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Physica Scripta

Quantum teleportation via quantum channels with non-maximal Schmidt rank

M. A. Solís-Prosser, O. Jiménez, Leonardo Neves, A. Delgado

Published Mar 1, 2013• 5 citations
Publisher

Abstract

We study the problem of teleporting unknown pure states of a single qudit via a pure quantum channel with non-maximal Schmidt rank. We relate this process to the discrimination of linearly dependent symmetric states with the help of the maximum-confidence discrimination strategy. We show that with a certain probability, it is possible to teleport with a fidelity larger than the fidelity optimal deterministic teleportation.

DOI
10.1088/0031-8949/2013/t153/014058

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We study the problem of teleporting unknown pure states of a single qudit via a pure quantum channel with non-maximal Schmidt rank. We relate this process to the discrimination of linearly dependent symmetric states with the help of the maximum-confidence discrimination strategy. We show that with a certain probability, it is possible to teleport with a fidelity larger than the fidelity optimal deterministic teleportation.
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We study the process of quantum telecloning of d -dimensional pure quantum states using partially entangled pure states as quantum channel. This process efficiently mixes optimal universal symmetric cloning with quantum teleportation. It is shown that it is possible to implement universal symmetric telecloning in a probabilistic way using unambiguous state discrimination and quantum state separation schemes. It is also shown that other strategies, such as minimum error discrimination, lead to a decrease in the fidelity of the copies and that certain partially entangled pure states with maximal Schmidt rank lead to an average telecloning fidelity which is always above the optimal fidelity of measuring and preparation of quantum states. We also discuss the case of partially entangled pure states with non-maximal Schmidt rank. The results presented here are valid for arbitrary numbers of copies of a single-input qudit state of any dimension.
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.
We analyze entanglement swapping (ES) of partially entangled pure states with arbitrary Schmidt rank from the perspective of quantum state discrimination. It is shown that the standard deterministic ES protocol is related with an optimal minimum-error strategy. In this case the amount of entanglement of the states resulting from swapping is, in general, lower than the maximum achievable for the quantum channels involved. In this regard, we show that the ES protocol can be probabilistically improved resorting to optimal maximum-confidence (MC) discrimination strategy. Additionally, we show that the success probability of achieving entanglement above a prescribed value from standard deterministic ES can be increased by applying sequential MC measurements.
In this paper, we propose a protocol to deterministically teleport an unknown mixed state of qubit by utilizing a maximally bipartite entangled state of qubits as quantum channel. If a non-maximally entangled bipartite pure state is employed as quantum channel, the unknown mixed quantum state of qubit can be teleported with 1−(1− C 2 ) 1/2 probability, where C is the concurrence of the quantum channel. The protocol can also be generalized to teleport a mixed state of qudit or a multipartite mixed state. More important purpose is that, on the basis of the protocol, the teleportation of an arbitrary multipartite (pure or mixed) quantum state can be decomposed into the teleportation of each subsystem by employing separate entangled states as quantum channels. In the case of deterministic teleportation, Bob only needs to perform unitary transformations on his single particles in order to recover the initial teleported multipartite quantum state.
In this study,we will investigate the problem of teleportation of an arbitrary two-qubit state.Firstly,we show how the two-qubit state can be teleported with unit fidelity and unit probability by using a maximally entangled four-dimensional qudit pair as a quantum channel.Then,we put forward a scheme for probabilistic teleporting the state with unit fidelity via a partially entangled quantum qudit channel.The probability of successful teleportation is determined by the smallest Schmidt coefficient of the entangled qudit pair.