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arXiv:0811.1092 · Optics and Spectroscopy

Continuous-variable quantum information processing with squeezed states of light

Hidehiro Yonezawa, Akira Furusawa

Published Feb 1, 2010• 33 citations
arXivHTMLPDF

Abstract

We investigate experiments of continuous-variable quantum information processing based on the teleportation scheme. Quantum teleportation, which is realized by a two-mode squeezed vacuum state and measurement-and-feedforward, is considered as an elementary quantum circuit as well as quantum communication. By modifying ancilla states or measurement-and-feedforwards, we can realize various quantum circuits which suffice for universal quantum computation. In order to realize the teleportation-based computation we improve the level of squeezing, and fidelity of teleportation. With a high-fidelity teleporter we demonstrate some advanced teleportation experiments, i.e., teleportation of a squeezed state and sequential teleportation of a coherent state. Moreover, as an example of the teleportation-based computation, we build a QND interaction gate which is a continuous-variable analog of a CNOT gate. A QND interaction gate is constructed only with ancillary squeezed vacuum states and measurement-and-feedforwards. We also create continuous-variable four mode cluster type entanglement for further application, namely, one-way quantum computation.

DOI
10.1134/s0030400x10020189

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We investigate experiments of continuous-variable quantum information processing based on the teleportation scheme. Quantum teleportation, which is realized by a two-mode squeezed vacuum state and measurement-and-feedforward, is considered as an elementary quantum circuit as well as quantum communication. By modifying ancilla states or measurement-and-feedforwards, we can realize various quantum circuits which suffice for universal quantum computation. In order to realize the teleportation-based computation we improve the level of squeezing, and fidelity of teleportation. With a high-fidelity teleporter we demonstrate some advanced teleportation experiments, i.e., teleportation of a squeezed state and sequential teleportation of a coherent state. Moreover, as an example of the teleportation-based computation, we build a QND interaction gate which is a continuous-variable analog of a CNOT gate. A QND interaction gate is constructed only with ancillary squeezed vacuum states and measurement-and-feedforwards. We also create continuous-variable four mode cluster type entanglement for further application, namely, one-way quantum computation.
Quantum teleportation is one of the most fundamental subjects in quantum information technology. This is because quantum teleportation can be used as not only a communication network but also a building block for universal quantum information processing. It is well known that there are two approaches (i. e. discrete and continuous variable approaches) in quantum information processing. In particular, continuous variable one has some advantages, that is, capability for deterministic and efficient quantum operations. In the case of continuous variable quantum teleportation, however, we cannot teleport quantum states perfectly due to finite level of quadrature squeezed states. Hence it is important to improve the fidelity of teleportation to realize more advanced quantum network and circuits. Thanks to the recent improvement of squeezing level, fidelity up to F=0.83 has been achieved. In this article, we review the experiment of high fidelity quantum teleportation for continuous variables, and its applications.
Continuous-variable (CV) gate teleportation using cluster states is a cornerstone of quantum information processing. However, its performance is constrained by technical hurdles in preparing high-quality squeezed states, which are a critical resource for CV quantum protocols. Imperfect preparation of these squeezed states introduces noise, which in turn degrades quantum correlations. Photon subtraction has been shown to mitigate the adverse effects of imperfect squeezing by enhancing the equivalent squeezing of quantum resources. Accordingly, this study investigates the application of photon subtraction in CV gate teleportation. We first present a Wigner characteristic function representation for the two-mode quantum non-demolition gate teleportation protocol. Building on this representation, we establish a theoretical model incorporating photon subtraction, derive expressions for the fidelity and log-negativity of the output states, and verify the system performance through numerical simulations. Our results demonstrate that photon subtraction can effectively compensate for the losses both in fidelity and entanglement caused by imperfect squeezed states. In contrast to standard state teleportation based on two-mode entangled resources, such an enhancement is only achievable when photon subtraction is implemented prior to the generation of the final cluster state. This discovery represents a crucial practical advancement in the field of quantum teleportation, potentially paving the way for more efficient and reliable quantum communication systems.
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
Measurement-based one-way quantum computation using cluster states as resources provides an efficient model to perform computation and information processing of quantum codes. Arbitrary Gaussian quantum computation can be implemented sufficiently by long single-mode and two-mode gate sequences. However, continuous variable gate sequences have not been realized so far due to an absence of cluster states larger than four submodes. Here we present the first continuous variable gate sequence consisting of a single-mode squeezing gate and a two-mode controlled-phase gate based on a six-mode cluster state. The quantum property of this gate sequence is confirmed by the fidelities and the quantum entanglement of two output modes, which depend on both the squeezing and controlled-phase gates. The experiment demonstrates the feasibility of implementing Gaussian quantum computation by means of accessible gate sequences. Measurement-based one-way quantum computation with cluster states is an efficient route to processing quantum information, yet gate sequences for large states remain elusive. Su et al. present a continuous variable squeezed gate and controlled-phase gate sequence using a six-mode cluster state.
This thesis is concerned with variations on, and improvements to, optical strategies of implementing quantum teleportation. In particular, I investigate four continuous variable teleportation schemes. Two schemes are based upon number-phase entanglement between two coupled harmonic oscillator modes. Joint measurements of number and phase on the coupled states are the basis for the protocols. The effects of phase decoherence on output quality are analysed and an equivalent classical protocol is introduced. The two remaining schemes improve and extend standard continuous variable teleportation. In one, coincidence measurements on the two-mode squeezed vacuum condition the entanglement resource, improving the efficacy of the protocol. In the other, the measurements made by the sender and displacements performed by the receiver are tailored to make more efficient use of the available information. In each case the protocol is described and relevant output parameters derived. The trends in output quality with respect to input parameters are interpreted and discussed.
We exploit quantum information processing on a traveling wave of light, expecting emancipation from thermal noise, easy coupling to fiber communication, and potentially high operation speed. Although optical memories are technically challenging, we have an alternative approach to apply multi-step operations on traveling light, that is, continuous-variable one-way computation. So far our achievement includes generation of a one-million-mode entangled chain in time-domain, mode engineering of nonlinear resource states, and real-time nonlinear feedforward. Although they are implemented with free space optics, we are also investigating photonic integration and performed quantum teleportation with a passive liner waveguide chip as a demonstration of entangling, measurement, and feedforward. We also suggest a loop-based architecture as another model of continuous-variable computing.