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.

Qubit spaces and states

Definition

The qubit space is the one-qubit register $Q_{2} = C^{2}$ of Finite registers and their ordered computational bases, with ordered computational basis $(∣ 0 ⟩, ∣ 1 ⟩) = (e_{0}, e_{1})$ . This basis is orthonormal by The computational basis is orthonormal. A qubit state is a density operator on $Q_{2}$ in the sense of Density operator, namely a non-negative endomorphism of trace one. A pure qubit state is a pure-state ray on $Q_{2}$ in the sense of Pure state and ray. The Bloch coordinates and their state-space constraints are defined and proved in the following items on this page.

The term qubit here names the two-dimensional register and its mathematical state space. No physical preparation or measurement postulate is part of this definition.

Depends on

Used by

Bloch coordinate maps Definition
The Pauli matrices Definition
Bloch coordinates of |0> and H|0> Example
Existence and uniqueness of Bloch coordinates Theorem
Hadamard conjugation of the Pauli matrices Theorem
Pauli formula for an axis rotation Theorem

Dependency tree · two levels

17 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

John Preskill, Quantum Computation, Chapter 2: Foundations I: States and Ensembles (updated July 2015) (standard reference, not scraped)
Ronald de Wolf, Quantum Computing: Lecture Notes, arXiv:1907.09415v6 (2026-08-27) (standard reference, not scraped)
Aram Harrow, 6.443/8.371/18.436 Quantum Information Science II, Lecture 1: Quantum states and operations (2018) (standard reference, not scraped)