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arXiv:quant-ph/0012121 · Physical Review A

Quantum cloning and teleportation criteria for continuous quantum variables

Frédéric Grosshans, Philippe Grangier

Published Jun 12, 2001• 213 citations
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Abstract

We discuss the criteria presently used for evaluating the efficiency of quantum teleportation schemes for continuous variables. Using an argument based upon the difference between 1-to-2 quantum cloning (quantum duplication) and 1-to-infinity cloning (classical measurement), we show that a fidelity value larger than 2/3 warrants that the teleported state is the best possible remaining copy of the input state. This value has not been reached experimentally so far.

DOI
10.1103/physreva.64.010301

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We discuss the criteria presently used for evaluating the efficiency of quantum teleportation schemes for continuous variables. Using an argument based upon the difference between 1-to-2 quantum cloning (quantum duplication) and 1-to-infinity cloning (classical measurement), we show that a fidelity value larger than 2/3 warrants that the teleported state is the best possible remaining copy of the input state. This value has not been reached experimentally so far.
The continuous variables regime offers much promise for quantum information and computation protocols. In particular, the continuous variable polarisation teleportation is of great interest, both theoretically and experimentally, at the moment. In this thesis three schemes for continuous variable polarisation teleportation are analysed and their performance is rated. The double teleporter setup, the quantum nondemolition teleporter scheme and the biased entanglement teleporter setup are each discussed and evaluated. Two methods are employed for the evaluation of the teleportation success. The TV diagram which stresses the usefulness of the experimental design and the fidelity, which measures the quantum input to output state preservation. It is later shown that these two independent assessments, which consider physically different attributes, yield contradicting conclusions. Further it is shown that it is important to decide whether the objective of the polarisation teleportation is the transfer of information or the quantum state recreation before meaningful analysis using TV or fidelity can be made. Finally, a study of a special cloning limit for a particular input state is made, related to the two of the above polarisation teleportation schemes. A new cloning fidelity limit is derived for these cases and TV cloning limits of information transfer and correlations are discussed.
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.