Hidden Nonlocality Research Articles

Nonlocality, entanglement and quantum teleportation for mixed spin-1/2 states

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.

Signaling between time steps does not allow for nonlocality beyond hidden nonlocality

Hidden nonlocality is the phenomenon that entangled states can be local in the standard Bell scenario but display nonlocality after local filtering. However, there exist entangled states for which all measurement statistics can be described via a local hidden variable model even after local filtering. In this work we consider the scenario that measurement outcomes and settings of Alice can influence measurements of Bob in subsequent time steps (and vice versa), however, there is no signaling among them for measurements at the same time step. We show that in this scenario states that only display local statistics after local filtering remain local even when considering the complete statistics of arbitrary sequences and therefore no advantage can be gained by performing longer sequences in this scenario. We first determine the extreme points of the polytope defined by the no-signaling conditions within the same time step and the arrow-of-time constraints. Based on these results we introduce a notion of locality and provide a complete representation of the corresponding local polytope in terms of inequalities in the simplest scenario. These results imply that in the scenario considered here there is no nonlocality beyond hidden nonlocality. We further propose a device-dependent Schmidt number witness and we compare our finding to known local models in the sequential scenario.

On the Activation of Quantum Nonlocality

<p>We report on some quantum properties of physical systems, namely, entanglement, nonlocality, k-copy nonlocality (superactivation of nonlocality), hidden nonlocality (activation of nonlocality through local filtering) and the activation of nonlocality through tensoring and local filtering. The aim of this work is two-fold. First, we provide a review of the numerical procedures that must be followed in order to calculate the aforementioned properties, in particular, for any two-qubit system, and reproduce the bounds for two-qudit Werner states. Second, we use such numerical tools to calculate new bounds of these properties for two-qudit Isotropic states and two-qubit Hirsch states.</p>

Nonlocality in sequential correlation scenarios

As first shown by Popescu (1995 Phys. Rev. Lett. 74 2619), some quantum states only reveal their nonlocality when subjected to a sequence of measurements while giving rise to local correlations in standard Bell tests. Motivated by this manifestation of ‘hidden nonlocality’ we set out to develop a general framework for the study of nonlocality when sequences of measurements are performed. Similar to Gallego et al (2013 Phys. Rev. Lett. 109 070401) our approach is operational, i.e. the task is to identify the set of allowed operations in sequential correlation scenarios and define nonlocality as the resource that cannot be created by these operations. This leads to a characterization of sequential nonlocality that contains as particular cases standard nonlocality and hidden nonlocality.

Experimental Entanglement Distillation of Two-Qubit Mixed States under Local Operations

We experimentally demonstrate optimal entanglement distillation from two forms of two-qubit mixed states under local filtering operations according to the constructive method introduced by [F. Verstraete, Phys. Rev. A 64, 010101(R) (2001)10.1103/PhysRevA.64.010101]. In principle, our setup can be easily applied to distilling entanglement from arbitrary two-qubit partially mixed states. We also test the violation of the Clauser-Horne-Shinmony-Holt inequality for the distilled state from the first form of mixed state to show its "hidden nonlocality."

Generalized quantum measurements and local realism

The structure of a local hidden variable model for experiments involving sequences of measurements rigorously is analyzed. Constraints imposed by local realism on the conditional probabilities of the outcomes of such measurement schemes are explicitly derived. The violation of local realism in the case of ``hidden nonlocality'' is illustrated by an operational example.