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arXiv:1410.1857 · Physical Review A

Analysis of N -qubit perfect controlled teleportation schemes from the controller's point of view

Xihan Li, Shohini Ghose

Published Jan 14, 2015• 33 citations
arXivHTMLPDF

Abstract

We quantitatively analyze and evaluate the controller's power in $N$-qubit controlled teleportation schemes. We calculate the minimum control power required to ensure the controller's authority such that the teleportation fidelity without the controller's permission is no more than the classical bound. We revisit several typical controlled teleportation schemes from the controller's point of view and evaluate the control power in these schemes. We find that for teleporting arbitrary $N$-qubit states, each controller should control at least $N$ bits of useful information to ensure his or her authority over the protocol. We also discuss the general rules that must be satisfied by controlled teleportation schemes to ensure both teleportation fidelity and control power.

DOI
10.1103/physreva.91.012320

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We quantitatively analyze and evaluate the controller's power in NNN-qubit controlled teleportation schemes. We calculate the minimum control power required to ensure the controller's authority such that the teleportation fidelity without the controller's permission is no more than the classical bound. We revisit several typical controlled teleportation schemes from the controller's point of view and evaluate the control power in these schemes. We find that for teleporting arbitrary NNN-qubit states, each controller should control at least NNN bits of useful information to ensure his or her authority over the protocol. We also discuss the general rules that must be satisfied by controlled teleportation schemes to ensure both teleportation fidelity and control power.
We analyze and evaluate perfect controlled teleportation via three-qubit entangled channels from the point of view of the controller. The key idea in controlled teleportation is that the teleportation is performed only with the participation of the controller. We calculate a quantitative measure of the controller's power and establish a lower bound on the control power required for controlled teleportation. We show that the maximally entangled Greenberger-Horne-Zeilinger state is a suitable channel for controlled teleportation of arbitrary single qubits---the controller's power meets the bound and the teleportation fidelity without the controller's permission is no better than the fidelity of a classical channel. We also construct partially entangled channels that exceed the bound for controlled teleportation of a restricted set of states called the equatorial states. We calculate the minimum entanglement required in these channels to exceed the bound. Moreover, we find that in these restricted controlled teleportation schemes, the partially entangled channels can outperform maximally entangled channels with respect to the controller's power. Our results provide an alternative perspective on controlled teleportation schemes and are of practical interest since we propose useful partially entangled channels.
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As a variant of the original quantum teleportation, port-based teleportation has been proposed, and its various kinds of useful applications in quantum information processing have been explored. Two users in the port-based teleportation initially share an arbitrary pure state, which can be represented by applying one user's local operation to a bipartite maximally entangled state. If the maximally entangled state is a 2M2M2M-qudit state, then it can be expressed as MMM copies of a two-qudit maximally entangled state, where MMM is the number of ports. We here consider a generalization of the original port-based teleportation obtained from employing copies of an arbitrary bipartite (mixed) resource instead of copies of a pure maximally entangled one. By means of the generalization, we construct a concept of controlled port-based teleportation by combining controlled teleportation with port-based teleportation, and analyze its performance in terms of several meaningful quantities such as the teleportation fidelity, the entanglement fidelity, and the fully entangled fraction. In addition, we present quantities called the control power and the minimal control power for the controlled version on a given tripartite quantum state.
Controlled quantum teleportation involves a third party as a controller for the teleportation of state. Here, we present the novel protocols for controlling teleportation of the arbitrary two-qubit and three-qubit states through five-qubit and seven-qubit cluster states respectively. In these schemes, Alice sends the arbitrary qubit states to the remote receiver Bob through the cluster states as quantum channels under the control of Charlie. Bob can recover the mentioned states by making appropriate unitary operations, and we point out that the efficiency in our schemes is 100%. In the process of our analysis, we find the classical communication cost in our protocols is remarkably reduced when compared to the previous protocols. We perform the experimental realization of the above protocols on "IBM 16 Melbourne" quantum computer and "IBM quantum simulator" and we calculate the fidelity. We also examine the security analysis against Charlie, and these schemes which we considered here are secure against Charlie's attacks.