Greenberger-Horne-Zeilinger theorem for N qudits
arXiv:1303.5326 · doi:10.1103/PhysRevA.88.042101
Abstract
We generalize Greenberger-Horne-Zeilinger (GHZ) theorem to an arbitrary number of D-dimensional systems. Contrary to conventional approaches using compatible composite observables, we employ incompatible and concurrent observables, whose common eigenstate is still a generalized GHZ state. It is these concurrent observables which enable to prove a genuinely N-partite and D-dimensional GHZ theorem. Our principal idea is illustrated for a four-partite system with D which is an arbitrary multiple of 3. By extending to N qudits, we show that GHZ theorem holds as long as N is not divisible by all nonunit divisors of D, smaller than N.
5 pages, journal version
References in corpus (5)
- Device-independent security of quantum cryptography against collective attacks
- An experimental test of non-local realism
- Experimental non-classicality of an indivisible quantum system
- Greenberger-Horne-Zeilinger paradoxes from qudit graph states
- Greenberger-Horne-Zeilinger Nonlocality in Arbitrary Even Dimensions
Cited by in corpus (19)
- Bell nonlocality
- Twisted Photons: New Quantum Perspectives in High Dimensions
- Advances in High Dimensional Quantum Entanglement
- Experimental GHZ Entanglement beyond Qubits
- Unified quantification of nonclassicality and entanglement
- Experimental high-dimensional Greenberger-Horne-Zeilinger entanglement with superconducting transmon qutrits
- Quantum Indistinguishability by Path Identity: The awakening of a sleeping beauty
- Experimental High-Dimensional Entanglement by Path Identity
- Rotational covariance and GHZ contradictions for three or more particles of any dimension
- Multi-setting Greenberger-Horne-Zeilinger theorem
- Mermin inequalities for perfect correlations in many-qutrit systems
- Experimental Test of Irreducible Four-Qubit Greenberger-Horne-Zeilinger Paradox
- Exponentially Enhanced Scheme for the Heralded Qudit GHZ State in Linear Optics
- Multi-qudit states generated by unitary braid quantum gates based on Temperley-Lieb algebra
- Virtual Reality for Understanding Artificial-Intelligence-driven Scientific Discovery with an Application in Quantum Optics
- Greenberger-Horne-Zeilinger test for multi-dimension and arbitrary time nodes entangled histories
- Exploring Non-Multiplicativity in the Geometric Measure of Entanglement
- Graph-theoretic insights on the constructability of complex entangled states
- Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategies