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Frontiers in Optics

Continuous Variable Teleportation of Gaussian and Non-Gaussian Light

H. J. Carmichael, Changsuk Noh

Published Jan 1, 2006• 0 citations
Publisher

Abstract

The continuous variable quantum teleportation of an optical field is reviewed, contrasting three different points of view: those of stochastic electrodynamics, quantum trajectory theory, and an operator-based treatment of the classical channel. Article not available.
DOI
10.1364/ls.2006.ltug1

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Quantum trajectory equations are formulated for continuous variable teleportation, which model the generation of finite bandwidth squeezed light, the homodyne measurements carried out by Alice, and take into account the continuous feed-forward of Alice's measurement results to Bob. The formulation is multi-mode and provides direct access to correlation functions of the output field detected by Victor. Three unravellings of the dynamics are considered, corresponding to Victor's choice of direct, homodyne, or heterodyne detection of the output field. Numerical results for the teleportation of a vacuum-state input field are presented.
The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.
Teleportation of optical field states (as continuous quantum variables) is usually described in terms of Wigner functions. This is in marked contrast to the theoretical treatment of teleportation of qubits. In this paper we show that by using the holomorphic representation of the canonical commutation relations, teleportation of continuous quantum variables can be treated in complete analogy to the case of teleportation of qubits. In order to emphasize this analogy, short descriptions of the basic experimental schemes both for teleportation of qubits and of continuous variables are included. We conclude our paper with a brief discussion of the effectiveness of our description of continuous variable teleportation and of the role of localization of quantum states in teleportation problems.
The non-negative Wigner function of all quantum states involved in teleportation of Gaussian states using the standard continuous-variable teleportation protocol means that there is a local realistic phase-space description of the process. This includes the coherent states teleported up to now in experiments. We extend the phase-space description to teleportation of non-Gaussian states using the standard protocol and conclude that teleportation of non-Gaussian pure states with a fidelity of 2/3 is a "gold standard" for this kind of teleportation.
Continuous variable quantum teleportation provides a path to the long-distance transmission of quantum states. Photon-varying non-Gaussian operations have been shown to improve the fidelity of quantum teleportation when integrated into the protocol. However, for a given type of non-Gaussian operation, the achievable fidelity varies with the parameters associated with the operation. Previous work only focused on particular settings of the parameters, over which an optimization was missing. The potential of such operations is not fully uncovered. Given a fixed non-Gaussian operation, the achievable fidelity also varies with input states. An operation that increases the fidelity for teleporting one class of states might do the contrary for other classes of states. A performance metric, upon which an operation is optimized, suitable for different input states, is also missing. In this work, we build a framework for photon-varying non-Gaussian operations for multimode states, upon which we propose a performance metric suitable for arbitrary teleportation input states. We then apply the new metric to evaluate different types of non-Gaussian operations. Starting from simple multiphoton photon subtraction and photon addition, we find that increasing the number of ancillary photons involved in the operation does not guarantee performance improvement. We then investigate a generalization of the operations mentioned above, finding that operations that approximate a particular form provide the best improvement. The results provided here will be valuable for real-world implementations of quantum teleportation networks and applications that harness the non-Gaussianity of quantum states. Published by the American Physical Society 2024