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NATO science for peace and security series. D, Information and communication security

Nonmultiplicativity of probability of faithful teleportation in the Knill-Laflamme-Milburn scheme

Grudka Andrzej, Joanna Modławska

Published Jan 1, 2010• 0 citations
Publisher

Abstract

We discuss linear optical quantum teleportation in the Knill-Laflamme-Milburn scheme. We calculate the probability of faithful teleportation when one uses nonmaximally entangled states. We show that for single teleportation maximally entangled state is optimal. On the other hand for a sequence of teleportations nonmaximally entangled state is optimal. Hence, probability of faithful teleportation is nonmultiplicative. We also introduce measure of nonmultiplicativity and show that nonmultiplicativity increases with the number of teleportations.

DOI
10.3233/978-1-60750-547-1-195

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We discuss linear optical quantum teleportation in the Knill-Laflamme-Milburn scheme. We calculate the probability of faithful teleportation when one uses nonmaximally entangled states. We show that for single teleportation maximally entangled state is optimal. On the other hand for a sequence of teleportations nonmaximally entangled state is optimal. Hence, probability of faithful teleportation is nonmultiplicative. We also introduce measure of nonmultiplicativity and show that nonmultiplicativity increases with the number of teleportations.
We investigate multiple linear optical teleportation in the Knill-Laflamme-Milburn scheme with both maximally and nonmaximally entangled states. We show that if the qubit is teleported several times via a nonmaximally entangled state, then the errors introduced in the previous teleportations can be corrected by the errors introduced in the following teleportations. This effect is so strong that it leads to another interesting phenomenon: i.e., the total probability of successful multiple linear optical teleportation is higher for nonmaximally entangled states than maximally entangled states.
We consider multiple teleportation in the Knill-Laflamme-Milburn (KLM) scheme. We introduce adaptive teleportation, i.e., such that the choice of entangled state used in the next teleportation depends on the results of the measurements performed during the previous teleportations. We show that adaptive teleportation enables an increase in the probability of faithful multiple teleportation in the KLM scheme. In particular if a qubit is to be teleported more than once then it is better to use nonmaximally entangled states than maximally entangled ones in order to achieve the highest probability of faithful teleportation.
We show that the multiple teleportation protocol (MTP) given in reference (J Modławska and A Grudka 2008 Phys. Rev. Lett. 100 110503) is not restricted to the Knill–Laflamme–Milburn (KLM) framework. Rather, we show that MTP can be implemented using any teleportation scheme. We also present two new MTPs which, under certain situations, are more efficient than the original one, requiring half of the number of its teleportations to achieve at least the same probability of success ( ). One of the protocols, however, uses less entanglement than the others yielding, surprisingly, the greatest .