Greenberger–Horne–Zeilinger state

A multipartite entangled state formed by a coherent superposition of all subsystems in one basis state and all in its complementary basis state.

Version

v1 · 2026-09-08 · History

Domain-specific #

4781

Origin domain

quantum information and foundations

Subdomain

quantum information and foundations

Core Idea

For three qubits the canonical state is (|000⟩+|111⟩)/sqrt(2); relative phase, subsystem dimension and local-basis variants preserve GHZ-type entanglement, which is fragile under particle loss. Coherent preparation correlates every subsystem without selecting either collective alternative; joint measurements in incompatible bases yield deterministic correlations that contradict local hidden-variable assignments without a statistical inequality. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application

Greenberger–Horne–Zeilinger state belongs to quantum information and foundations and is useful where the analyst can specify the typed quantum information and foundations carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the number and dimension of subsystems, computational basis, two collective product states, normalization and relative phase, density operator and purity, entanglement class, stabilizers, measurement settings and correlation predictions, locality assumptions, noise and loss behavior and distinction from W states are explicit.

Clarity

The abstraction clarifies a crowded vocabulary by making the number and dimension of subsystems, computational basis, two collective product states, normalization and relative phase, density operator and purity, entanglement class, stabilizers, measurement settings and correlation predictions, locality assumptions, noise and loss behavior and distinction from W states are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Greenberger–Horne–Zeilinger state. Greenberger–Horne–Zeilinger state compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: the typed quantum information and foundations carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2.

Knowledge Transfer

Knowledge transfers strongly among subfields of quantum information and foundations because they reuse the typed quantum information and foundations carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Coherent preparation correlates every subsystem without selecting either collective alternative; joint measurements in incompatible bases yield deterministic correlations that contradict local hidden-variable assignments without a statistical inequality., and type the carrier, state every parameter and convention in the definition, test that the number and dimension of subsystems, computational basis, two collective product states, normalization and relative phase, density operator and purity, entanglement class, stabilizers, measurement settings and correlation predictions, locality assumptions, noise and loss behavior and distinction from W states are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Greenberger–Horne–Zeilinger state Domain-specific

Parents (1) — more general patterns this builds on

• Greenberger–Horne–Zeilinger state is a kind of Entanglement Prime

  The proposed strict upward parent is prime:entanglement.

Hierarchy paths (3) — routes to 3 parentless roots

• Greenberger–Horne–Zeilinger state → Entanglement → Coupling

Show alternative paths (2)

Neighborhood in Abstraction Space

Greenberger–Horne–Zeilinger state sits in a crowded region of the domain-specific corpus (6^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Quantum Information & State Structure (41 abstractions)

Nearest neighbors

• State-merging — 0.94
• Quantum cloning — 0.94
• Einselection — 0.93
• Spin squeezing — 0.93
• Reflected entropy — 0.93

Computed from structural-signature embeddings · 2026-09-08