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arXiv:1203.0211 · Physical Review A

Nonlocality activation in entanglement-swapping chains

Waldemar Kłobus, Wiesław Laskowski, Marcin Markiewicz, Andrzej Grudka

Published Aug 2, 2012• 29 citations
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Abstract

We consider multiple entanglement swappings performed on a chain of bipartite states. Each state does not violate Clauser-Horne-Shimony-Holt (CHSH) inequality. We show that before some critical number of entanglement swappings is achieved the output state does not violate this inequality either. However, if this number is achieved, then for some results of Bell measurements obtained in the protocol of entanglement swapping the output state violates CHSH inequality. Moreover, we show that for different states we have different critical numbers for which CHSH inequality is activated.

DOI
10.1103/physreva.86.020302

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We consider multiple entanglement swappings performed on a chain of bipartite states. Each state does not violate Clauser-Horne-Shimony-Holt (CHSH) inequality. We show that before some critical number of entanglement swappings is achieved the output state does not violate this inequality either. However, if this number is achieved, then for some results of Bell measurements obtained in the protocol of entanglement swapping the output state violates CHSH inequality. Moreover, we show that for different states we have different critical numbers for which CHSH inequality is activated.
One of the most significant and well-known properties of entangled states is that they may lead to violations of Bell inequalities and are thus inconsistent with any local-realistic theory. However, there are entangled states that cannot violate any Bell inequality, and in general the precise relationship between entanglement and observable nonlocality is not well understood. We demonstrate that a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality can be demonstrated in a certain kind of Bell experiment for all entangled states. Our proof of the result consists of two main steps. We first provide a simple characterization of the set of states that do not violate the CHSH inequality even after general local operations and classical communication. Second, we prove that for each entangled state sigma, there exists another state rho not violating the CHSH inequality, such that rhomultiply sign in circlesigma violates the CHSH inequality.
We find two two-qubit bipartite states ${\ensuremath{\rho}}_{1},{\ensuremath{\rho}}_{2}$ such that arbitrarily many copies of one or the other cannot exhibit nonlocal correlations in a two-setting--two-outcome Bell scenario. However, the bipartite state ${\ensuremath{\rho}}_{1}\ensuremath{\bigotimes}{\ensuremath{\rho}}_{2}$ violates the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).] by an amount of 2.023. We also identify a CHSH-local state $\ensuremath{\rho}$ such that ${\ensuremath{\rho}}^{\ensuremath{\bigotimes}2}$ is CHSH inequality-violating. The tools employed can be easily adapted to find instances of nonlocality activation in arbitrary Bell scenarios.
It is well-known that in certain scenarios weakly entangled states can generate stronger nonlocal effects than their maximally entangled counterparts. In this paper, we consider violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality when one party has inefficient detectors, a scenario known as an asymmetric Bell experiment. For any fixed detection efficiency, we derive a simple upper bound on the entanglement needed to violate the inequality by more than some specified amount $\ensuremath{\kappa}\ensuremath{\ge}0$. When $\ensuremath{\kappa}=0$, the amount of entanglement in all states violating the inequality goes to zero as the detection efficiency approaches 5050%50 from above. We finally consider the scenario in which detection inefficiency arises for only one choice of local measurement. In this case, it is shown that the CHSH inequality can always be violated for any nonzero detection efficiency and any choice of noncommuting measurements.
Abstract The Clauser–Horne–Shimony–Holt (CHSH) inequality test is widely used as a mean of invalidating the local deterministic theories. Most attempts to experimentally test nonlocality have presumed unphysical idealizations that do not hold in real experiments, namely, noiseless measurements. We demonstrate an experimental violation of the CHSH inequality that is free of idealization and rules out local models with high confidence. We show that the CHSH inequality can always be violated for any nonzero noise parameter of the measurement. Intriguingly, less entanglement exhibits more nonlocality in the CHSH test with noisy measurements. Furthermore, we theoretically propose and experimentally demonstrate how the CHSH test with noisy measurements can be used to detect weak entanglement on two-qubit states. Our results offer a deeper insight into the relation between entanglement and nonlocality.
We propose and experimentally implement an efficient procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995)] and the fully entangled fraction of Bennett et al. [Phys. Rev. A 54, 3824 (1996)] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. This is an experimental determination of these quantities without quantum state tomography or continuous monitoring of all measurement bases in the usual CHSH inequality tests. We analyze how well the measured degrees of Bell nonlocality and other entanglement witnesses (including the fully entangled fraction and a nonlinear entropic witness) of an arbitrary two-qubit state can estimate its entanglement. In particular, we measure these witnesses and estimate the negativity of various two-qubit Werner states. Our approach could especially be useful for quantum communication protocols based on entanglement swapping.
We explore nonlocality of three-qubit pure symmetric states shared between Alice, Bob and Charlie using the Clauser-Horne-Shimony-Holt (CHSH) inequality. We show that the reduced two-qubit states, extracted from an arbitrary pure entangled symmetric three-qubit state, do not violate the CHSH inequality and hence they are CHSH-local . However, when Alice and Bob perform the CHSH test, after conditioning over measurement results of Charlie, nonlocality of the state is revealed. It is also shown that two different classes of three-qubit pure symmetric states, consisting of two and three distinct constituent spinors (qubits) respectively, can be distinguished through the conditional CHSH non-locality test.