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Communications in Theoretical Physics

Increasing Success Probability of a Probabilistic Quantum Teleportation

Chunjie Xu, Wen Ji Zhang, Zhanjun Zhang

Published Dec 1, 2010• 2 citations
Publisher

Abstract

The probabilistic quantum teleportation scheme [ Phys. Lett. A 305 (2002) 12 ] is improved via two seemingly different methods (i.e., the usual ancilla method and the so-called Kraus method), respectively. The essence of the improvements is to fetch a part from the residues so that the success probability is accordingly increased. The two improved versions and a similar protocol proposed by Li et al. [ Phys. Rev. A 61 (2000) 034301 ] are compared mutually and discussed. It is found that they are equally efficient and can reach the success probability threshold determined by the inherent entanglement of the quantum channel.

DOI
10.1088/0253-6102/54/6/12

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Communications in Theoretical Physics•Dec 1, 2010•0 citations
The probabilistic quantum teleportation scheme [ Phys. Lett. A 305 (2002) 12 ] is improved via two seemingly different methods (i.e., the usual ancilla method and the so-called Kraus method), respectively. The essence of the improvements is to fetch a part from the residues so that the success probability is accordingly increased. The two improved versions and a similar protocol proposed by Li et al. [ Phys. Rev. A 61 (2000) 034301 ] are compared mutually and discussed. It is found that they are equally efficient and can reach the success probability threshold determined by the inherent entanglement of the quantum channel.
We extend the research program initiated in [Phys. Rev. A 92, 012338 (2015)] from noisy deterministic teleportation protocols to noisy probabilistic (conditional) protocols. Our main goal now is to study how we can increase the fidelity of the teleported state in the presence of noise by working with probabilistic protocols. We work with several scenarios involving the most common types of noise in realistic implementations of quantum communication tasks and find many cases where adding more noise to the probabilistic protocol increases considerably the fidelity of the teleported state, without decreasing the probability of a successful run of the protocol. Also, there are cases where the entanglement of the channel connecting Alice and Bob leading to the greatest fidelity is not maximal. Moreover, there exist cases where the optimal fidelity for the probabilistic protocols are greater than the maximal fidelity (2/3)(2/3)(2/3) achievable by using only classical resources, while the optimal ones for the deterministic protocols under the same conditions lie below this limit. This result clearly illustrates that in some cases we can only get a truly quantum teleportation if we use probabilistic instead of deterministic protocols.
Very recently, Lee et al. proposed a secure quantum teleportation protocol to transfer shared quantum secret between multiple parties in a network [Phys. Rev. Lett. 124 060501 (2020)]. This quantum network is encoded with a maximally entangled GHZ state. In this paper, we consider a partially entangled GHZ state as the entanglement channel, where it can achieve, probabilistically, unity fidelity transfer of the state. Two kinds of strategies are given. One arises when an auxiliary particle is introduced and a general evolution at any receiver’s location is then adopted. The other one involves performing a single generalized Bell-state measurement at the location of any sender. This could allow the receivers to recover the transmitted state with a certain probability, in which only the local Pauli operators are performed, instead of introducing an auxiliary particle. In addition, the successful probability is provided, which is determined by the degree of entanglement of the partially multipartite entangled state. Moreover, the proposed protocol is robust against the bit and phase flip noise.
In this paper we redesign the probabilistic teleportation scheme considered in Phys. Rev. A 61 , 034301 (2000) by Wan-Li Li et al. , where the optimal state extraction protocol complements the basic teleportation process with a partially entangled pure state channel, in order to transfer the unknown state with fidelity 1. Unlike that scheme, where the information of the unknown state is lost if the state extraction fails, our proposal teleports exactly and optimally an unknown state, and allows to recover faithfully that state when the process has not succeeded. In order to study the resilience of the scheme, we apply it to the teleportation problem through a quantum channel in a mixed state with pure dephasing. We find that a successful process transfers an unfaithful state, namely, the outcome state acquires the decoherence of the channel, but the unknown state is recovered by the sender with fidelity 1 if the teleportation fails. In addition, in this case, the fidelity of the teleported state has quantum features only if the channel has an amount of entanglement different from zero.
Teleportation of a qubit with two partially entangled qubit states linking three nodes as quantum channels is extensively studied via the usual ancilla method. With the method two realization approaches, i.e., the node progression approach and the global accumulation approach, are presented. Their resource consumptions, operation complexities, and efficiencies are evaluated and compared. It is found that the latter approach is better than the former one besides the error is partially self-corrected. The latter approach is further improved so that two merits are resultant. The improved version is compared with a similar protocol [M.Y. Wang and F.L. Yan, Eur. Phys. J. D 54 (2009) 111 ]. Their merits and additional costs are exposed.