Entanglement between two macroscopic atomic ensembles induced by measurement on an ancillary light system has proven to be a powerful method for engineering quantum memories and quantum state transfer. Here we investigate the feasibility of such methods for generation, manipulation, and detection of genuine multipartite entanglement ͑Greenberger-Horne-Zeilinger and clusterlike states͒ between mesoscopic atomic ensembles without the need of individual addressing of the samples. Our results extend in a nontrivial way the Einstein-Podolsky-Rosen entanglement between two macroscopic gas samples reported experimentally in ͓B. Julsgaard, A. Kozhekin, and E. Polzik, Nature ͑London͒ 413, 400 ͑2001͔͒. We find that under realistic conditions, a second orthogonal light pulse interacting with the atomic samples, can modify and even reverse the entangling action of the first one leaving the samples in a separable state.

We demonstrate that the Byzantine Agreement (detectable broadcast) is also solvable in the continuous-variable scenario with multipartite entangled Gaussian states and Gaussian operations (homodyne detection). Within this scheme we find that Byzantine Agreement requires a minimum amount of entanglement in the multipartite states used in order to achieve a solution. We discuss realistic implementations of the protocol, which consider the possibility of having inefficient homodyne detectors, not perfectly correlated outcomes, and noise in the preparation of the resource states. The proposed protocol is proven to be robust and efficiently applicable under such non-ideal conditions.

We quantify correlations (quantum and/or classical) between two continuous variable modes in terms of how many correlated bits can be extracted by measuring the sign of two local quadratures. On Gaussian states, such 'bit quadrature correlations' majorize entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, ideal and real de-Gaussified photon-subtracted states, and mixtures of pure Gaussian states, the bit correlations are shown to be a monotonic function of the negativity. This yields a feasible, operational way to quantitatively measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without a full tomographical reconstruction of the Wigner function.PACS numbers: 03.67. Mn, 42.50.Dv Quantum information with continuous variables (CVs), relying on quadrature entanglement as a resource, has witnessed rapid and exciting progresses recently, also thanks to the high degree of experimental control achievable in the context of quantum optics [1]. While Gaussian states (coherent, squeezed, and thermal states) have been originally the preferred resources for both theoretical and practical implementations, a new frontier emerges with non-Gaussian states (Fock states, Schrödinger's cats, ...). The latter can be highly nonclassical, possess in general more entanglement than Gaussian states [2], and are useful to overcome some limitations of the Gaussian framework such as entanglement distillation [3] and universal quantum computation [4]. Therefore, it is of central relevance to provide proper ways to quantify non-Gaussian entanglement in a way which is experimentally accessible.At a fundamental level, the difficulty in the investigation of entanglement -quantum correlations -can be traced back to the subtle task of distinguishing it from classical correlations [5]. Correlations can be regarded as classical if they can be induced onto the subsystems solely by local operations and classical communication, necessarily resulting in a mixed state. On the other hand, if a pure quantum state displays correlations between the subsystems, they are of genuinely quantum nature (entanglement). We adopt here a pragmatic approach: if two systems are in toto correlated, then this correlation has to be retrieved between the outcomes of some local measurements performed on them. We, therefore, investigate quadrature correlations in CV states. We are also motivated by the experimental adequacy: field quadratures can be efficiently measured by homodyne detection, without the need for complete state tomography. Specifically, in this paper, we study optimal correlations in bit strings obtained by digitalizing the outcomes of joint quadrature measurements on a two-mode CV system. First, we apply our procedure to Gaussian states (GS), finding that bit quadrature correlations provide a clearcut quantification of the total correlations between the two modes. They are monotonic with the entanglement on pure states, and can be arbitraril...

to reach a common decision. Classically, there is a bound in the number of possible traitors that can be involved in the game if only classical secure channels are used. In the simplest case where three parties are involved, one of them being a traitor, no classical solution exists. Nevertheless, a quantum solution exist, i.e. letting a traitor being involved and using as a fundamental resource multipartite entanglement it is permitted to reach a common agreement. We demonstrate that detectable broadcast is also solvable within Continuous Variable using multipartite entangled Gaussian states and Gaussian operations (homodyne detection). Furthermore, we show under which premises concerning entanglement content of the state, noise, inefficient homodyne detectors, our protocol is efficient and applicable with present technology. Our results are reported in [2].In chapter 5, we move to the problem of quantification of correlations (quantum and/or classical) between two Continuous Variable modes. We propose to define correlations between the two modes as the maximal number of correlated bits extracted via local quadrature measurements on each mode. On Gaussian states, where entanglement is accessible via their covariance matrix our quantification majorizes entanglement, reducing to an entanglement monotone for pure states. For mixed Gaussian states we provide an operational receipt to quantify explicitly the classical correlations presents in the states. We then address non-Gaussian states with our operational quantification that is based on and up to second moments only in contrast to the exact detection of entanglement that generally involves measurements of high-order moments. For non-Gaussian states, such as photonic Bell states, photon subtracted states and mixtures of Gaussian states, the bit quadrature correlations are shown to be also a monotonic function of the negativity. This quantification yields a feasible, operational way to measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without needing a complete state tomography. Our analysis demonstrates the rather surprising feature that entanglement in the considered non-Guassian examples can thus be detected and experimentally quantified with the same complexity as if dealing with Gaussian states. Our results are reported in [3].In chapter 6, we focus to atomic ensembles described as CV systems. Entanglement between distant mesoscopic atomic ensembles can be induced by measuring an ancillary light system. We show how to generate, manipulate and detect mesoscopic entanglement between an arbitrary number of atomic samples through a quantum non-demolition matter-light interface. Measurement induced entanglement between two macroscopical atomic samples was reported experimentally in 2001. There, the interaction between a single laser pulse propagating through two spatially separated atomic samples combined with a final projective measurement on the light led to the creation of pure EPR entanglement between the two sample...

Abstract. Quantum key distribution (QKD) refers to specific quantum strategies which permit the secure distribution of a secret key between two parties that wish to communicate secretly. Quantum cryptography has proven unconditionally secure in ideal scenarios and has been successfully implemented using quantum states with finite (discrete) as well as infinite (continuous) degrees of freedom. Here, we analyze the efficiency of QKD protocols that use as a resource entangled gaussian states and gaussian operations only. In this framework, it has already been shown that QKD is possible [1] but the issue of its efficiency has not been considered. We propose a figure of merit (the efficiency E) to quantify the number of classical correlated bits that can be used to distill a key from a sample of N entangled states. We relate the efficiency of the protocol to the entanglement and purity of the states shared between the parties.