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Journal of Shanxi University

Criteria of Quantum Teleportation for Different Continuous Variables

Kunchi Peng

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

The state evolution of quantum teleportation for different types of continuous variables is mathematically analyzed based on the measurement theory of quantum mechanics.The fidelities in different systems are deduced.Our results show that for different input state the expressions of fidelity and the nonclassical boundary are different.Comparing with the coherent state,when the input state is a nonclassical state higher quantum entanglement is required for obtaining the same fidelity.

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The state evolution of quantum teleportation for different types of continuous variables is mathematically analyzed based on the measurement theory of quantum mechanics.The fidelities in different systems are deduced.Our results show that for different input state the expressions of fidelity and the nonclassical boundary are different.Comparing with the coherent state,when the input state is a nonclassical state higher quantum entanglement is required for obtaining the same fidelity.
We derive an experimentally testable criterion for the teleportation of quantum states of continuous variables. This criterion is especially relevant to the recent experiment of Furusawa et al. [Science 282, 706-709 (1998)] where an input-output fidelity of 0.58pm0.020.58 \\pm 0.020.58pm0.02 was achieved for optical coherent states. Our derivation demonstrates that fidelities greater than 1/2 could not have been achieved through the use of a classical channel alone; quantum entanglement was a crucial ingredient in the experiment.
The fidelity of quantum teleportation of a single-mode squeezed state of light is calculated based on the general theory of quantum-mechanical measurement in the Schrödinger picture. It is shown that the criterion for the nonclassical state teleportation is different from that for coherent state. F = 1/2 is no longer the rigorous boundary between classical and quantum teleportation for a squeezed state of light. When the quantum entanglement of an Einstein–Podolsky–Rosen (EPR) beam used for teleportation and the parameters of the system are given, the fidelity depends on the squeezing of the input squeezed state. The higher the squeezing is, the smaller the fidelity is, and the lower the classical limitation of fidelity is. The dependence of the optimum gain for teleporting a squeezed vacuum state upon the EPR entanglement is also calculated. The results obtained provide important references for designing experimental systems of teleporting a non-classical state and judging the quality of the teleported quantum state.