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arXiv:1310.3187 · Journal of the Optical Society of America B

High-fidelity teleportation of continuous-variable quantum states with discrete-variable resources

Kevin Marshall, Daniel F. V. James

Published Feb 3, 2014• 12 citations
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Abstract

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.

DOI
10.1364/josab.31.000423

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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.
Traditional continuous-variable teleportation can only approach unit fidelity in the limit of an infinite (and unphysical) amount of squeezing. We describe a new method for continuous-variable teleportation that approaches unit fidelity with finite resources. The protocol is not based on squeezed states as in traditional teleportation but on an ensemble of single photon entangled states. We characterize the teleportation scheme with coherent states, mesoscopic superposition states, and two-mode squeezed states and we find several situations in which near-unity teleportation fidelity can be obtained with modest resources.
Achieving near-unity fidelity in conventional continuous-variable quantum teleportation schemes based on two-mode squeezed vacuum states is fundamentally unattainable. To overcome this limitation, alternative approaches utilizing ensembles of two-dimensional entangled qubits have been proposed. In this work, we investigate continuous-variable quantum teleportation employing entangled qutrit resources under realistic noise effects. The results demonstrate that the proposed scheme performs well in both ideal and noisy conditions, enabling high-fidelity teleportation with a reasonable success probability.
Quantum teleportation protocols of continuous variable (CV) Greeberger–Horne–Zeilinger (GHZ) and Einstein–Podolsky–Rosen (EPR) entangled states are proposed, and are generalized to teleportation of arbitrary multimode GHZ entangled states described by Van Loock and Braunstein (2000 Phys. Rev. Lett. 84 3482). Each mode of a multimode entangled state is teleported using a CV EPR entangled pair and classical communication. The analytical expression of fidelity for the multimode Gaussian states which evaluates the teleportation quality is presented. The analytical results show that the fidelity is a function of both the squeezing parameter r, which characterizes the multimode entangled state to be teleported, and the channel parameter p, which characterizes the EPR pairs shared by Alice and Bob. The fidelity increases with increasing p, but decreases with increasing r, i.e., it is more difficult to teleport the more perfect multimode entangled states. The entanglement degree of the teleported multimode entangled states increases with increasing both r and p. In addition, the fact is proved that our teleportation protocol of EPR entangled states using parallel EPR pairs as quantum channels is the best case of the protocol using four-mode entangled states (Adhikari et al 2008 Phys. Rev. A 77 012337).
The continuous-variable (CV) quantum state of light allows for the teleportation of a discrete-variable (DV) photonic qubit. Such an operation is useful in the realm of hybrid quantum networks. However, it is known that the teleportation of a DV qubit via a Gaussian CV resource state is severely limited under channel loss, with a teleportation fidelity beyond the classical limit unattainable for losses exceeding a small threshold. In this paper, we present a nondeterministic teleportation protocol that combines a Gaussian CV resource state with a modified form of the Bell state measurement that accommodates significantly improved DV-qubit fidelity over a wide range of channel losses. Beyond this improvement, we also show how the use of non-Gaussian operations on the CV resource state can lead to a DV-qubit fidelity approaching unity for any channel loss.
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.
We investigate the resources needed for secure teleportation of coherent states. We extend continuous variable teleportation to include quantum teleamplification protocols that allow nonunity classical gains and a preamplification or postattenuation of the coherent state. We show that, for arbitrary Gaussian protocols and a significant class of Gaussian resources, two-way steering is required to achieve a teleportation fidelity beyond the no-cloning threshold. This provides an operational connection between Gaussian steerability and secure teleportation. We present practical recipes suggesting that heralded noiseless preamplification may enable high-fidelity heralded teleportation, using minimally entangled yet steerable resources.