Quantum codewords contradict local realism

Abstract

Quantum codewords are highly entangled combinations of two-state systems. The standard assumptions of local realism lead to logical contradictions similar to those found by Bell, Kochen and Specker, Greenberger, Horne and Zeilinger, and Mermin. The new contradictions have some noteworthy features that did not appear in the older ones.

9 pages LaTeX, 1 figure

References in corpus (2)

• Hidden Variables and the Two Theorems of John Bell
• Quantum Error Correction and Orthogonal Geometry

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• Bell Inequalities for Graph States
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• Popescu-Rohrlich correlations as a unit of nonlocality
• Computing Local Invariants of Qubit Systems
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• Quantum Information is Physical
• Quantum Gates and Circuits
• Experimental violation of multipartite Bell inequalities with trapped ions
• Greenberger-Horne-Zeilinger paradoxes for many qudits
• Entanglement and nonclassical properties of hypergraph states
• Two-setting Bell Inequalities for Graph States
• Quantum advantages in classically defined tasks
• Mermin inequalities for perfect correlations
• Entanglement in eight-qubit graph states
• Greenberger-Horne-Zeilinger paradoxes from qudit graph states
• Device-Independent Certification of Genuinely Entangled Subspaces
• Generalized Ardehali-Bell inequalities for graph states
• Rotational covariance and GHZ contradictions for three or more particles of any dimension
• Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell
• Experimental Classification of Entanglement in Arbitrary Three-Qubit States on an NMR Quantum Information Processor
• Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8
• Bipartite Units of Non-Locality
• Mermin inequalities for perfect correlations in many-qutrit systems
• Qudit Hypergraph States
• Bipartite all-versus-nothing proofs of Bell's theorem with single-qubit measurements
• Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets
• Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem
• Multi-setting Greenberger-Horne-Zeilinger Paradoxes
• Five-Qubit Contextuality, Noise-Like Distribution of Distances Between Maximal Bases and Finite Geometry
• Experimentally identifying the entanglement class of pure tripartite states
• Benchmarks of Nonclassicality for Qubit Arrays
• GHZ paradoxes based on an even number of qubits
• Experimental Test of Irreducible Four-Qubit Greenberger-Horne-Zeilinger Paradox
• Primitive Nonclassical Structures of the $N$-qubit Pauli Group
• Detecting Quantum Entanglement
• Combinatorial Approaches in Quantum Information Theory
• Bell's Inequalities: Foundations and Quantum Communication
• The Golay codes and Quantum Contextuality
• All-versus-nothing proofs with n qubits distributed between m parties
• Irreducible magic sets for $n$-qubit systems
• Quantum Communication and Decoherence
• Nonclassical Structures within the N-qubit Pauli Group
• Contextuality of Quantum Error-Correcting Codes