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arXiv:0708.4018

Concealed Quantum Information

Luis Roa

Published Aug 29, 2007• 0 citations
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Abstract

We study the teleportation scheme performed by means of a partially entangled pure state. We found that the information belonging to the quantum channel can be distributed into both the system of the transmitter and the system of the receiver. Thus, in order to complete the teleportation process it is required to perform an "unambiguous non-orthogonal quantum states discrimination" and an "extraction of the quantum information" processes. This general scheme allows one to design a strategy for concealing the unknown information of the teleported state. Besides, we showed that the teleportation and the "concealing the quantum information" process, can be probabilistically performed even though the bipartite quantum channel is maximally entangled.

DOI
10.48550/arxiv.0708.4018

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Quantum teleportation is of significant meaning in quantum information. We study the probabilistic teleportation of unknown two-qubit entangled state utilizing non-maximally entangled GHZ state as quantum channel. We formulate it as unambiguous state discrimination problem and derive exact optimal POVM operator for maximizing the success probability of unambiguous state discrimination. Only one three-qubit POVM for the sender, one two-qubit unitary operation for the receiver and two cbits for outcome notification are required in this scheme. The unitary operation is given in the form of concise formula and average fidelity is calculated. We show that our scheme is applicable in the situation where the information of quantum channel is only available for the sender.
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We found a scheme for teleporting probabilistically an unknown pure state with optimal probability and without losing the information of the state to be teleported. Accordingly, without having to have copies of the unknown state, the teleportation process can be repeated as many times as one has available quantum channels. Thus, although the quantum channels have a weak entanglement, teleportation is achievable with a high number of repetitions, whereas for channels with strong entanglement only a small number of repetitions are required to guarantee successful teleportation.
Quantum teleportation is of significant meaning in quantum information. In this paper, we study the probabilistic teleportation of a two-qubit entangled state via a partially entangled Greenberger-Horne-Zeilinger (GHZ) state when the quantum channel information is only available to the sender. We formulate it as an unambiguous state discrimination problem and derive exact optimal positive-operator valued measure (POVM) operators for maximizing the probability of unambiguous discrimination. Only one three-qubit POVM for the sender, one two-qubit unitary operation for the receiver, and two cbits for outcome notification are required in this scheme. The unitary operation is given in the form of a concise formula, and the fidelity is calculated. The scheme is further extended to more general case for transmitting a two-qubit entangled state prepared in arbitrary form. We show this scheme is flexible and applicable in the hop-by-hop teleportation situation.
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