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arXiv:quant-ph/0110031 · Journal of Optics B Quantum and Semiclassical Optics

Quantum channel of continuous variable teleportation and nonclassicality of quantum states

Masahiro Takeoka, Masashi Ban, Masahide Sasaki

Published Feb 7, 2002• 23 citations
arXivHTMLPDF

Abstract

Noisy teleportation of nonclassical quantum states via a two-mode squeezed-vacuum state is studied with the completely positive map and the Glauber-Sudarshan P -function. Using the nonclassical depth as a measure of transmission performance, we compare the teleportation scheme with the direct transmission through a noisy channel. The noise model is based on the coupling to the vacuum field. It is shown that the teleportation channel has better transmission performance than the direct transmission channel in a certain region. The bounds for such a region and for obtaining the nonvanished nonclassicality of the teleported quantum states are also discussed. Our model shows a reasonable agreement with the teleportation fidelity observed in the experiment performed by Furusawa et al (1998 Science 282 706). We finally mention the required conditions for transmitting nonclassical features in real experiments.

DOI
10.1088/1464-4266/4/2/306

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Noisy teleportation of nonclassical quantum states via a two-mode squeezed-vacuum state is studied with the completely positive map and the Glauber-Sudarshan P -function. Using the nonclassical depth as a measure of transmission performance, we compare the teleportation scheme with the direct transmission through a noisy channel. The noise model is based on the coupling to the vacuum field. It is shown that the teleportation channel has better transmission performance than the direct transmission channel in a certain region. The bounds for such a region and for obtaining the nonvanished nonclassicality of the teleported quantum states are also discussed. Our model shows a reasonable agreement with the teleportation fidelity observed in the experiment performed by Furusawa et al (1998 Science 282 706). We finally mention the required conditions for transmitting nonclassical features in real experiments.
A quantum channel consisting of continuous variable quantum teleportation based on the standard protocol is investigated. It is shown that a quantum channel for continuous variable teleportation by an aribitrary entangled state is equivalent to a generalized thermalizing channel. We also study the transmission of nonclassical states by a teleportation channel with a two-mode squeezed-vacuum state in a noisy environment. The transmisson performance is evaluated by using the Glauber-Sudarshan P function and the nonclassical depth. Finally, we compare the results obtained to those of a noisy direct transmission channel. It is shown that the teleportation channel performs better than the direct transmission channel in a certain region.
Properties of quantum states transmitted by means of continuous variable quantum teleportation are investigated. The necessary condition is obtained such that continuous variable quantum teleportation can transmit nonclassical properties of input states from a sender to a receiver. Furthermore, when a sender and receiver share a two-mode squeezed-vacuum state through a noisy quantum channel and a sender transmits Gaussian quantum states, the fidelity between the input state and the teleported state is calculated to evaluate the performance of the continuous variable quantum teleportation.
Quantum teleportation of a continuous-variable state is studied for the quantum channel of a two-mode squeezed vacuum influenced by a thermal environment. Each mode of the squeezed vacuum is assumed to undergo the same thermal influence. It is found that when the mixed two-mode squeezed vacuum for the quantum channel is separable, any nonclassical features, which may be imposed in an original unknown state, cannot be transferred to a receiving station. A two-mode Gaussian state, one of which is a mixed two-mode squeezed vacuum, is separable if and only if a positive well-defined P function can be assigned to it. The fidelity of teleportation is considered in terms of the noise factor given by the imperfect channel. It is found that quantum teleportation may give more noise than direct transmission of a field under the thermal environment, which is due to the fragile nature of quantum entanglement of the quantum channel.
Summary form only given. An unknown continuous-variable state can he teleported by use of the two-mode squeezed state as the quantum channel. If the quantum channel is maximally squeezed (100% squeezing), the unknown state will be perfectly reproduced at a remote place. However the assumption of the maximally squeezed quantum channel is unphysical as it means the infinite average photon number of the channel state. Moreover, the interaction of the channel state with the environment degrades the entanglement and purity of the channel. We are interested in how the nonclassical features of the unknown state is revived by quantum teleportation in the real world. It is obvious that a nonclassical nature in the unknown state can be lost during the teleportation even when the channel is entangled unless it is maximally entangled Is it also obvious that any nonclassical feature, cannot be teleported by a classical correlated channel? We find the relation between the entanglement of the channel and teleportation of nonclassical nature in the unknown state.
Influences of an asymmetric noisy quantum channel on continuous variable entanglement and quantum teleportation are investigated. It is shown that when the resource of entanglement is a two-mode squeezed-vacuum state, the amount of the shared entanglement and the performance of the quantum teleportation are greater (smaller) in the symmetric quantum channel than in the asymmetric one if , where and are the average photon numbers of the two-mode squeezed-vacuum state and the thermal noise. When the quantum teleportation is carried out in the asymmetric quantum channel, introducing an additional loss makes better the performance of the quantum teleportation under certain conditions. The introduction of an additional loss makes smaller not only the shared entanglement but also the degree of the channel asymmetry.
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.