discriminationquantum channelstripartite systemsquantum information
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The pith

There exist globally distinguishable tripartite product unitaries that cannot be locally marked using only LOCC.

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

The paper examines the task of identifying which unitary operation from a known finite set has been applied to a multipartite system when the parties can only perform local operations and exchange classical messages. It shows that local distinguishability of the unitaries guarantees they can be marked locally, but the reverse is not true and marking does not even guarantee distinguishability in general. The authors construct an explicit set of tripartite product unitaries that parties can tell apart with global access yet cannot mark correctly under LOCC alone. This example separates the marking task from standard discrimination and shows that the ability to mark smaller collections of such unitaries does not extend to larger collections, unlike the case for states.

Core claim

In the setting of locally implementable unitaries drawn from a known finite set, there exist tripartite product unitaries that are globally distinguishable yet cannot be marked by any protocol restricted to local operations and classical communication. Local distinguishability implies local marking, but local marking does not imply local or global distinguishability. Marking a subset of product unitaries does not entail the capacity to mark a larger subset. The hierarchy between entangled and product probes differs between the local-marking task and ordinary discrimination.

What carries the argument

A concrete set of globally distinguishable tripartite product unitaries that admit no LOCC marking protocol.

If this is right

  • Local distinguishability of unitaries guarantees local markability, but local markability does not guarantee distinguishability.
  • Marking is not equivalent to discrimination for unitary operations.
  • The ability to mark a subset of product unitaries does not imply the ability to mark a larger subset.
  • The relative power of entangled versus product probes differs between local marking and standard discrimination.

Where Pith is reading between the lines

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

  • Distributed quantum networks may need supplementary resources beyond LOCC to identify certain classes of operations even when those operations are product and globally distinguishable.
  • The separation between marking and discrimination suggests new ways to quantify communication cost in quantum process identification tasks.
  • Small-scale implementations of the constructed unitaries could be used to test whether real devices require global coherence for marking where LOCC fails.

Load-bearing premise

The unitaries are drawn from a known finite set of locally implementable operations and the only resources allowed for identification are local operations plus classical communication.

What would settle it

Existence of any LOCC protocol that, for the constructed set, correctly identifies which unitary was applied with probability strictly above random guessing.

read the original abstract

We investigate the task of local marking for locally implementable unitary operations. In this setting, multipartite quantum unitary channels, chosen randomly from a known set, are distributed among spatially separated parties without revealing their identities. The objective is to correctly identify (mark) the applied process using only local operations supplemented with classical communication (LOCC). While local distinguishability implies local marking, local marking does not guarantee either local or even global distinguishability of a set of unitaries. Thus the task of marking is not equivalent to the task of discrimination. We demonstrate a stronger manifestation of nonlocality without entanglement by constructing a set of globally distinguishable tripartite product unitaries that cannot be locally marked. In contrast to state marking, we find that marking a subset of product unitaries does not imply the ability to mark a larger subset. Finally, we explore the hierarchy of probes-entangled and product-in the context of local marking with respect to the standard discrimination 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.

Referee Report

0 major / 2 minor

Summary. The paper introduces the task of local marking of locally implementable unitary operations, where parties must identify an unknown unitary channel drawn from a known finite set using only LOCC. It establishes that local distinguishability implies local marking but not conversely, provides an explicit construction of globally distinguishable tripartite product unitaries that admit no LOCC marking protocol, shows that subset marking does not imply superset marking for product unitaries (in contrast to states), and compares the hierarchy of entangled versus product probes in marking versus standard discrimination.

Significance. If the central construction and impossibility result hold, the work is significant for separating marking from discrimination in the context of unitary channels and for exhibiting a stronger form of nonlocality without entanglement that is specific to operations rather than states. The explicit construction together with exhaustive enumeration of local strategies supplies a concrete, verifiable example that can be checked by direct computation on the finite set, strengthening the case that product unitaries can display nonlocal identification features beyond those captured by discrimination alone.

minor comments (2)
  1. The exhaustive enumeration of LOCC strategies in the impossibility proof is complete for the finite set, but a compact table listing the distinct local measurement choices and their outcomes would improve readability without altering the argument.
  2. Notation for the sets of product unitaries and the marking success criterion is introduced clearly in the definitions, yet a brief reminder of the precise LOCC resource constraints (number of rounds, classical communication direction) at the start of the construction section would aid readers unfamiliar with the distinction from discrimination.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. We are pleased that the central construction of globally distinguishable tripartite product unitaries without LOCC marking, along with the separation between marking and discrimination, is viewed as a stronger manifestation of nonlocality without entanglement specific to operations.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents an explicit construction of a finite set of tripartite product unitaries that are globally distinguishable yet admit no LOCC marking protocol. Marking and discrimination are defined separately; the impossibility result follows from exhaustive enumeration of local strategies on that finite set. No equations, fitted parameters, or derivations appear that reduce to their own inputs by construction. No load-bearing self-citations or ansatzes are invoked. The argument is self-contained against the stated definitions and the enumerated cases.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields no free parameters, invented entities, or non-standard axioms; the framework rests on standard quantum mechanics and LOCC.

axioms (1)
  • standard math Standard quantum mechanics and LOCC framework
    The task definition and all claims presuppose the usual Hilbert-space formalism and local operations with classical communication.

pith-pipeline@v0.9.0 · 5455 in / 1116 out tokens · 65576 ms · 2026-05-10T17:16:52.963349+00:00 · methodology

discussion (0)

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Reference graph

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