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The Review of Laser Engineering

High Fidelity Quantum Teleportation

Hidehiro Yonezawa

Published Jan 1, 2008• 0 citations
Publisher

Abstract

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.

DOI
10.2184/lsj.36.404

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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.
The progress in quantum operations of continuous-variable (CV) schemes can be reduced to that in CV quantum teleportation. The fidelity of quantum teleportation of an optical setup is limited by the finite degree of quantum correlation that can be prepared with a pair of finitely squeezed states. Reports of improvement of squeezing level have appeared recently, and we adopted the improved methods in our experimental system of quantum teleportation. As a result, we teleported a coherent state with a fidelity $F=0.83\ifmmode\pm\else\textpm\fi{}0.01$, which is better than any other figures reported to date, to our knowledge. In this paper, we introduce a measure ns{n}_{s}ns​, the number of teleportations expected to be carried out sequentially. Our result corresponds to ${n}_{s}=5.0\ifmmode\pm\else\textpm\fi{}0.4$. It suggests that our improvement would enable us to proceed toward more advanced quantum operations involving multiple steps.
The need for high-fidelity quantum teleportation arises in a variety of quantum algorithms and protocols. Unfortunately, conventional continuous-variable teleportation schemes rely on Einstein–Podolsky–Rosen states that yield a fidelity that approaches unity only in the limit of an unphysical amount of squeezing. A new method that utilizes an ensemble of single photon entangled states, qubits, to teleport continuous variable (CV) states with fidelity approaching unity with finite resources was recently proposed by Andersen and Ralph [Phys. Rev. Lett.111, 050504 (2013)]. We extend these ideas to consider the general case of using maximally entangled d-level states, qudits, to teleport a CV state and discuss how the corresponding results are affected. In particular, we find that, by using qudits with dimension greater than two, we can achieve a higher fidelity with comparable resources.
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.
The efficiency of continuous-variable quantum teleportation is typically quantified by fidelity especially in experiment. From the original definition of fidelity in two pure states, we give an expansion of fidelity which is related to the variances of output and input states. With a coherent or a squeezed input state, it is convenient to quantify the quantum teleportation experiment, since the variances of quadrature components of the input and output states are measurable. Furthermore, the fidelity was discussed when the quantum channel lies in the phase- and amplitude-noisy environment, which is unavoidable in experiment, and this showed that the effect of phase noise on teleportation is more sensitive than that of the amplitude-noisy environment. The classical fidelity limit of squeezed state quantum teleportation is also obtained when the entanglement resources do not exist.
Very recently, we took part in a new development of quantum information, the so-called continuous variable (CV) quantum information theory. Such a further development is mainly due to the experimental and theoretical advantages offered by CV systems, i.e., quantum systems described by a set of observables, like position and momentum, which have a continuous spectrum of eigenvalues. According to this novel trend, quantum information protocols like quantum teleportation have been suitably extended to the CV framework. Here, we briefly review some mathematical tools relative to CV systems, and we consequently develop the concepts of quantum entanglement and teleportation in the CV framework by analogy with the qubit-based approach. Some connections between teleportation fidelity and entanglement properties of the underlying quantum channel are inspected. Next, we address the study of CV quantum teleportation networks where more users share a multipartite state and an arbitrary pair of them performs quantum teleportation. In this context, we show alternative protocols, and we investigate the optimal strategy that maximizes the performance of the network.