Analytical proof of Gisin’s theorem for three qubits (original) (raw)
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Complete proof of Gisin's theorem for three qubits
2009
Gisin's theorem assures that for any pure bipartite entangled state, there is violation of Bell-CHSH inequality revealing its contradiction with local realistic model. Whether, similar result holds for three-qubit pure entangled states, remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy's non-locality argument.
Bell-CHSH inequalities and non-locality of pure symmetric three-qubit States
2020
We explore non-locality of three-qubit pure symmetric states using the Clauser-Horne-Shimony-Holt (CHSH) inequality. We show that reduced two qubit density matrices, extracted from any arbitrary pure entangled symmetric three qubit state, do not violate the CHSH inequality and hence, are CHSH-local. However, conditional CHSH inequalities are useful in bringing out nonlocal features of two qubit correlations recorded by Alice and Bob, when there is a conditioning based on the outcomes of Charlie's measurement on his qubit.
Gisin's Theorem for Three Qubits
Physical Review Letters, 2004
We present a Theorem that all generalized Greenberger-Horne-Zeilinger states of a three-qubit system violate a Bell inequality in terms of probabilities. All pure entangled states of a three-qubit system are shown to violate a Bell inequality for probabilities; thus, one has Gisin's theorem for three qubits.
Information and Computation
We show that all n-qubit entangled states, with the exception of tensor products of single-qubit and bipartite maximally-entangled states, admit Hardy-type proofs of non-locality without inequalities or probabilities. More precisely, we show that for all such states, there are local, one-qubit observables such that the resulting probability tables are logically contextual in the sense of Abramsky and Brandenburger, this being the general form of the Hardy-type property. Moreover, our proof is constructive: given a state, we show how to produce the witnessing local observables. In fact, we give an algorithm to do this. Although the algorithm is reasonably straightforward, its proof of correctness is non-trivial. A further striking feature is that we show that n + 2 local observables suffice to witness the logical contextuality of any n-qubit state: two each for two for the parties, and one each for the remaining n − 2 parties.
Entangled qutrits violate local realism stronger than qubits-an analytical proof
2001
In Kaszlikowski et al. [Phys. Rev. Lett. 85, 4418 (2000)], it has been shown numerically that the violation of local realism for two maximally entangled N -dimensional (3 ≤ N ) quantum objects is stronger than for two maximally entangled qubits and grows with N . In this paper we present the analytical proof of this fact for N = 3.
Nonlocality without inequalities for almost all entangled states for two particles
Physical Review Letters, 1994
It is shown that it is possible to rule out all local and stochastic hidden variable models accounting for the quantum mechanical predictions implied by almost any entangled quantum state vector of any number of particles whose Hilbert spaces have arbitrary dimensions, without resorting to Belltype inequalities. The present proof makes use of the mathematically precise notion of Bell locality and it involves only simple set theoretic arguments.
Do All Pure Entangled States Violate Bell’s Inequalities for Correlation Functions?
Physical Review Letters, 2002
Any pure entangled state of two particles violates a Bell inequality for two-particle correlation functions (Gisin's theorem). We show that there exist pure entangled N > 2 qubit states that do not violate any Bell inequality for N particle correlation functions for experiments involving two dichotomic observables per local measuring station. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description.