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Chapman & Hall/CRC eBooks

Probabilistic Teleportation Protocols

Binayak S. Choudhury, Soumen Samanta

Published Dec 10, 2025• 0 citations
Publisher

Abstract

The protocols presented in this chapter are probabilistic teleportation protocols in which there are cases of failures with certain probabilities. Probabilistic teleportation schemes of various kinds have been discussed in works like [ 1 , 41 , 45 , 76 , 82 , 85 , 98 , 118 , 135 , 168 , 169 , 180 ]. Generally the quantum resources used in these protocols are not maximally entangled. This is one explanation for the probabilistic nature of these protocols. The justification of studying these protocols is that the generation and preservation of resources for these protocols are less difficult compared to that of those where maximally entangled states are used. Also, there is a class of resumable protocols in which the probabilistic teleportation process can be repeated in the case where the attempt fails in the first place [ 21 , 52 , 104 , 105 ].

DOI
10.1201/9781003561439-13

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The protocols presented in this chapter are probabilistic teleportation protocols in which there are cases of failures with certain probabilities. Probabilistic teleportation schemes of various kinds have been discussed in works like [ 1 , 41 , 45 , 76 , 82 , 85 , 98 , 118 , 135 , 168 , 169 , 180 ]. Generally the quantum resources used in these protocols are not maximally entangled. This is one explanation for the probabilistic nature of these protocols. The justification of studying these protocols is that the generation and preservation of resources for these protocols are less difficult compared to that of those where maximally entangled states are used. Also, there is a class of resumable protocols in which the probabilistic teleportation process can be repeated in the case where the attempt fails in the first place [ 21 , 52 , 104 , 105 ].
We describe a new protocol where, by using a non-maximally entangled basis as the measurement basis, one can use a general pure entangled state as a resource for quantum teleportation. Using this protocol one can teleport a state with unit fidelity though less than unit probability. We also use the more natural language of quantum operations to describe this probabilistic teleportation. We also provide success and failure probabilities for this protocol. This scheme could be of use in real experiments which may be tested in the near future.
Abstract In this paper we describe two different probabilistic teleportation protocols for teleporting the same unknown 3-qubit state from the sender Alice to the receiver Bob. The speciality of the state is that it remains a 2-qubit entangled state after any of the three involved qubits is eliminated by partial trace operation. One of the protocols utilizes a two and a three-qubit separate channels while in the other protocol, a five-qubit channel is utilized. One of the channels in the first protocol is a non-maximally entangled Bell state while the 5-qubit channel used in the case of the second protocol is non-maximally entangled. Both the teleportation schemes are probabilistic with the feature that in the case of failure of the teleportation, the state to be teleported is not lost to the sender. So the process can be repeated after failure till success is achieved. Moreover, one of the channels is recovered in the failure case. Both protocols are resumable in the above sense. The above is the speciality of the present work. We analyze the efficiency of our protocol which shows that the present two protocols are better performing than some existing ones.
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.
We explicitly present a generalized quantum teleportation of a two-qubit entangled state protocol, which uses two pairs of partially entangled particles as quantum channel. We verify that the optimal probability of successful teleportation is determined by the smallest superposition coefficient of these partially entangled particles. However, the two-qubit entangled state to be teleported will be destroyed if teleportation fails. To solve this problem, we show a more sophisticated probabilistic resumable quantum teleportation scheme of a two-qubit entangled state, where the state to be teleported can be recovered by the sender when teleportation fails. Thus the information of the unknown state is retained during the process. Accordingly, we can repeat the teleportion process as many times as one has available quantum channels. Therefore, the quantum channels with weak entanglement can also be used to teleport unknown two-qubit entangled states successfully with a high number of repetitions, and for channels with strong entanglement only a small number of repetitions are required to guarantee successful teleportation.
We consider a generalized quantum teleportation protocol for an unknown qubit using non-maximally entangled state as a shared resource. Without recourse to local filtering or entanglement concentration, using standard Bell-state measurement and classical communication one cannot teleport the state with unit fidelity and unit probability. We show that using non-maximally entangled measurements one can teleport an unknown state with unit fidelity albeit with reduced probability. We also give a generalized protocol for entanglement swapping using non-maximally entangled states. I.
Abstract We propose two probabilistic resumable quantum teleportation schemes for an arbitrary two-qubit entangled state with different quantum channels. The characteristic of our schemes is that the initial state in the sender’s hand can be recovered instead of being destroyed when teleportation fails, so we can improve the success probabilities by repeating the teleportation process more times. The analysis results show that the number of repetitions required for successful teleportation depends on the entanglement strength of the quantum channels, and even weak entanglement enables a high probability of success.