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arxiv: 2605.02840 · v1 · submitted 2026-05-04 · 🪐 quant-ph

Recognition: 3 theorem links

· Lean Theorem

Entanglement cost in non-local quantum computation

Alex May
Authors on Pith no claims yet

Pith reviewed 2026-05-08 18:04 UTC · model grok-4.3

classification 🪐 quant-ph
keywords non-local quantum computationentanglement costquantum cryptographyquantum complexityquantum gravitycommunication complexity
0
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The pith

Entanglement cost in non-local quantum computation is closely tied to questions in cryptography, complexity, and gravity.

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

This paper reviews upper and lower bounds on the amount of shared entanglement needed to perform non-local quantum computation, a method that lets two distant quantum systems carry out a joint operation using only one round of communication plus pre-shared entanglement instead of direct interaction. A reader would care because these resource costs determine what is feasible in quantum cryptography protocols, computational tasks, communication problems, and models of quantum gravity. The review gathers known constructions that achieve certain operations with limited entanglement as well as proofs that some operations require large amounts. It also maps out how NLQC appears in multiple research areas and what the current bounds imply for each.

Core claim

The paper presents a comprehensive review of entanglement cost in NLQC, establishing that the quantity of shared entanglement required to implement joint unitaries on separated systems is a central object whose upper and lower bounds connect directly to open questions in quantum cryptography, computational complexity, communication complexity, quantum gravity, and related applications.

What carries the argument

Non-local quantum computation (NLQC), the process of realizing a joint quantum operation on two systems that never interact directly, using only pre-shared entanglement together with a single round of communication.

Load-bearing premise

The literature reviewed on upper and lower bounds is accurately and comprehensively summarized without major omissions or errors in interpretation.

What would settle it

A new explicit protocol that uses strictly less entanglement than the lowest upper bound summarized for a given task, or a new impossibility proof showing that a task requires more entanglement than the highest lower bound given, would contradict the review's account of the current state.

Figures

Figures reproduced from arXiv: 2605.02840 by Alex May.

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read the original abstract

This is a book-length treatment of the subject of non-local quantum computation (NLQC). NLQC is a method for implementing quantum operations that interact two systems without directly bringing the systems together. Instead, a single round of communication and shared entanglement is used. NLQC has appeared in the context of quantum cryptography, computational complexity, communication complexity, quantum gravity, and other applications. The understanding of entanglement cost in NLQC is closely tied to questions in all of these areas. We review upper and lower bounds on entanglement cost, as well as some of the applications of NLQC and its connections to other subjects.

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 manuscript is a book-length review of non-local quantum computation (NLQC), a protocol for implementing quantum operations between two separated systems using only shared entanglement and one round of classical communication. It surveys known upper and lower bounds on the entanglement cost of such protocols and examines their connections to quantum cryptography, computational complexity, communication complexity, quantum gravity, and related applications. The central claim is that a thorough understanding of entanglement cost in NLQC is closely tied to open questions across these fields.

Significance. If the literature synthesis is accurate and comprehensive, the review provides a valuable consolidated reference for researchers working at the intersection of quantum information, cryptography, and gravity. By compiling bounds and highlighting interdisciplinary links without introducing new unverified derivations, it offers a foundation that could guide future work in these areas. The strength lies in the breadth of coverage and the explicit framing of NLQC entanglement cost as a unifying concept.

minor comments (2)
  1. Abstract: The abstract effectively outlines the scope but does not indicate the specific bounds or key results that will be emphasized, which would help readers assess relevance quickly.
  2. Given the book-length format, the manuscript would benefit from an explicit table of contents or section roadmap early in the introduction to improve navigability for readers consulting it as a reference.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary and assessment of the manuscript as a valuable consolidated reference on non-local quantum computation and its interdisciplinary connections. We note the recommendation for minor revision. Since the report contains no specific major comments or points requiring clarification, we have no point-by-point responses to provide. We will perform a final check for any minor issues such as typographical errors or updates to references to ensure the literature synthesis remains accurate and comprehensive.

Circularity Check

0 steps flagged

No circularity: synthesis review with no original derivations

full rationale

The manuscript is explicitly a book-length review that surveys and summarizes known upper and lower bounds on entanglement cost for NLQC protocols, along with their established links to cryptography, complexity, communication complexity, and quantum gravity. No new derivations, predictions, fitted parameters, or first-principles results are introduced; the text states that it reviews existing literature without presenting original equations or claims that could reduce to self-definitions or self-citations. All load-bearing content is therefore external to the paper and independently established in the cited prior work, rendering the derivation chain self-contained with no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a review paper, no new free parameters, axioms, or invented entities are introduced by the authors; the content synthesizes prior work.

pith-pipeline@v0.9.0 · 5379 in / 980 out tokens · 41262 ms · 2026-05-08T18:04:06.756077+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

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

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

Works this paper leans on

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