Using macroscopic entanglement to close the detection loophole in Bell-inequality tests

We consider a Bell-like inequality performed using various instances of multiphoton entangled states to demonstrate that losses occurring after the unitary transformations used in the nonlocality test can be counteracted by enhancing the size of such entangled states. In turn, this feature can be used to overcome detection inefficiencies affecting the test itself: a slight increase in the size of such states, pushing them towards a more macroscopic form of entanglement, significantly improves the state robustness against detection inefficiency, thus easing the closing of the detection loophole. Differently, losses before the unitary transformations cause decoherence effects that cannot be compensated using macroscopic entanglement.

Bitwise bell-inequality violations for an entangled state involving 2N ions

Following on from previous work [J.-A. Larsson, Phys. Rev. A 67, 022108 (2003)], Bell inequalities based on correlations between binary digits are considered for a particular entangled state involving 2N trapped ions. These inequalities involve applying displacement operations to half of the ions and then measuring correlations between pairs of corresponding bits in the binary representations of the number of center-of-mass phonons of N particular ions. It is shown that the state violates the inequalities and thus displays nonclassical correlations. It is also demonstrated that it violates a Bell inequality when the displacements are replaced by squeezing operations.

Better Bell-inequality violation by collective measurements

The standard Bell-inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a Bell inequality by making collective measurements. We show that the nonlocality of bipartite pure entangled states, quantified by their maximal violation of the Bell-Clauser-Horne inequality, can always be enhanced by collective measurements, even without communication between the parties. For mixed states we also show that collective measurements can increase the violation of Bell inequalities, although numerical evidence suggests that the phenomenon is not common as it is for pure states.

Greenberger-Horne-Zeilinger-type and W-type entangled coherent states: Generation and Bell-type inequality tests without photon counting

We study Greenberger-Horne-Zeilinger-type (GHZ-type) and W-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for W-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate W-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the W-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.

Joint measurements and Bell inequalities

Joint quantum measurements of noncommuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the measurement. This fact suggests that there may be a link with Bell inequalities, as these will be satisfied if and only if a joint probability distribution for all involved observables exists. We investigate the connections between Bell inequalities and conditions for joint quantum measurements to be possible. Mermin's inequality for the three-particle Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition for a joint measurement on two out of the three quantum systems to exist. Gisin's Bell inequality for three coplanar measurement directions, meanwhile, is shown to be less strict than the condition for the corresponding joint measurement.

Influence of detector motion in Bell inequalities with entangled fermions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bell inequalities for K-0(K)over-bar(0) pairs from Phi-resonance decays

We analyze the premises of recent propositions to test local realism via the Bell inequalities using neutral kaons from φ resonance decays as entangled Einstein-Podolsky-Rosen pairs. We pay special attention to the derivation of the Bell inequalities, or related expressions, for unstable and oscillating kaon quasispin states and to the possibility of the actual identification of these states through their associated decay modes. We discuss an indirect method to extract probabilities to find these states by combining experimental information with theoretical input. However, we still find inconsistencies in previous derivations of the Bell inequalities. We show that the identification of the quasispin states via their associated decay mode does not allow the free choice to perform different tests on them, a property which is crucial to establish the validity of any Bell inequality in the context of local realism. In view of this we propose a different kind of Bell inequality in which the free choice or adjustability of the experimental setup is guaranteed. We also show that the proposed inequalities are violated by quantum mechanics. ©1999 The American Physical Society.

Testing for the non-separability of bi-ambiguous compounds

Separability is a concept that is very difficult to define, and yet much of our scientific method is implicitly based upon the assumption that systems can sensibly be reduced to a set of interacting components. This paper examines the notion of separability in the creation of bi-ambiguous compounds that is based upon the CHSH and CH inequalities. It reports results of an experiment showing that violations of the CHSH and CH inequality can occur in human conceptual combination.

Testing genuine multipartite nonlocality in phase spacea

We demonstrate genuine three-mode nonlocality based on phase-space formalism. A Svetlichny-type Bell inequality is formulated in terms of the s-parametrized quasiprobability function. We test such a tool using exemplary forms of three-mode entangled states, identifying the ideal measurement settings required for each state. We thus verify the presence of genuine three-mode nonlocality that cannot be reproduced by local or nonlocal hidden variable models between any two out of three modes. In our results, GHZ- and W-type nonlocality can be fully discriminated. We also study the behavior of genuine tripartite nonlocality under the effects of detection inefficiency and dissipation induced by local thermal environments. Our formalism can be useful to test the sharing of genuine multipartite quantum correlations among the elements of some interesting physical settings, including arrays of trapped ions and intracavity ultracold atoms. DOI: 10.1103/PhysRevA.87.022123

Nonlocality of two- and three-mode continuous variable systems

We address the nonlocality of fully inseparable three-mode Gaussian states generated either by bilinear three-mode Hamiltonians or by a sequence of bilinear two-mode Hamiltonians. Two different tests revealing nonlocality are considered, in which the dichotomic Bell operator is represented by the displaced parity and by the pseudospin operator respectively. Three-mode states are also considered as a conditional source of two-mode non-Gaussian states, whose nonlocality properties are analysed. We found that the non-Gaussian character of the conditional states allows violation of Bell's inequalities (by parity and pseudospin tests) stronger than with a conventional twin-beam state. However, the non-Gaussian character is not sufficient to reveal nonlocality through a dichotomized quadrature measurement strategy.

Tests of multimode quantum nonlocality with homodyne measurements

We investigate the violation of local realism in Bell tests involving homodyne measurements performed on multimode continuous-variable states. By binning the measurement outcomes in an appropriate way, we prove that the Mermin-Klyshko inequality can be violated by an amount that grows exponentially with the number of modes. Furthermore, the maximum violation allowed by quantum mechanics can be attained for any number of modes, albeit requiring a quantum state whose generation is hardly practicable. Interestingly, this exponential increase of the violation holds true even for simpler states, such as multipartite GHZ states. The resulting benefit of using more modes is shown to be significant in practical multipartite Bell tests by analyzing the increase of the robustness to noise with the number of modes. In view of the high efficiency achievable with homodyne detection, our results thus open a possible way to feasible loophole-free Bell tests that are robust to experimental imperfections. We provide an explicit example of a three-mode state (a superposition of coherent states) which results in a significantly high violation of the Mermin-Klyshko inequality (around 10%) with homodyne measurements.

Experimental linear-optics simulation of multipartite non-locality in the ground state of a quantum Ising ring

Critical phenomena involve structural changes in the correlations of its constituents. Such changes can be reproduced and characterized in quantum simulators able to tackle medium-to-large-size systems. We demonstrate these concepts by engineering the ground state of a three-spin Ising ring by using a pair of entangled photons. The effect of a simulated magnetic field, leading to a critical modification of the correlations within the ring, is analysed by studying two- and three-spin entanglement. In particular, we connect the violation of a multipartite Bell inequality with the amount of tripartite entanglement in our ring.

Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

Influence of detector motion in entanglement measurements with photons

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)