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arXiv:0707.0759 · Physical Review A

Optimal state in the Knill-Laflamme-Milburn scheme of linear optical teleportation

Andrzej Grudka, Joanna Modławska

Published Jan 14, 2008• 13 citations
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Abstract

We discuss some properties of the Knill-Laflamme-Milburn scheme for quantum teleportation with both maximally and nonmaximally entangled states. We derive the error correction scheme when one performs teleportation with nonmaximally entangled states and we find the probability for perfect teleportation. We show that the maximally entangled state is optimal in such a case. We also show how the error correction scheme can be implemented experimentally when one uses polarization encoding.

DOI
10.1103/physreva.77.014301

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We discuss some properties of the Knill-Laflamme-Milburn scheme for quantum teleportation with both maximally and nonmaximally entangled states. We derive the error correction scheme when one performs teleportation with nonmaximally entangled states and we find the probability for perfect teleportation. We show that the maximally entangled state is optimal in such a case. We also show how the error correction scheme can be implemented experimentally when one uses polarization encoding.
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 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.
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Quantum teleportation of qudits is revisited. In particular, we analyze the case where the quantum channel corresponds to a nonmaximally entangled state and show that the success of the protocol is directly related to the problem of distinguishing nonorthogonal quantum states. The teleportation channel can be seen as a coherent superposition of two channels, one of them being a maximally entangled state, thus leading to perfect teleportation, and the other, corresponding to a nonmaximally entangled state living in a subspace of the d-dimensional Hilbert space. The second channel leads to a teleported state with reduced fidelity. We calculate the average fidelity of the process and show its optimality.