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Beijing Youdian Xueyuan xuebao

Clients Transparency Properties in Probabilistic Teleportation

DU Jian-zhong

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

A bidirectional protocol of probabilistic teleportation on the clients/server model is proposed,leading to the maximal probability of successful teleportation.It is proved that the partially entangled quantum channel ∑dj=1∑di=1∑nk=1u(ji)biv(ik)|j〉|k〉 by the Schmidt decomposition is transparent to the clients.To perform probabilistic teleportation via the generally entangled quantum channel,the clients must know a unitary operator that transforms the quantum channel into the clients' transparent quantum channel.

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arXiv:1601.02501•Jan 3, 2016•0 citations
A bidirectional protocol of probabilistic teleportation on the clients/server model is proposed,leading to the maximal probability of successful teleportation.It is proved that the partially entangled quantum channel ∑dj=1∑di=1∑nk=1u(ji)biv(ik)|j〉|k〉 by the Schmidt decomposition is transparent to the clients.To perform probabilistic teleportation via the generally entangled quantum channel,the clients must know a unitary operator that transforms the quantum channel into the clients' transparent quantum channel.
Probabilistic unitary maps and probabilistic unitary quantum channels are introduced, many quantum information applications, including (unambiguous) teleportation, can be described as probabilistic unitary quantum channels. Some properties of probabilistic unitary maps and probabilistic unitary quantum channels are derived. The property of a probabilistic unitary quantum channel ensures certain simple form for the measurements involved in realizing the probabilistic unitary quantum channel. The relation between a probabilistic unitary quantum channel and a uniformly entangled state is established. The combined operation of a noisy quantum channel and the error correction operation is a probabilistic unitary channel, from this point of view the condition for the errors to be correctable is easily derived. The condition for the errors caused by a noisy channel to be correctable with any nonzero probability is also obtained. Dense coding with a partially entangled state can also be viewed as a probabilistic unitary quantum channel when all messages are required to be transmitted with equal probability of success, the maximal achievable probability of success is derived and the optimum protocol is also obtained. 1
Two-qubit quantum teleportation is closely related to quantum computation,so a teleportation protocol in which an arbitrary bipartite quantum state is perfectly teleported probabilistically from sender to receiver is proposed. One of 16 generalized non-maximally entangled Bell states (G states for simplicity) functions as quantum channel. The teleportation can be successfully realized with a certain probability if sender performs generalized Bell state measurements (G measurements) and receiver introduces an auxiliary particle and operates appropriate unitary transformations and single-qubit measurements. The probability of successful teleportation is determined by the smallest one among the coefficients' absolute values of the quantum channel.
Teleporation with partially entangled quantum channel cannot achieve unit fidelity and unit probability. We show that the conditions for faithful teleportation of a pure state or a mixed state can be described by the same general relation ρqρm=pI\rho_{q}\rho_{m} = pIρq​ρm​=pI, where ρq\rho_{q}ρq​ is the reduced density matrix of the quantum channel, ρm\rho_{m}ρm​ is the reduced density matrix of the measurement basis, and ppp is the probability of faithful teleportaion. These conditions are unchanged under unitary transformation. We also prove that using a four dimensional partially entangled quantum channel, it is not possible to find a set of orthogonal measurement basis that contains more than two faithfully teleporting measurements.