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arXiv:quant-ph/0410100 · Reviews of Modern Physics

Quantum information with continuous variables

Samuel L. Braunstein, Peter van Loock

Published Jun 29, 2005• 3,841 citations
arXivHTMLPDF

Abstract

Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement. This article reviews the progress in quantum information based on continuous quantum variables, with emphasis on quantum optical implementations in terms of the quadrature amplitudes of the electromagnetic field.

DOI
10.1103/revmodphys.77.513

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Quantum information is a rapidly advancing area of interdisciplinary research. It may lead to real-world applications for communication and computation unavailable without the exploitation of quantum properties such as nonorthogonality or entanglement. This article reviews the progress in quantum information based on continuous quantum variables, with emphasis on quantum optical implementations in terms of the quadrature amplitudes of the electromagnetic field.
A variety of optical quantum information networks based on the multipartite entanglement of amplitude and phase quadratures of an electromagnetic field have been proposed and experimentally realized in recent years. The multipartite entanglement of optical continuous variables provides flexible and reliable quantum resources for developing unconditional quantum information networks. In this paper, we review the generation schemes of the multipartite entangled states of optical continuous quantum variables and some applications in the quantum communication networks with emphasis on the experimental implementations.
In parallel with quantum information systems based on single photons,optical quantum information science with continuous variables based on the quadrature components of optical fields is also developing rapidly.For this,multipartite entangled states of light are the fundamental resources.In this paper we first introduce the concepts and preparation of multipartite entangled states,then discuss the basic models of quantum computation with continuous variables and the progress in experimental investigations.
Tremendous progress in experimental quantum optics in recent decades has enabled the advent of quantum technologies, one of which is quantum communication. Aimed at novel methods for more secure or more efficient information transfer, quantum communication has developed into an active field of research and proceeds toward full-scale implementations and industrialization. Continuous-variable methods of multiphoton quantum state preparation, manipulation, and coherent detection, as well as the respective theoretical tools of phase-space quantum optics, offer the possibility of making quantum communication efficient, applicable, and accessible, thus boosting the development of the field. We review the methodology, techniques, and protocols of continuous-variable quantum communication from the first theoretical ideas through milestone implementations to recent developments. The review covers quantum key distribution as well as other quantum communication schemes that are suggested on the basis of continuous-variable states and measurements.
Quantum information with continuous variables conventionally exploits quantum variables with canonic: commutation relations, like position and momentum, or quadrature field components. In contrast, this contribution is devoted to quantum continuous polarization variables. The relevant observabIes are quantum Stokes operators which obey the SU(2) algebra with a commutator which is not a c-number but an operator. In this paper, we review the concept of polarization squeezing and the new concept of continuous-variable polarization entanglement using quantum Stokes parameters. We discuss the prospects and specific features of such nonclassical polarization states for quantum communication.
Summary form only given. Traditionally quantum information research has centred on discrete quantum variables, particularly binary variables (qubits). However, recently much attention has focused on quantum information manipulations with continuous variables such as the amplitude and phase of the electromagnetic field. As well as offering the possibility of high data rates, continuous variables also exhibit greater versatility in realizing certain operations. For example teleportation, in which quantum information is passed intact through a classical channel with the assistance of shared entanglement, can be achieved more efficiently using continuous variable techniques. I review recent work on the characterization of teleportation and entanglement swapping and present new work on interferometric tests of teleportation. These interferometric tests are important because they allow the efficacy of teleportation to be checked without knowledge of the input quantum state. They can be applied equally to the cases of discrete and continuous variable inputs and in so doing highlight unexpected similarities. I contrast the various classical limits which emerge from the different ways of assessing teleportation. An obvious omission from the list of continuous variable quantum information manipulations is any proposal for direct analogues of 2 photon interference effects, especially those that lead to Bell inequality type tests of local realism. Bell-type correlations are the defining feature of discrete variable entanglement experimentally. I discuss new work that shows how entanglement of the Bell-type can be observed in continuous variable, homodyne measurement schemes.
Quantum information describes the new field which bridges quantum physics and information science. The quantum world allows for completely new architectures and protocols. While originally formulated in continuous quantum variables, the field worked almost exclusively with discrete variables, such as single photons and photon pairs. The renaissance of continuous variables came with European research consortia such as ACQUIRE (Advanced Coherent Quantum Information Research) in the late 1990s, and QUICOV (Quantum Information with Continuous Variables) from 2000–2003. The encouraging research results of QUICOV and the new conference series CVQIP (Continuous Variable Quantum Information Processing) triggered the idea for this book.This book presents the state of the art of quantum information with continuous quantum variables. The individual chapters discuss results achieved in QUICOV and presented at the first five CVQIP conferences from 2002-2006. Many world-leading scientists working on continuous variables outside Europe also contribute to the book.