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arXiv:quant-ph/0510105 · Journal of Optics B Quantum and Semiclassical Optics

Manipulating quantum information by propagation

Álvaro Perales, Martin Bodo Plenio

Published Nov 16, 2005• 17 citations
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Abstract

We study the creation of bipartite and multipartite continuous variable entanglement in structures of coupled quantum harmonic oscillators. By adjusting the interaction strengths between nearest neighbours we show how to maximize the entanglement production between the arms in a Y-shaped structure where an initial single mode squeezed state is created in the first oscillator of the input arm. We also consider the action of the same structure as an approximate quantum cloner. For a specific time in the system dynamics the last oscillators in the output arms can be considered as imperfect copies of the initial state. By increasing the number of arms in the structure, multipartite entanglement is obtained, as well as cloning. Finally, we consider configurations that implement the symmetric splitting of an initial entangled state. All calculations are carried out within the framework of the rotating wave approximation in quantum optics, and our predictions could be tested with current available experimental techniques.

DOI
10.1088/1464-4266/7/12/023

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We study the creation of bipartite and multipartite continuous variable entanglement in structures of coupled quantum harmonic oscillators. By adjusting the interaction strengths between nearest neighbours we show how to maximize the entanglement production between the arms in a Y-shaped structure where an initial single mode squeezed state is created in the first oscillator of the input arm. We also consider the action of the same structure as an approximate quantum cloner. For a specific time in the system dynamics the last oscillators in the output arms can be considered as imperfect copies of the initial state. By increasing the number of arms in the structure, multipartite entanglement is obtained, as well as cloning. Finally, we consider configurations that implement the symmetric splitting of an initial entangled state. All calculations are carried out within the framework of the rotating wave approximation in quantum optics, and our predictions could be tested with current available experimental techniques.
We study creation of bi- and multipartite continuous variable entanglement in structures of coupled quantum harmonic oscillators. By adjusting the interaction strengths between nearest neighbors we show how to maximize the entanglement production between the arms in a Y-shaped structure where an initial single mode squeezed state is created in the first oscillator of the input arm. We also consider the action of the same structure as an approximate quantum cloner. For a specific time in the system dynamics the last oscillators in the output arms can be considered as imperfect copies of the initial state. By increasing the number of arms in the structure, multipartite entanglement is obtained, as well as 1 to M cloning. Finally, we are considering configurations that implement the symmetric splitting of an initial entangled state. All calculations are carried out within the framework of the rotating wave approximation in quantum optics, and our predictions could be tested with current available experimental techniques.
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest-neighbour interactions. For a one-dimensional chain, we provide compact analytical solutions and approximations to the dynamical evolution of the entanglement between spatially separated oscillators. Key properties such as the speed of entanglement propagation, the maximum amount of transferred entanglement and the efficiency for the entanglement transfer are computed. For harmonic oscillators coupled by springs, corresponding to a phonon model, we observe a non-monotonic transfer efficiency in the initially prepared amount of entanglement, i.e. an intermediate amount of initial entanglement is transferred with the highest efficiency. In contrast, within the framework of the rotating-wave approximation (as appropriate, e.g. in quantum optical settings) one finds a monotonic behaviour. We also study geometrical configurations that are analogous to quantum optical devices (such as beamsplitters and interferometers) and observe characteristic differences when initially thermal or squeezed states are entering these devices. We show that these devices may be switched on and off by changing the properties of an individual oscillator. They may therefore be used as building blocks of large fixed and pre-fabricated but programmable structures in which quantum information is manipulated through propagation. We discuss briefly possible experimental realizations of systems of interacting harmonic oscillators in which these effects may be confirmed experimentally
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest-neighbour interactions. For a one-dimensional chain, we provide compact analytical solutions and approximations to the dynamical evolution of the entanglement between spatially separated oscillators. Key properties such as the speed of entanglement propagation, the maximum amount of transferred entanglement and the efficiency for the entanglement transfer are computed. For harmonic oscillators coupled by springs, corresponding to a phonon model, we observe a non-monotonic transfer efficiency in the initially prepared amount of entanglement, i.e. an intermediate amount of initial entanglement is transferred with the highest efficiency. In contrast, within the framework of the rotating-wave approximation (as appropriate, e.g. in quantum optical settings) one finds a monotonic behaviour. We also study geometrical configurations that are analogous to quantum optical devices (such as beamsplitters and interferometers) and observe characteristic differences when initially thermal or squeezed states are entering these devices. We show that these devices may be switched on and off by changing the properties of an individual oscillator. They may therefore be used as building blocks of large fixed and pre-fabricated but programmable structures in which quantum information is manipulated through propagation. We discuss briefly possible experimental realizations of systems of interacting harmonic oscillators in which these effects may be confirmed experimentally.
We investigate a simple arrangement of coupled harmonic oscillators which brings out some interesting effects concerning creation of entanglement. It is well known that if each member in a linear chain of coupled harmonic oscillators is prepared in a ``classical state,'' such as a pure coherent state or a mixed thermal state, no entanglement is created in the rotating wave approximation. On the other hand, if one of the oscillators is prepared in a nonclassical state (pure squeezed state, for instance), entanglement may be created between members of the chain. In the setup considered here, we found that a great family of nonclassical (squeezed) states can localize entanglement in such a way that distant oscillators never become entangled. We present a detailed study of this particular localization phenomenon. Our results may find application in future solid state implementations of quantum computers, and we suggest an electromechanical system consisting of an array of coupled micromechanical oscillators as a possible implementation.
We consider the quantum cloning of continuous variable entangled states. This is achieved by introducing two symmetric entanglement cloning machines (or eee-cloners): a local eee-cloner and a global eee-cloner; where we look at the preservation of entanglement in the clones under the condition that the fidelity of the clones is maximized. These cloning machines are implemented using simple linear optical elements such as beam splitters and homodyne detection along with squeeze gates. We show that the global eee-cloner out-performs the local eee-cloner both in terms of the fidelity of the cloned states as well as the strength of the entanglement of the clones. There is a minimum strength of entanglement (3 dB using the inseparability criterion) of the input state of the global eee-cloner that is required to preserve the entanglement in the clones.
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)\mathrm{SU}(m,1)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)\mathrm{SU}(m,1)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 $1\ensuremath{\rightarrow}m$ telecloning and derive explicitly the optimal relation among the different fidelities of the mmm 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.