| GHZ | |
|---|---|
| Name | GHZ state |
| Caption | Schematic of three-particle entanglement |
| Introduced | 1989 |
| Inventors | Daniel M. Greenberger, M. A. Horne, A. Zeilinger |
| Field | Quantum mechanics |
| Notable experiments | Zeilinger experiments, Clauser experiments |
GHZ
The GHZ (Greenberger–Horne–Zeilinger) state is a class of multipartite entangled quantum states, most famously the three-qubit state introduced by Daniel M. Greenberger, Michael A. Horne and Anton Zeilinger in 1989. GHZ states play a central role in foundational tests of quantum mechanics versus local realism and have become a key resource in quantum information theory and experimental platforms for studying entanglement across multiple particles.
The GHZ construction originated in papers by Greenberger–Horne–Zeilinger and subsequent elaborations by Abner Shimony and others, extending the implications of the Bell results of John S. Bell and the EPR paradox. The original GHZ argument provided an all-or-nothing contradiction with local hidden variable theories for three or more particles, strengthening earlier statistical inequalities such as the CHSH inequality derived by John Clauser and colleagues. The GHZ concept has influenced experimental programs at institutions including the University of Vienna, the University of Innsbruck, NIST, and IBM Quantum.
The standard three-qubit GHZ state is written as (1/√2)(|000⟩ + |111⟩), a superposition in the Hilbert space of three two-level systems (qubits). More generally, an n-party GHZ state takes the form (1/√2)(|0⟩^{⊗n} + |1⟩^{⊗n}). Key properties include maximal multipartite entanglement, nonlocal correlations without mixed-state analogues like the W state, and fragility under single-particle measurements. The GHZ state is a representative of the SLOCC inequivalent class of genuinely multipartite entangled states and is central to discussions of entanglement measures such as three-tangle and concurrence. It also features in theoretical constructions using stabilizer formalism and graph states in quantum error correction.
GHZ states have been generated in multiple physical platforms: photonic systems using spontaneous parametric down-conversion at groups led by Anton Zeilinger and Paul Kwiat; trapped-ion systems at NIST and University of Innsbruck (notably experiments by Rainer Blatt); superconducting qubits developed by companies such as IBM and Google; and neutral atoms in optical lattices and Rydberg atom arrays at institutions like MIT and Harvard University. Techniques include entangling gates (e.g., Mølmer–Sørensen gate) for ions, linear optical circuits with beam splitters and postselection, cavity quantum electrodynamics (cQED), and adiabatic or driven interactions in superconducting circuits. Notable experimental milestones include three- and four-photon GHZ demonstrations in the 1990s, ion-trap three-qubit GHZ generation in the early 2000s, and scalable generation efforts toward ten-plus qubit GHZ states in modern superconducting and trapped-ion devices.
The GHZ paradox provides a deterministic contradiction between quantum mechanical predictions and any theory based on local hidden variables, avoiding statistical inequalities. By measuring complementary observables on each qubit (typically Pauli operators σ_x, σ_y, σ_z), one derives exact algebraic contradictions under locality assumptions. This sharpened refutation influenced debates in the philosophy of physics involving figures like Niels Bohr and Albert Einstein historically, and later led to refined experimental tests that closed locality and detection loopholes pioneered by researchers including Alain Aspect and Sergio Belloni?. GHZ experiments have been combined with spacelike separation and random measurement choices, connecting to projects such as cosmic Bell tests using astrophysical sources from groups at University of Vienna and Perimeter Institute.
GHZ states are resources for protocols in quantum cryptography and quantum networking, including quantum secret sharing and multipartite quantum teleportation. They underpin distributed quantum tasks like consensus protocols in quantum communication complexity and are useful in quantum metrology for achieving enhanced phase sensitivity in NOON state-like interferometry. In quantum computing, GHZ states serve in benchmarking entangling capability, generating logical qubits in stabilizer codes such as the Steane code, and as ancilla states for fault-tolerant quantum computation schemes. They are also studied as components in proposals for quantum repeaters and multipartite entanglement distribution over quantum networks being developed by national laboratories and corporations.
GHZ states are highly sensitive to decoherence and local noise: loss or dephasing of a single qubit typically destroys global coherence. This fragility contrasts with more robust multipartite states like the W state. Studies of GHZ decoherence examine amplitude damping, phase damping, and collective noise channels, with mitigation strategies including dynamical decoupling, error-detecting codes, and entanglement purification protocols developed by researchers in quantum information theory such as Charles H. Bennett and Gilles Brassard. Experimental error mitigation in superconducting and ion-trap platforms employs randomized benchmarking, parity measurements, and quantum error correction primitives to protect GHZ-type entanglement during preparation and transmission.
Category:Quantum mechanics Category:Quantum information theory Category:Entanglement