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Conference on Lasers and Electro-Optics

Quantum teleportation of wavefronts

I. V. Sokolov, Mikhail I. Kolobov, A. Gatti, L. A. Lugiato

Published Aug 29, 2005• 0 citations
Publisher

Abstract

Summary form only given. The concept of quantum teleportation of continuous variables was suggested by Vaidman [see Phys. Rev. A, vol. 49, p. 1473, 1994]. The protocol for this kind of teleportation was elaborated and demonstrated experimentally by Kimble with collaborators [see Science, vol. 282, p. 706, 1998]. In this scheme the state being teleported is that of a single transverse mode of the electromagnetic field with finite frequency bandwidth. We describe the quantum teleportation scheme that allows one to teleport the quantum state of the wavefront of an electromagnetic wave. In other words we propose teleportation of the quantum state of a spatially multimode electromagnetic field.

DOI
10.1109/iqec.2000.907994

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Summary form only given. The concept of quantum teleportation of continuous variables was suggested by Vaidman [see Phys. Rev. A, vol. 49, p. 1473, 1994]. The protocol for this kind of teleportation was elaborated and demonstrated experimentally by Kimble with collaborators [see Science, vol. 282, p. 706, 1998]. In this scheme the state being teleported is that of a single transverse mode of the electromagnetic field with finite frequency bandwidth. We describe the quantum teleportation scheme that allows one to teleport the quantum state of the wavefront of an electromagnetic wave. In other words we propose teleportation of the quantum state of a spatially multimode electromagnetic field.
Quantum teleportation of an unknown broadband electromagnetic field is investigated. The continuous-variable teleportation protocol by Braunstein and Kimble [Phys. Rev. Lett. 80, 869 (1998)] for teleporting the quantum state of a single mode of the electromagnetic field is generalized for the case of a multimode field with finite bandwith. We discuss criteria for continuous-variable teleportation with various sets of input states and apply them to the teleportation of broadband fields. We first consider as a set of input fields (from which an independent state preparer draws the inputs to be teleported) arbitrary pure Gaussian states with unknown coherent amplitude (squeezed or coherent states). This set of input states, further restricted to an alphabet of coherent states, was used in the experiment by Furusawa et al. [Science 282, 706 (1998)]. It requires unit-gain teleportation for optimizing the teleportation fidelity. In our broadband scheme, the excess noise added through unit-gain teleportation due to the finite degree of the squeezed-state entanglement is just twice the (entanglement) source's squeezing spectrum for its ``quiet quadrature.'' The teleportation of one half of an entangled state (two-mode squeezed vacuum state), i.e., ``entanglement swapping,'' and its verification are optimized under a certain nonunit gain condition. We will also give a broadband description of this continuous-variable entanglement swapping based on the single-mode scheme by van Loock and Braunstein [Phys. Rev. A 61, 10 302 (2000)].
We describe a continious variable teleportation scheme that allows to teleport the quantum state of distributed in space-time multimode electromagnetic field. Our teleportation protocol uses the spatially-multimode entangled Einstein-Podolsky-Rosen lihgt beams. We evaluate the "resolving power" of teleportation in space-time and specify the degrees of freedom of electromagnetic field whose quantum state can be effectively teleported. We call this scheme "quantum holographic teleportation" because it can be considered as an extension of conventional holography to quantum domain.
We develop a simple and efficient theoretical model to understand the quantum properties of broadband continuous variable quantum teleportation. We show that, if stated properly, the problem of multimode teleportation can be simplified to teleportation of a single effective mode that describes the input state temporal characteristic. Using that model, we show how the finite bandwidth of squeezing and external noise in the classical channel affect the output teleported quantum field. We choose an approach that is especially relevant for the case of non-Gaussian nonclassical quantum states and we finally back-test our model with recent experimental results.
ABSTRACT We propose a setup for teleportation of continuous quantum variables which is optimized for teleportation ofsqueezed coherent states. Our scheme is a modified version of the original setup proposed by Braunstein andKimble [Phys. Rev. Lett. 80, 869, 1998] and it involves an unbalanced beam splitter on the sender's side and asingle mode squeezer on receiver's side. We show that the quality of the teleportation can be evaluated by meansof a fidelity of entanglement swapping and we prove that our modified setup and the original Braunstein-Kimblesetup are equivalent with respect to this fidelity measure.Keywords: Quantum teleportation, squeezed states, completely positive maps, fidelity 1. INTRODUCTION Quantum teleportation, a disembodied transfer of a quantum state between two distant parties, is perhaps themost remarkable and exciting development in the rapidly growing field of quantum information processing. Intheir seminal paper, Bennett et al.1 proposed a protocol for teleportation of a single qubit from the sender Aliceto the receiver Bob. The information about the teleported state is sent to Bob via dual classical and quantumEPR channels. The latter is established by a maximally entangled state shared by Alice and Bob.Recently, there has been much interest in quantum information processing with continuous quantum van-ables. Here, the focus is on systems with infinite dimensional Hubert spaces such as quantized electromagneticfield. Teleportation of continuous quantum variables was first considered by Vaidman,2 and an experimentallyfeasible setup was suggested by Braunstein and Kimble.3 Subsequent experiment4 demonstrated that theteleportation of a single mode of optical field is fully within the reach of current technology. Since then, manyauthors discussed various aspects of the teleportation,5'° including fidelity of teleportation of various quantumstates and influence of losses on the degradation of the quantum channel.Besides teleportation, many other protocols developed originally in the framework of discrete quantum van-ables, have been successfully formulated also for continuous variables. These include quantum cloning,11'3quantum