New Bell inequalities for three-qubit pure 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.

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.

In this paper the phenomenon of quantum entanglement is studied from its first appearance in the EPR paper(1935). Its historical progress and development is mentioned briefly and the non-locality argument is made by the use of a simplified version of CHSH inequality. In addition, comparison with classical models is made by the use of classical probability theory and using negative probability distribution theory. As conclusion, the need for a quantum mechanical model is discussed with respect to Einstein’s description of reality and locality argument.

Commun. Theor. Phys. 56, 679 (2011)

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states. we find a link to some entanglement measures through some new parameters (amplitudes of coherent states). Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of entanglement by applying the formalism of Horodecki et al.

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.

Physical Review A, 2002

It was shown in Phys. Rev. Lett. 87, 230402 (2001) that N (N ≥ 4) qubits described by a certain one parameter family F of bound entangled states violate Mermin-Klyshko inequality for N ≥ 8. In this paper we prove that the states from the family F violate Bell inequalities derived in Phys. Rev. A56, R1682 (1997), in which each observer measures three non-commuting sets of orthogonal projectors, for N ≥ 7. We also derive a simple one parameter family of entanglement witnesses that detect entanglement for all the states belonging to F. It is possible that these new entanglement witnesses could be generated by some Bell inequalities.

Physical Review A, 2008

Physical Review A, 2010

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.

Physical review letters, 2008

Physical Review Letters, 2003

All the states of N qubits can be classified into N −1 entanglement classes from 2-entangled to Nentangled (fully entangled) states. Each class of entangled states is characterized by an entanglement index that depends on the partition of N . The larger the entanglement index of an state, the more entangled or the less separable is the state in the sense that a larger maximal violation of Bell's inequality is attainable for this class of state.