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Physica Scripta

Resumable probabilistic teleportation of a three qubit state using different quantum channels

Manoj Kumar Mandal, Binayak Samadder Choudhury, Soumen Samanta, Arpan Dhara

Published Apr 8, 2024• 6 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ad3bf3

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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 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.
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.
Abstract Teleportation across short distances has become relevant in view of some recent developments in quantum technology. The advantage here is that certain auxiliary qubits can be accessed and utilized by both the sender and the receiver. Such act reduces the requirement of the number of qubits in the entangled quantum channel which would have been otherwise necessary. In this paper we present a short-distance teleportation protocol by which an arbitrary three-qubit state can be transferred with the help of auxiliary qubits and a maximally entangled Bell-State. In the second part of the paper we introduce a probabilistic short-distance protocol for the same arbitrary three-qubit state by using a non-maximally entangled Bell-state. The success probability of the protocol is calculated and its relation with the first protocol is discussed. We presented a circuit diagram for the first protocol and execute it in the IBM-QE platform.
In this paper, we present two different quantum teleportation schemes of an arbitrary single-particle, one is perfect teleportation and the other is probabilistic teleportation.In the first scheme, a four-particle maximally entangled state is used as the quantum channel.Besides, Bob needs to apply appropriate unitary transformations according to Alice's measurement results to recover the unknown state and the success probability is 1.In the latter scheme, the quantum channel is a four-particle non-maximally entangled state, which is a more general state.Furthermore, Bob needs to introduce an auxiliary qubit so that he can reconstruct the unknown state with the success probability of ( ).
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.
This study presents a nondestructive scheme for the probabilistic quantum teleportation (QT) of two arbitrary unknown single-qudit states. The protocol enables one sender to simultaneously transfer these states to two distinct receivers under supervisory control, utilizing a partially entangled five-qudit state as the quantum channel. As a detailed exemplar, the specific case of three-dimensional probabilistic controlled QT with dual outputs is examined. We demonstrate that the optimal success probability is governed by the smallest superposition coefficient within the two product states constituting the partially entangled channel. A key feature of our approach involves the sender employing two auxiliary qudits. These qudits function as a quantum measurement apparatus; if the QT attempt fails, the information recorded in them can be erased, allowing the sender to restore the original unknown states, thus preserving their information. This nondestructive characteristic facilitates repeated attempts of the controlled two-output QT process, limited only by the availability of quantum channels. Our findings confirm that successful high-dimensional QT can be achieved even with weakly entangled channels through numerous repetitions, whereas strongly entangled channels require considerably fewer attempts.