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International Journal of Quantum Information

AN ECONOMICAL PROTOCOL FOR TELEPORTING M-QUNIT ENTANGLEMENT

Nguyen Ba An

Published Apr 1, 2006• 4 citations
Publisher

Abstract

We propose a protocol to teleport a type of unknown M-quNit entanglement using a single maximally entangled quNit pair as a quantum channel. The faithful teleportation is possible at the expense of consuming local resources together with additional bi-quNit operations at the receiving site. Although the full set of measurement outcomes at the sending site consists of M + 1 Nits, the classical data necessary to rebuild the original teleported state at the receiving site can be managed so that a message of only two Nits suffices. The proposed protocol is economical in the sense that the cost of both quantum nonlocal resource and classical communication is minimal and does not depend on M.

DOI
10.1142/s0219749906001840

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We propose a protocol to teleport a type of unknown M-quNit entanglement using a single maximally entangled quNit pair as a quantum channel. The faithful teleportation is possible at the expense of consuming local resources together with additional bi-quNit operations at the receiving site. Although the full set of measurement outcomes at the sending site consists of M + 1 Nits, the classical data necessary to rebuild the original teleported state at the receiving site can be managed so that a message of only two Nits suffices. The proposed protocol is economical in the sense that the cost of both quantum nonlocal resource and classical communication is minimal and does not depend on M.
We propose a scheme to realize quantum cloning of an unknown M -qudit equatorial-like entangled state. The first stage of the protocol requires teleportation. After the teleportation is accomplished, the receiver can reestablish the original state. In the second stage of the protocol, with the assistance (through a single-particle projective measurement) of the preparer, the perfect copy of an original state can be produced at the site of the sender. Our scheme requires a single maximally entangled qudit pair as the quantum channel and three dits classical communication. The scheme is feasible at the expense of consuming local resources which include M −1 ancillary qudits introduced by the receiver and additional bi-qudit operations. Moreover, we construct a sort of unitary transformations which ensure ancillary qudits are not necessarily introduced by the sender. Comparing to the previous protocols, the proposed protocol is economical due to that the cost of both quantum nonlocal resources and classical communication is lowest.
A simple scheme for teleporting an unknown M-qubit cat-like state is proposed. The steps of this scheme can be summarized simply: disentangle-teleport-reconstruct entanglement. If proper unitary operations and measurements from senders are given, the teleportation of an unknown M-qubit cat-like state can be converted into single qubit teleportation. In the meantime, the receiver should also carry out right unitary operations with the introduction of appropriate ancillary qubits to confirm the successful teleportation of the demanded entangled state. The present scheme can be generalized to teleport an unknown M-quNit state, i.e., an M-quNit state can be teleported by a single quNit entangled pair.
I propose to replace the dual classical and nonlocal channels used for teleporting unknown quantum states in the original protocol (OP) [Bennett, C. H., et al. Phys. Rev. Lett. 70 1895 (1993)] by either (i) one single quantum channel or (ii) two nonlocal channels in order to turn the OP into an all-quantum teleportation (AQT) protocol. Ideally, N runs of single channel AQT can be achieved with a single Einstein-Podolsky-Rosen (EPR) pair, in contrast with the OP, which consumes N EPR pairs. In the two nonlocal channels proposal, Alice uses the superdense coding technique to send Bob her result, which makes AQT more economical than OP.
We suggest a method for teleporting an unknown quantum state. In this method the sender Alice first uses a Controlled-Not operation on the particle in the unknown quantum state and an ancillary particle which she wants to send to the receiver Bob. Then she sends ancillary particle to Bob. When Alice is informed by Bob that the ancillary particle is received, she performs a local measurement on the particle and sends Bob the outcome of the local measurement via a classical channel. Depending on the outcome Bob can restore the unknown quantum state, which Alice destroyed, on the ancillary particle successfully. As an application of this method we propose a quantum secure direct communication protocol.