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.

Accumulation of entanglement in a continuous variable memory

We study entanglement accumulation in a memory built out of two continuous variable systems interacting with a qubit that mediates their indirect coupling. We show that, in contrast with the case of bidimensional Hilbert spaces, entanglement superior to one ebit can be accumulated in the memory, even though no entangled resource is used. The protocol is immediately implementable and we assess the role of the main imperfections.

Correspondence between continuous-variable and discrete quantum systems of arbitrary dimensions

We establish a mapping between a continuous-variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite-dimensional Hilbert space and thus can be considered as a universal resource of entanglement. An explicit example of the map and a proposal for its experimental realization are discussed.

Towards variance-matrix characterization of complementarity relations in a continuous variable system

We discuss complementarity relations in a bipartite continuous variable system. Building up from the work done on discrete d-dimensional systems, we prove that for symmetric two-mode states, quantum complementarity relations can be put in a simple relation with the elements of the variance matrix. When this condition is not satisfied, such a connection becomes non-trivial. Our investigation is the first step towards an operative characterization of the complementarity in a scenario that has not been investigated so far.

Gapped Two-Body Hamiltonian for Continuous-Variable Quantum Computation

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv) possess a constant energy gap proportional to the squared inverse of the squeezing. Their ground states are the celebrated Gaussian graph states, which are universal resources for quantum computation in the limit of infinite squeezing. These Hamiltonians constitute the basic ingredient for the adiabatic preparation of graph states and thus open new venues for the physical realization of continuous-variable quantum computing beyond the standard optical approaches. We characterize the correlations in these systems at thermal equilibrium. In particular, we prove that the correlations across any multipartition are contained exactly in its boundary, automatically yielding a correlation area law. © 2011 American Physical Society.

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.

Experimentally realizable characterizations of continuous- variable Gaussian states

Measures of entanglement, fidelity, and purity are basic yardsticks in quantum-information processing. We propose how to implement these measures using linear devices and homodyne detectors for continuous-variable Gaussian states. In particular, the test of entanglement becomes simple with some prior knowledge that is relevant to current experiments.

Testing quantum contextuality of continuous-variable states

We investigate the violation of noncontextuality by a class of continuous-variable states, including variations of entangled coherent states and a two-mode continuous superposition of coherent states. We generalize the Kochen-Specker (KS) inequality discussed by Cabello [A. Cabello, Phys. Rev. Lett. 101, 210401 (2008)] by using effective bidimensional observables implemented through physical operations acting on continuous-variable states, in a way similar to an approach to the falsification of Bell-Clauser-Horne-Shimony-Holt inequalities put forward recently. We test for state-independent violation of KS inequalities under variable degrees of state entanglement and mixedness. We then demonstrate theoretically the violation of a KS inequality for any two-mode state by using pseudospin observables and a generalized quasiprobability function.

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.

Driven optomechanical systems for mechanical entanglement distribution

We consider the distribution of entanglement from a multimode optical driving source to a network of remote and independent optomechanical systems. By focusing on the tripartite case, we analyse the effects that the features of the optical input states have on the degree and sharing structure of the distributed, fully mechanical, entanglement. This study, which is conducted looking at the mechanical steady state, highlights the structure of the entanglement distributed among the nodes and determines the relative efficiency between bipartite and tripartite entanglement transfer. We discuss a few open points, some of which are directed towards the bypassing of such limitations.

Controllable Gaussian-Qubit Interface for Extremal Quantum State Engineering

We study state engineering through bilinear interactions between two remote qubits and two-mode Gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode Gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode Gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, which can be realized in realistic matter-light scenarios.

Classical and quantum aspects of multimode parametric interactions

Parametric interactions in nonlinear crystals represent a powerful tool in the optical manipulation of information, both in the classical and the quantum regime. Here, we analyze in detail classical and quantum aspects of three-and five-mode parametric interactions in chi(2) nonlinear crystals. The equations of motion are explicitly derived and then solved within the parametric approximation. We describe several applications, including holography, all-optical gates, generation of entanglement, and telecloning. Experimental results on the photon distributions and correlations of the generated beams are also reported and discussed.

Multimode entanglement and telecloning in a noisy environment

We address the generation, propagation, and application of multipartite continuous variable entanglement in a noisy environment. In particular, we focus our attention on the multimode entangled states achievable by second-order nonlinear crystals-i.e., coherent states of the SU(m,1) group-which provide a generalization of the twin-beam state of a bipartite system. The full inseparability in the ideal case is shown, whereas thresholds for separability are given for the tripartite case in the presence of noise. We find that entanglement of tripartite states is robust against thermal noise, both in the generation process and during propagation. We then consider coherent states of SU(m,1) as a resource for multipartite distribution of quantum information and analyze a specific protocol for telecloning, proving its optimality in the case of symmetric cloning of pure Gaussian states. We show that the proposed protocol also provides the first example of a completely asymmetric 1 -> m telecloning and derive explicitly the optimal relation among the different fidelities of the m clones. The effect of noise in the various stages of the protocol is taken into account, and the fidelities of the clones are analytically obtained as a function of the noise parameters. In turn, this permits the optimization of the telecloning protocol, including its adaptive modifications to the noisy environment. In the optimized scheme the clones' fidelity remains maximal even in the presence of losses (in the absence of thermal noise), for propagation times that diverge as the number of modes increases. In the optimization procedure the prominent role played by the location of the entanglement source is analyzed in details. Our results indicate that, when only losses are present, telecloning is a more effective way to distribute quantum information than direct transmission followed by local cloning.

Geometrical characterization of non-Markovianity

We introduce a tool for the quantitative characterization of the departure from Markovianity of a given dynamical process. Our tool can be applied to a generic N-level system and extended straightforwardly to Gaussian continuous-variable systems. It is linked to the change of the volume of physical states that are dynamically accessible to a system and provides qualitative expectations in agreement with some of the analogous tools proposed so far. We illustrate its predictive power by tackling a few canonical examples.