Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states

We present a novel, detailed study on the usefulness of three-mode Gaussian states states for realistic processing of continuous-variable quantum information, with a particular emphasis on the possibilities opened up by their genuine tripartite entanglement. We describe practical schemes to engineer several classes of pure and mixed three-mode states that stand out for their informational and/or entanglement properties. In particular, we introduce a simple procedure -- based on passive optical elements -- to produce pure three-mode Gaussian states with {\em arbitrary} entanglement structure (upon availability of an initial two-mode squeezed state). We analyze in depth the properties of distributed entanglement and the origin of its sharing structure, showing that the promiscuity of entanglement sharing is a feature peculiar to symmetric Gaussian states that survives even in the presence of significant degrees of mixedness and decoherence. Next, we discuss the suitability of the considered tripartite entangled states to the implementation of quantum information and communication protocols with continuous variables. This will lead to a feasible experimental proposal to test the promiscuous sharing of continuous-variable tripartite entanglement, in terms of the optimal fidelity of teleportation networks with Gaussian resources. We finally focus on the application of three-mode states to symmetric and asymmetric telecloning, and single out the structural properties of the optimal Gaussian resources for the latter protocol in different settings. Our analysis aims to lay the basis for a practical quantum communication with continuous variables beyond the bipartite scenario.Comment: 33 pages, 10 figures (some low-res due to size constraints), IOP style; (v2) improved and reorganized, accepted for publication in New Journal of Physic

Optical implementation and entanglement distribution in Gaussian valence bond states

We study Gaussian valence bond states of continuous variable systems, obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of $N$ sites of an harmonic chain. The entanglement distribution in Gaussian valence bond states can be controlled by varying the input amount of entanglement engineered in a (2M+1)-mode Gaussian state known as the building block, which is isomorphic to the projector applied at a given site. We show how this mechanism can be interpreted in terms of multiple entanglement swapping from the chain of ancillary bonds, through the building blocks. We provide optical schemes to produce bisymmetric three-mode Gaussian building blocks (which correspond to a single bond, M=1), and study the entanglement structure in the output Gaussian valence bond states. The usefulness of such states for quantum communication protocols with continuous variables, like telecloning and teleportation networks, is finally discussed.Comment: 15 pages, 6 figures. To appear in Optics and Spectroscopy, special issue for ICQO'2006 (Minsk). This preprint contains extra material with respect to the journal versio

Dynamics of Atom-Atom Correlations in the Fermi problem

We present a detailed perturbative study of the dynamics of several types of atom-atom correlations in the famous Fermi problem. This is an archetypal model to study micro-causality in the quantum domain where two atoms, the first initially excited and the second prepared in its ground state, interact with the vacuum electromagnetic field. The excitation can be transferred to the second atom via a flying photon and various kinds of quantum correlations between the two are generated during this process. Among these, prominent examples are given by entanglement, quantum discord and nonlocal correlations. It is the aim of this paper to analyze the role of the light cone in the emergence of such correlations.Comment: 14 pages, 7 figure

Asymptotically optimal quantum channel reversal for qudit ensembles and multimode Gaussian states

We investigate the problem of optimally reversing the action of an arbitrary quantum channel C which acts independently on each component of an ensemble of n identically prepared d-dimensional quantum systems. In the limit of large ensembles, we construct the optimal reversing channel R* which has to be applied at the output ensemble state, to retrieve a smaller ensemble of m systems prepared in the input state, with the highest possible rate m/n. The solution is found by mapping the problem into the optimal reversal of Gaussian channels on quantum-classical continuous variable systems, which is here solved as well. Our general results can be readily applied to improve the implementation of robust long-distance quantum communication. As an example, we investigate the optimal reversal rate of phase flip channels acting on a multi-qubit register.Comment: 17 pages, 3 figure

Entanglement, Purity, and Information Entropies in Continuous Variable Systems

Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal ({\em i.e.}referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or in general by information entropies, provides an accurate characterization of its entanglement. In particular, for Gaussian states of continuous variable systems, we classify the entanglement of two--mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized $p-$entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entanglement in highly symmetric Gaussian states of arbitrary $1 \times N$-mode partitions.Comment: 16 pages, 5 low-res figures, OSID style. Presented at the International Conference ``Entanglement, Information and Noise'', Krzyzowa, Poland, June 14--20, 200

Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states

We address the estimation of the loss parameter of a bosonic channel probed by arbitrary signals. Unlike the optimal Gaussian probes, which can attain the ultimate bound on precision asymptotically either for very small or very large losses, we prove that Fock states at any fixed photon number saturate the bound unconditionally for any value of the loss. In the relevant regime of low-energy probes, we demonstrate that superpositions of the first low-lying Fock states yield an absolute improvement over any Gaussian probe. Such few-photon states can be recast quite generally as truncations of de-Gaussified photon-subtracted states.Comment: 4 pages, 3 figure

Measurement-induced disturbances and nonclassical correlations of Gaussian states

We study quantum correlations beyond entanglement in two-mode Gaussian states of continuous-variable systems by means of the measurement-induced disturbance (MID) and its ameliorated version (AMID). In analogy with the recent studies of the Gaussian quantum discord, we define a Gaussian AMID by constraining the optimization to all bi-local Gaussian positive operator valued measurements. We solve the optimization explicitly for relevant families of states, including squeezed thermal states. Remarkably, we find that there is a finite subset of two-mode Gaussian states comprising pure states where non-Gaussian measurements such as photon counting are globally optimal for the AMID and realize a strictly smaller state disturbance compared to the best Gaussian measurements. However, for the majority of two-mode Gaussian states the unoptimized MID provides a loose overestimation of the actual content of quantum correlations, as evidenced by its comparison with Gaussian discord. This feature displays strong similarity with the case of two qubits. Upper and lower bounds for the Gaussian AMID at fixed Gaussian discord are identified. We further present a comparison between Gaussian AMID and Gaussian entanglement of formation, and classify families of two-mode states in terms of their Gaussian AMID, Gaussian discord, and Gaussian entanglement of formation. Our findings provide a further confirmation of the genuinely quantum nature of general Gaussian states, yet they reveal that non-Gaussian measurements can play a crucial role for the optimized extraction and potential exploitation of classical and nonclassical correlations in Gaussian states. © 2011 American Physical Society

Probabilistic Distillation of Quantum Coherence

© 2018 American Physical Society. The ability to distill quantum coherence is pivotal for optimizing the performance of quantum technologies; however, such a task cannot always be accomplished with certainty. Here we develop a general framework of probabilistic distillation of quantum coherence in a one-shot setting, establishing fundamental limitations for different classes of free operations. We first provide a geometric interpretation for the maximal success probability, showing that under maximally incoherent operations (MIO) and dephasing-covariant incoherent operations (DIO) the problem can be simplified into efficiently computable semidefinite programs. Exploiting these results, we find that DIO and its subset of strictly incoherent operations have equal power in the probabilistic distillation of coherence from pure input states, while MIO are strictly stronger. We then prove a fundamental no-go result: Distilling coherence from any full-rank state is impossible even probabilistically. We further find that in some conditions the maximal success probability can vanish suddenly beyond a certain threshold in the distillation fidelity. Finally, we consider probabilistic coherence distillation assisted by a catalyst and demonstrate, with specific examples, its superiority to the unassisted and deterministic cases

Gaussian quantum resource theories

© 2018 American Physical Society. We develop a general framework to assess capabilities and limitations of the Gaussian toolbox in continuous-variable quantum information theory. Our framework allows us to characterize the structure and properties of quantum resource theories specialized to Gaussian states and Gaussian operations, establishing rigorous methods for their description and yielding a unified approach to their quantification. We show in particular that, under a few intuitive and physically motivated assumptions on the set of free states, no Gaussian quantum resource can be distilled with free Gaussian operations, even when an unlimited supply of the resource state is available. This places fundamental constraints on state manipulations in all such Gaussian resource theories. We discuss in particular the applications to quantum entanglement, where we extend previously known results by showing that Gaussian entanglement cannot be distilled even with Gaussian operations preserving the positivity of the partial transpose, as well as to other Gaussian resources such as steering and optical nonclassicality. A comprehensive semidefinite programming representation of all these resources is explicitly provided

Gaussian quantum marginal problem

The quantum marginal problem asks what local spectra are consistent with a given spectrum of a joint state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn's Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d1, ..., dn) and (c1, ..., cn) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of several modes. We find that this result implies a solution to the problem of sharing of entanglement in pure Gaussian states and allows for estimating the global entropy of non-Gaussian states based on local measurements. Implications to the actual preparation of multi-mode continuous-variable entangled states are discussed. We compare the findings with the marginal problem for qubits, the solution of which for pure states has a strikingly similar and in fact simple form.Comment: 18 pages, 1 figure, material added, references updated, except from figure identical with version to appear in Commun. Math. Phy