Quantum nonlocality test for continuous-variable states with dichotomic observables

There have been theoretical and experimental studies on quantum nonlocality for continuous variables, based on dichotomic observables. In particular, we are interested in two cases of dichotomic observables for the light field of continuous variables: One case is even and odd numbers of photons and the other case is no photon and the presence of photons. We analyze various observables to give the maximum violation of Bell's inequalities for continuous-variable states. We discuss an observable which gives the violation of Bell's inequality for any entangled pure continuous-variable state. However, it does not have to be a maximally entangled state to give the maximal violation of Bell's inequality. This is attributed to a generic problem of testing the quantum nonlocality of an infinite- dimensional state using a dichotomic observable.

d-outcome measurement for a nonlocality test

For the purpose of a nonlocality test, we propose a general correlation observable of two parties by utilizing local d- outcome measurements with SU(d) transformations and classical communications. Generic symmetries of the SU(d) transformations and correlation observables are found for the test of nonlocality. It is shown that these symmetries dramatically reduce the number of numerical variables, which is important for numerical analysis of nonlocality. A linear combination of the correlation observables, which is reduced to the Clauser- Home-Shimony-Holt (CHSH) Bell's inequality for two outcome measurements, leads to the Collins-Gisin-Linden-Massar-Popescu (CGLMP) nonlocality test for d-outcome measurement. As a system to be tested for its nonlocality, we investigate a continuous- variable (CV) entangled state with d measurement outcomes. It allows the comparison of nonlocality based on different numbers of measurement outcomes on one physical system. In our example of the CV state, we find that a pure entangled state of any degree violates Bell's inequality for d(greater than or equal to2) measurement outcomes when the observables are of SU(d) transformations.

Quantum nonlocality for a mixed entangled coherent state

Quantum nonlocality is tested for an entangled coherent state, interacting with a dissipative environment. A pure entangled coherent state violates Bell's inequality regardless of its coherent amplitude. The higher the initial nonlocality, the more rapidly quantum nonlocality is lost. The entangled coherent state can also be investigated in the framework of 2x2 Hilbert space. The quantum nonlocality persists longer in 2x2 Hilbert space. When it decoheres it is found that the entangled coherent state fails the nonlocality test, which contrasts with the fact that the decohered entangled state is always entangled.

Greenberger-Horne-Zeilinger nonlocality in arbitrary even dimensions

We generalize Greenberger-Horne-Zeilinger (GHZ) nonlocality to every even-dimensional and odd-partite system. For the purpose we employ concurrent observables that are incompatible and nevertheless have a common eigenstate. It is remarkable that a tripartite system can exhibit the genuinely high-dimensional GHZ nonlocality.

Genuine multipartite nonlocality of entangled thermal states

We assess quantum nonlocality of multiparty entangled thermal states by studying, quantitatively, both tripartite and quadripartite states belonging to the Greenberger-Horne-Zeilinger, W, and linear cluster-state classes and showing violation of relevant Bell-like inequalities. We discuss the conditions for maximizing the degree of violation against the local thermal character of the states and the inefficiency of the detection apparatuses. We demonstrate that such classes of multipartite entangled states can be made to last quite significantly, notwithstanding adverse operating conditions. This opens up the possibility for coherent exploitation of multipartite quantum channels made out of entangled thermal states. Our study is accompanied by a detailed description of possible generation schemes for the states analyzed.

Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality

All-optical signal processing enables modulation and transmission speeds not achievable using electronics alone(1,2). However, its practical applications are limited by the inherently weak nonlinear effects that govern photon-photon interactions in conventional materials, particularly at high switching rates(3). Here, we show that the recently discovered nonlocal optical behaviour of plasmonic nanorod metamaterials(4) enables an enhanced, ultrafast, nonlinear optical response. We observe a large (80%) change of transmission through a subwavelength thick slab of metamaterial subjected to a low control light fluence of 7 mJ cm(-2), with switching frequencies in the terahertz range. We show that both the response time and the nonlinearity can be engineered by appropriate design of the metamaterial nanostructure. The use of nonlocality to enhance the nonlinear optical response of metamaterials, demonstrated here in plasmonic nanorod composites, could lead to ultrafast, low-power all-optical information processing in subwavelength-scale devices.

Multipartite nonlocality in a thermalized Ising spin chain

We study multipartite correlations and nonlocality in an isotropic Ising ring under transverse magnetic field at both zero and finite temperature. We highlight parity-induced differences between the multipartite Bell-like functions used in order to quantify the degree of nonlocality within a ring state and reveal a mechanism for the passive protection of multipartite quantum correlations against thermal spoiling effects that is clearly related to the macroscopic properties of the ring model.

Tripartite nonlocality and continuous-variable entanglement in thermal states of trapped ions

We study a system of three trapped ions in an anisotropic bidimensional trap. By focusing on the transverse modes of the ions, we show that the mutual ion-ion Coulomb interactions set entanglement of a genuine tripartite nature, to some extent persistent to the thermal nature of the vibronic modes. We tackle this issue by addressing a nonlocality test in the phase space of the ionic system and quantifying the genuine residual tripartite entanglement in the continuous variable state of the transverse modes.

Non-Markovian effects on the nonlocality of a qubit-oscillator system

Non-Markovian evolutions are responsible for a wide variety of physically interesting effects. Here, we study nonlocality of the nonclassical state of a system consisting of a qubit and an oscillator exposed to the effects of non-Markovian evolutions. We find that the different facets of non-Markovianity affect nonlocality in different and nonobvious ways, ranging from pronounced insensitivity of the Bell function to quite spectacular evidence of information kickback.

Effect of spatial nonlocality on the density functional band gap

We show that for a large class of exchange-correlation functionals the local exchange-correlation potential obtained within an optimized effective potential severely underestimates the band gap. On the other hand, the corresponding nonlocal potential obtained from a generalized Kohn-Sham scheme provides a much better description of the band gap, in good agreement with experiments. These results strongly indicate that a local exchange-correlation potential, however good the exchange-correlation approximation, cannot capture the delicate interplay between correlation effects and spatial localization in the KS band structure, unless the (cumbersome) contribution from the derivative discontinuity of the exchange-correlation energy functional is considered.

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.

More nonlocality with less entanglement in a tripartite atom-optomechanical system

Quantum effects in hybrid atomic optomechanics in a system comprising a cloud of atoms and a mobile mirror mediated by a single-mode cavity are studied. Tripartite non-locality is observed in the atom-light-mirror system, as demonstrated by the violation of the Mermin-Klyshko (MK) inequality. It has been shown [C. Genes, et al., PRA 77, 050307 (R) (2008)] that tripartite entanglement is optimized when the cavity is resonant with the anti-Stokes sideband of the driving laser and the atomic frequency matches the Stokes one. However, we show that this is not the case for the nonlocality. The MK function achieves minima when the atoms are resonant with both the Stokes and anti-Stokes sidebands, and unexpectedly, we find violation of the MK inequality only in a parameter region where entanglement is far from being maximum. A negative relation exists between nonlocality and entanglement with consideration of the possibility of bipartite nonlocality in the violation of the MK inequality. We also study the non-classicality of the mirror by post-selected measurements, e.g. Geiger-like detection, on the cavity and/or the atoms. We show that with feasible parameters Geiger-like detection on the atoms can effectively induce mechanical non-classicality.