DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Equality communication problem

Definition

For $n \geq 1$ , the Equality promise problem has $X = Y = {0, 1}^{n}$ , YES set ${(x, x) : x \in {0, 1}^{n}}$ and NO set ${(x, y) : x \neq y}$ . The required output is $1$ on YES and $0$ on NO. This is a total promise problem, and a bounded-error protocol must meet its error bound on every pair.

Depends on

Used by

Simultaneous-message equality by quantum fingerprints Algorithm
Public-coin and private-coin SMP are different models Counterexample
Code-based quantum fingerprint Definition
Constant private-coin error reduction by repetition Lemma
Private-coin SMP Equality lower bound and source recovery Remark
Deterministic SMP equality costs Ω(n) bits Theorem
Entanglement-free, randomness-free quantum fingerprints require Ω(log n) qubits Theorem
Fingerprint swap-test error and communication cost Theorem
Private-coin SMP equality requires Ω(√n) bits Theorem

Dependency tree · two levels

6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Ronald de Wolf, Quantum Computing: Lecture Notes, arXiv:1907.09415v6 (standard reference, not scraped)
Harry Buhrman, Richard Cleve, John Watrous, Ronald de Wolf, Quantum Fingerprinting (standard reference, not scraped)