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arXiv:1903.11339 · Journal of Experimental and Theoretical Physics

Probabilistic Teleportation of a Single Qubit: Unearthing New W-Class of States

Satyabrata Adhikari

Published Sep 1, 2020• 6 citations
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Abstract

Abstract In this work, we propose a probabilistic teleportation protocol to teleport a single qubit via three-qubit W-states using two-qubit measurement basis. We show that for the proper choice of the state parameter of the resource state, it is possible to make success probability of the protocol very high. We deduce the condition for the successful execution of our teleportation protocol and this gives us new class of three-qubit W-states which act as a resource state. We have constructed operators that can be used to verify the condition of teleportation in experiment. This verification is necessary for the detection of whether the given three-qubit state is useful in our teleportation protocol or not. Further we quantify the amount of entanglement contained in the newly identified shared W-class of states. Moreover, we show that the W-class of shared state used in the teleportation protocol can be prepared using NMR set up.

DOI
10.1134/s1063776120090010

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Abstract In this work, we propose a probabilistic teleportation protocol to teleport a single qubit via three-qubit W-states using two-qubit measurement basis. We show that for the proper choice of the state parameter of the resource state, it is possible to make success probability of the protocol very high. We deduce the condition for the successful execution of our teleportation protocol and this gives us new class of three-qubit W-states which act as a resource state. We have constructed operators that can be used to verify the condition of teleportation in experiment. This verification is necessary for the detection of whether the given three-qubit state is useful in our teleportation protocol or not. Further we quantify the amount of entanglement contained in the newly identified shared W-class of states. Moreover, we show that the W-class of shared state used in the teleportation protocol can be prepared using NMR set up.
Agrawal and Pati \cite{agrawal} had shown that there exist a class of three-qubit W-states, which act as a resource state for the perfect teleportation of a single qubit. They have used three-qubit measurement basis to execute their teleportation protocol. In this work, we modify Agrawal-Pati teleportation protocol. Our modified teleportation protocol is based on two-qubit measurement basis for the perfect teleportation of a single qubit. We deduce the condition for the successful execution of modified teleportation protocol and this leads us to new class of three-qubit W-states, which is required as a resource state to achieve the modified perfect teleportation protocol. We have constructed operators that can be used to verify the condition of teleportation in experiment. This verification is necessary for the detection of whether the given three-qubit state is useful in modified teleportation protocol or not. Then we have shown that the set containing three-qubit W-states used in modified teleportation scheme is larger than the set of shared three-qubit W-states used in Agrawal-Pati teleportation protocol. Further we quantify the amount of entanglement contained in the newly identified shared three-qubit W-class of states needed for the perfect teleportation of a single qubit. Moreover, we show that the three-qubit W-class of shared states used in the two teleportation protocols can be prepared using NMR set up.
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.
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.
We propose a quantum teleportation protocol to transmit two types of three-qubit states in the form of both specific three-qubit unentangled states and three-qubit entangled states_by using twofold of three-qubit W class states with Bob’s ancillary particle. This paper shows that Bob’s unitary transformation is performed in two steps. Firstly, we utilize two unitary operations into Bob’s particle. Lastly, a unitary transformation is applied to reconstruct Bob’s information. Both the success probability and fidelity of the protocol can attain the values of one.
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.