We show that a maximal violation of the Bell-CHSH inequality for two entangled qubits, i.e., Bell non-locality, is a direct consequence of a local bit erasure by means of a quasi-stochastic process, i.e., a stochastic process in which some transition probabilities are negative.
We investigate the behavior of the maximal violations of the CHSH inequality and Vèrtesi's inequality under the local filtering operations. An analytical method has been presented for general two-qubit systems to compute the maximal violation of the CHSH inequality and the lower bound of the maximal violation of Vértesi's inequality over the local filtering operations. We show by examples that there exist quantum states whose non-locality can be revealed after local filtering operation by the Vértesi's inequality instead of the CHSH inequality.
Abstract Bell non-locality is closely related with device independent quantum randomness. In this paper, we present a kind of sum-of-squares (SOS) decomposition for general Bell inequalities in two qubits systems. By using the obtained SOS decomposition, we can then find the measurement operators associated with the maximal violation of considered Bell inequality. We also practice the SOS decomposition method by considering the (generalized) Clauser-Horne-Shimony-Holt (CHSH) Bell inequality, the Elegant Bell inequality, the Gisin inequality and the Chained Bell inequality as examples. The corresponding SOS decompositions and the measurement operators that cause the maximum violation values of these Bell inequalities are derived, which are consistent with previous results. We further discuss the device independent quantum randomness by using the SOS decompositions of Bell inequalities. We take the generalized CHSH inequality with the maximally entangled state and the Werner state that attaining the maximal violations as examples. Exact value or lower bound on the maximal guessing probability using the SOS decomposition are obtained. For Werner state, the lower bound can supply a much precise estimation of quantum randomness when p tends to 1.
In this paper,we will explore the essence of the phenomenon that state with less entanglement may generate greater Bell violation in the two-qubit Bell tests with CH-type inequalities,i.e.,more nonlocality with less entanglement.We will show that this interesting but counterintuitive phenomenon is caused by the rotational asymmetry of the nonmaximally entangled state in the measurement plane.This asymmetry allows the both-side detection probabilities and the one-side detection probabilities obtain their maximal values with nonmaximally entangled state.But the maximal Bell violation may not always happen on nonmaximally entangled state,because these probabilities will compete with each other,and the Bell violation behaves diferently for various CH-type inequalities.
In this paper, we will explore the essence of the phenomenon that state with less entanglement may generate greater Bell violation in the two-qubit Bell tests with CH-type inequalities, i.e., more nonlocality with less entanglement. We will show that this interesting but counterintuitive phenomenon is caused by the rotational asymmetry of the nonmaximally entangled state in the measurement plane. This asymmetry allows the both-side detection probabilities and the one-side detection probabilities obtain their maximal values with nonmaximally entangled state. But the maximal Bell violation may not always happen on nonmaximally entangled state, because these probabilities will compete with each other, and the Bell violation behaves differently for various CH-type inequalities.
The action of global unitary operations can have intriguing effects on the non-local manifestations of a quantum state. States which do not violate Bell-CHSH inequality, can violate it when transformed by a global unitary. This phenomena assumes significance when one exercises to augment non-local resources(in terms of violation of Bell-CHSH inequality) from these seemingly useless states(i.e., in terms of non-local tasks). However, equally intriguing is the existence of states from which no non-local resource can be generated with a global unitary. The present work confirms the existence of such a set, pertaining to two qubit states. The set exhibits counter intuitive features by containing within it some entangled states which remain Bell-CHSH local on the action of any unitary. Furthermore through an analytic characterization of the set we lay down a generic prescription through which one can operationally identify states which can generate non-local resources under the action of a unitary on the composite system. It has also been shown that our prescription remains valid for any linear Bell inequality.