Alessio Serafini

Distributed quantum computation via optical fibers

We investigate the possibility of realizing effective quantum gates between two atoms in distant cavities coupled by an optical fiber. We show that highly reliable swap and entangling gates are achievable. We exactly study the stability of these gates in the presence of imperfections in coupling strengths and interaction times and prove them to be robust. Moreover, we analyze the effect of spontaneous emission and losses and show that such gates are very promising in view of the high level of coherent control currently achievable in optical cavities.

Extremal entanglement and mixedness in continuous variable systems

ness provided by such measures with the one provided by the purity (defined as tr 2 for the state ) for generic n-mode states. We then review the analysis proving the existence of both maximally and minimally entangled states at given global and marginal purities, with the entan glement quantified by the logarithmic negativity. Based on these results, we extend such an analysis to generalized entropies, introducing and fully characterizing maximally and minimally entangled states for given global and local generalized entropies. We compare the different roles played by the purity and by the generalized p-entropies in quantifying the entanglement and the mixedness of continuous variable systems. We introduce the concept of average logarithmic negativity, showing that it allows a reliable quantitative estimate of continuo us variable entanglement by direct measurements of global and marginal generalized p-entropies.

Entanglement of two-mode Gaussian states : characterization and experimental production and manipulation

A powerful theoretical structure has emerged in recent years on the characterization and quantification of entanglement in continuous-variable systems. After reviewing this framework, we will illustrate it with an original set-up based on a type-II OPO (optical parametric oscillator) with adjustable mode coupling. Experimental results allow a direct verification of many theoretical predictions and provide a sharp insight into the general properties of two-mode Gaussian states and entanglement resource manipulation.

Quantum memory for entangled continuous-variable states

A quantum memory for light is a key element for the realization of future quantum information networks. Requirements for a good quantum memory are (i) versatility (allowing a wide range of inputs) and (ii) true quantum coherence (preserving quantum information). Here we demonstrate such a quantum memory for states possessing Einstein-Podolsky-Rosen (EPR) entanglement. These multi-photon states are two-mode squeezed by 6.0 dB with a variable orientation of squeezing and displaced by a few vacuum units. This range encompasses typical input alphabets for a continuous variable quantum information protocol. The memory consists of two cells, one for each mode, filled with cesium atoms at room temperature with a memory time of about 1msec. The preservation of quantum coherence is rigorously proven by showing that the experimental memory fidelity 0.52(2) significantly exceeds the benchmark of 0.45 for the best possible classical memory for a range of displacements.

Measuring Gaussian quantum information and correlations using the Rényi entropy of order 2.

We demonstrate that the Rényi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of the state. We prove that, in the Gaussian scenario, such an entropy satisfies the strong subadditivity inequality, a key requirement for quantum information theory. This allows us to define and analyze measures of Gaussian entanglement and more general quantum correlations based on such an entropy, which are shown to satisfy relevant properties such as monogamy.

Symplectic invariants, entropic measures and correlations of Gaussian states

We present a derivation of the Von Neumann entropy and mutual information of arbitrary two-mode Gaussian states, based on the explicit determination of the symplectic eigenvalues of a generic covariance matrix. The key role of the symplectic invariants in such a determination is pointed out. We show that the Von Neumann entropy depends on two symplectic invariants, while the purity (or the linear entropy) is determined by only one invariant, so that the two quantities provide two different hierarchies of mixed Gaussian states. A comparison between mutual information and entanglement of formation for symmetric states is considered, taking note of the crucial role of the symplectic eigenvalues in qualifying and quantifying the correlations present in a generic state.

Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence

We present a complete analysis of multipartite entanglement of three-mode Gaussian states of continuous variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed threemode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the gen eral Araki-Lieb inequality. Quantum correlations can be quantified by a proper convex roof extension of the squared logarithmic negativity, the continuous-variable tangle, or contangle. We review and elucidate in detail the proof that in multimode Gaussian states the contangle satisfies a monogamy inequality constraint [G. Adesso and F. Illuminati, New J. Phys. 8, 15 (2006)]. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communication and defines a measur e of genuine tripartite entanglement. We determine the analytical expression of the residual contangle for arb itrary pure three-mode Gaussian states and study in detail the distribution of quantum correlations in such sta tes. This analysis yields that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/W states of continuous variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the W states of three qubits. We finally consider the effect of deco herence on three-mode Gaussian states, studying the decay of the residual contangle. The GHZ/W states are shown to be maximally robust against losses and thermal noise.

Correlation matrices of two-mode bosonic systems

We present a detailed analysis of all the algebraic conditions an arbitrary 4x4 symmetric matrix must satisfy in order to represent the correlation matrix of a two-mode bosonic system. Then, we completely clarify when this arbitrary matrix can represent the correlation matrix of a separable or entangled Gaussian state. In this analysis, we introduce alternative sets of conditions, which are expressed in terms of local symplectic invariants.

Multimode uncertainty relations and separability of continuous variable states

A multimode uncertainty relation (generalizing the Robertson-Schrödinger relation) is derived as a necessary constraint on the second moments of n pairs of canonical operators. In turn, necessary conditions for the separability of multimode continuous variable states under (m+n)-mode bipartitions are derived from the uncertainty relation. These conditions are proven to be necessary and sufficient for (1+n)-mode Gaussian states and for (m+n)-mode bisymmetric Gaussian states.

Determination of continuous variable entanglement by purity measurements

We classify the entanglement of two-mode Gaussian states according to their degree of total and partial mixedness. We derive exact bounds that determine maximally and minimally entangled states for fixed global and marginal purities. This characterization allows for an experimentally reliable estimate of continuous variable entanglement based on measurements of purity.