Unbounded violation of tripartite Bell inequalities

Abstract

We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck's constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized GHZ states is always bounded so that, in contrast to many other contexts, GHZ states do in this case not lead to extremal quantum correlations. The results are based on tools from the theories of operator spaces and tensor norms which we exploit to prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras.

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References in corpus (30)

• Device-independent security of quantum cryptography against collective attacks
• No Signalling and Quantum Key Distribution
• From Bell's Theorem to Secure Quantum Key Distribution
• All multipartite Bell correlation inequalities for two dichotomic observables per site
• Bell's theorem for general N-qubit states
• General properties of Nonsignaling Theories
• Evenly distributed unitaries: on the structure of unitary designs
• Aspects of generic entanglement
• The Communication Cost of Simulating Bell Correlations
• Violation of Bell's inequality: criterion for quantum communication complexity advantage
• The mother of all protocols: Restructuring quantum information's family tree
• Grothendieck's constant and local models for noisy entangled quantum states
• Entanglement versus Bell violations and their behaviour under local filtering operations
• Quantum Entanglement and Communication Complexity
• Experimental violation of a cluster state Bell inequality
• Secrecy extraction from no-signalling correlations
• Separable balls around the maximally mixed multipartite quantum states
• Multiplicativity of completely bounded p-norms implies a new additivity result
• Tight multipartite Bell's inequalities involving many measurement settings
• A separability criterion for density operators
• On the distinguishability of random quantum states
• Extremal quantum correlations for N parties with two dichotomic observables per site
• Qudit Entanglement
• Security of quantum bit string commitment depends on the information measure
• Bell inequalities and distillability in N-quantum-bit systems
• Bell inequality with an arbitrary number of settings and its applications
• The maximal p-norm multiplicativity conjecture is false
• Deciding separability with a fixed error
• Upper Bound on the region of Separable States near the Maximally Mixed State
• All tight multipartite Bell correlation inequalities for three dichotomic observables per observer

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