Teleportation versus Bell's inequalities. What is nonlocality?

Ryszard Horodecki, Michał Horodecki, Paweł Horodecki

Sandu Popescu

The nonlocality responsible for violations of Bell's inequalities is not equivalent to that used in teleportation, although they probably are two aspects of the same physical property. There are mixed states which do not violate any Bell type inequality, but still can be used for teleportation.

MM Ettefaghi, N Pour-Rahimi

The violation of Bell’s inequality in quantum mechanics implies that there exist nonlocality and entanglement. When the density matrix of a composite system cannot be written as a convex combination of the product of the density matrices of its subsystems, we say there exists entanglement. For pure states, the existence of entanglement always leads to the violation of Bell’s inequality. However, in the case of the mixed states, there may be entanglement, but Bell's inequality is not violated and in other words, the nonlocality is not manifested. In addition to Bell's inequality, quantum teleportation is also a manifestation of nonlocality. Quantum teleportation using entangled states is more successful than quantum teleportation with separable states. Therefore, the corresponding fidelity of teleported state with the initial state (in short, the fidelity) of the former is always greater than the fidelity of the latter. In this paper, for Werner's state, we will show that in a range of the related parameter, while the CHSH inequality is violated, the fidelity, which indicates the amount of success of quantum teleportation, is lower than the upper bound of the corresponding fidelity for states that can be simulated with a local hidden variable theory. Meanwhile, we will see that for Gisin's state with hidden nonlocality, filtering, which leads to the appearance of nonlocality and more specifically leads to the violation of the CHSH inequality, also increases the fidelity.

Peter Rastall

Jia-Qiang Zhao, Cao Lian-Zhen, Lu Huai-Xin +1 more

In this paper, we theoretically study the relation between concurrence and nonlocality depicted by Bell-type inequality violation of quantum mechanics prediction versus local realism prediction for the GHZ (Greenberger -Horne-Zeilinger) class states. Analytical expressions of concurrence, violations of the Mermin inequality and the Svetlichny inequality are obtained. Through numerical calculations, the relationship between entanglement and nonlocality of GHZ-class states is discussed. Our results show that the concurrence is consistent with the degree of nonlocality described by violations of the two Bell-type inequalities of GHZ-class states. The Bell operator and its parameters can obviously reveal the nonlocal features of quantum states.