ua nt - p h / 01 02 09 7 v 2 5 J ul 2 00 1 Information losses in continuous variable quantum teleportation

It is shown that the information losses due to the limited fidelity of continuous variable quantum teleportation are equivalent to the losses induced by a beam splitter of appropriate reflectivity. Quantum teleportation allows the transmission of an unknown quantum state by combining the nonlocal quantum coherence of entangled states with the transmission of classical information obtained in a joint measurement of the unknown input state and one part of the entangled pair [1]. Ideally, the classical information transmitted contains no information about the input state and the output state is exactly identical with the input state. However, this ideal form of quantum teleportation requires maximal entanglement. In continuous variable quantum teleportation [2–4], only non-maximal entanglement is available. As a consequence, the output state is not perfectly identical to the input state while the statistics of the joint measurement depend on the properties of the input state [5]. The classical information channel then carries information on the input state which may be extracted, e.g. in order to eavesdrop on a quantum communication channel [6]. The relationship between the measurement information extracted and the change of the quantum state can be described in terms of a measurement dependent transfer operator [5]. In the following, the transfer operator describing the continuous variable teleportation process is derived and the equivalence with a feedback compensated beam splitter is established. The information obtained in quantum teleportation can then be identified with the reflected amplitude at the beam splitter while the output state of the teleportation corresponds to the transmitted beam, displaced by the feedback. The loss of quantum information due to the limited fidelity of