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International Conference on Quantum, Nano and Micro Technologies (ICQNM)

Continuous-variable quantum information with three-mode Gaussian states: allotment,trade-off, teleportation, and telecloning

Gerardo Adesso, Alessio Serafini, Fabrizio Illuminati

Published Jan 1, 2007• 0 citations
Publisher

Abstract

We introduce a simple procedure - based on passive optical elements - to produce pure three-mode Gaussian states with arbitrary entanglement structure (upon availability of an initial single-mode squeezed state). We analyze in detail the properties of distributed entanglement, 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 entanglement, in terms of the optimal fidelity of teleportation networks with Gaussian resources. As a byproduct, optimal resource states for various communication protocols (among which asymmetric telecloning) will be exactly determined.

DOI
10.1109/icqnm.2007.6

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We introduce a simple procedure - based on passive optical elements - to produce pure three-mode Gaussian states with arbitrary entanglement structure (upon availability of an initial single-mode squeezed state). We analyze in detail the properties of distributed entanglement, 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 entanglement, in terms of the optimal fidelity of teleportation networks with Gaussian resources. As a byproduct, optimal resource states for various communication protocols (among which asymmetric telecloning) will be exactly determined.
The structural aspects of tripartite entanglement in three-mode Gaussian states of continuous variable systems have been studied in [Adesso G, Serafini A and Illuminati F 2006 Phys. Rev. A {\\bf 73} 032345]. Here we focus our attention on the usefulness of such states in the context of realistic processing of continuous-variable quantum information. We introduce and discuss in detail several examples of pure and mixed three-mode states that stand out for their informational and/or entanglement properties. We then describe practical schemes to engineer such states with linear optics. 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 single-mode squeezed state). We analyze in detail the properties of distributed entanglement, 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 entanglement, in terms of the optimal fidelity of teleportation networks with Gaussian resources. As a byproduct, optimal resource states for various communication protocols (among which asymmetric telecloning) will be exactly determined.
We present a novel, detailed study on the usefulness of three-mode Gaussian states for realistic processing of continuous variable (CV) 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 arbitrary entanglement structure (upon availability of an initial two-mode squeezed state). We analyse 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 CVs. This will lead to a feasible experimental proposal to test the promiscuous sharing of CV 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 CVs beyond the bipartite scenario.
We present a novel, detailed study on the usefulness of three-mode Gaussian states for realistic processing of continuous variable (CV) 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 arbitrary entanglement structure (upon availability of an initial two-mode squeezed state). We analyse 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 CVs. This will lead to a feasible experimental proposal to test the promiscuous sharing of CV 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 CVs beyond the bipartite scenario.
The telecloning protocol distributes quantum states from a single sender to multiple receivers via a shared entangled state by exploiting the notions of teleportation and approximate cloning. We investigate the optimal telecloning fidelities obtained using both Gaussian and non-Gaussian shared resources. When the shared non-Gaussian state is created by subtracting photons from both the modes of the Gaussian two-mode squeezed vacuum state, we demonstrate that higher telecloning fidelities can be achieved in comparison with its Gaussian counterpart. To quantify this advantage, we introduce a quadrature-based nonclassicality measure, which is capable of estimating the fidelity of the clones, both with Gaussian and non-Gaussian resource states. We further provide a linear optical setup for asymmetric telecloning of continuous variable states using a multimode entangled state.
Given a certain amount of entanglement available as a resource, what is the most efficient way to accomplish a quantum task? We address this question in the relevant case of continuous variable quantum teleportation protocols implemented using two-mode Gaussian states with a limited degree of entanglement and energy. We first characterize the class of single-mode phase-insensitive Gaussian channels that can be simulated via a Braunstein-Kimble protocol with nonunit gain and minimum shared entanglement, showing that infinite energy is not necessary apart from the special case of the quantum limited attenuator. We also find that apart from the identity, all phase-insensitive Gaussian channels can be simulated through a two-mode squeezed state with finite energy, albeit with a larger entanglement. We then consider the problem of teleporting single-mode coherent states with Gaussian-distributed displacement in phase space. Performing a geometrical optimization over phase-insensitive Gaussian channels, we determine the maximum average teleportation fidelity achievable with any finite entanglement and for any realistically finite variance of the input distribution.
We present a complete analysis of the multipartite entanglement of three-mode Gaussian states of continuous-variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode 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 general 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. Phys8, 15 (2006)]. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communications and defines a measure of genuine tripartite entanglements. We determine the analytical expression of the residual contangle for arbitrary pure three-mode Gaussian states and study in detail the distribution of quantum correlations in such states. 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\mathrm{GHZ}∕WGHZ∕W states of continuous-variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the WWW states of three qubits. We finally consider the effect of decoherence on three-mode Gaussian states, studying the decay of the residual contangle. The GHZ∕W\mathrm{GHZ}∕WGHZ∕W states are shown to be maximally robust against losses and thermal noise.