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Physical Review A

Control power of high-dimensional controlled teleportation

Tie-Jun Wang, Guan-qun Yang, Chuan Xi Wang

Published Jan 16, 2020• 34 citations
Publisher

Abstract

To quantitatively analyze the control power of arbitrary $d$-dimensional controlled teleportation (CT), this paper investigates channels of entangled high-dimensional three-qudit standard Greenberger-Horne-Zeilinger (GHZ) and GHZ-type states. The upper bound on the controller's power is established in the $d$-dimensional CT scheme. We identify a trade-off between the control power and the capacity of the quantum channels. The control power can be enhanced by reducing the dimension of the teleported information in a suitably high-dimensional quantum channel, or by increasing the dimension of the qudit held by the controller. Under controlled teleporting of a single qubit in a perfect CT scheme, the control power is maximized in the three-dimensional GHZ-type state channel. This maximum control power exceeds the highest predicted value in previous works and the upper bounds of control power in a two-dimensional quantum channel. Our studies provide a feasible method for achieving higher control power, and it may provide approaches to define high-dimensional entanglement of multibody systems.

DOI
10.1103/physreva.101.012323

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To quantitatively analyze the control power of arbitrary ddd-dimensional controlled teleportation (CT), this paper investigates channels of entangled high-dimensional three-qudit standard Greenberger-Horne-Zeilinger (GHZ) and GHZ-type states. The upper bound on the controller's power is established in the ddd-dimensional CT scheme. We identify a trade-off between the control power and the capacity of the quantum channels. The control power can be enhanced by reducing the dimension of the teleported information in a suitably high-dimensional quantum channel, or by increasing the dimension of the qudit held by the controller. Under controlled teleporting of a single qubit in a perfect CT scheme, the control power is maximized in the three-dimensional GHZ-type state channel. This maximum control power exceeds the highest predicted value in previous works and the upper bounds of control power in a two-dimensional quantum channel. Our studies provide a feasible method for achieving higher control power, and it may provide approaches to define high-dimensional entanglement of multibody systems.
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.
We quantitatively analyze and evaluate the control power in a high-dimensional noisy quantum channel for transmitting classical information. We calculate the control power of the controlled dense coding scheme in a four-dimensional extended Greenberger-Horne-Zeilinger (GHZ) class state channel. Different from controlled teleportation, there is no tradeoff between the control power and the classical capacity of the optimal four-dimensional GHZ state quantum channel. Only when the channel is noisy and the sender is allowed to gain some control authority can the tradeoff between the control power and the classical capacity be activated, and the overall control power for transmitting classical information will be enhanced by reducing the classical capacity of the high-dimensional quantum channel. This noise induced characteristic is very different from that of transmitting quantum information, and it may provide new ideas and methods to develop the resource theory of quantum channels.
A general scheme for controlled teleportation of an arbitrary multi-qudit state with d -dimensional Greenberger–Horne–Zeilinger (GHZ) states is proposed. For an arbitrary m -qudit state, the sender Alice performs m generalized Bell-state projective measurements on her 2 m qudits and the controllers need only take some single-particle measurements. The receiver Charlie can reconstruct the unknown m -qudit state by performing some single-qudit unitary operations on her particles if she cooperates with all the controllers. As the quantum channel is a sequence of maximally entangled GHZ states, the intrinsic efficiency for qudits in this scheme approaches 100% in principle.
We generalize the control power of a perfect controlled teleportation of an entangled three-qubit pure state, suggested by Li and Ghose [Phys. Rev. A 90, 052305 (2014)], to the control power of a general controlled teleportation of a multiqubit pure state. Thus, we define the minimal control power, and calculate the values of the minimal control power for a class of general three-qubit Greenberger-Horne-Zeilinger (GHZ) states and the three-qubit WWW class whose states have zero three-tangles. Moreover, we show that the standard three-qubit GHZ state and the standard three-qubit WWW state have the maximal values of the minimal control power for the two classes, respectively. This means that the minimal control power can be interpreted as not only an operational quantity of a three-qubit quantum communication but also a degree of three-qubit entanglement. In addition, we calculate the values of the minimal control power for general nnn-qubit GHZ states and the nnn-qubit WWW-type states.
Controlled quantum teleportation is an important extension of multipartite quantum teleportation, which plays an indispensable role in building quantum networks. Compared with discrete variable counterparts, continuous variable controlled quantum teleportation can generate entanglement deterministically and exhibit higher superiority of the supervisor's authority. Here, we define a measure to quantify the control power in continuous variable controlled quantum teleportation via Greenberger-Horne-Zeilinger-type entangled coherent state channels. Our results show that control power in continuous variable controlled quantum teleportation increases with the mean photon number of coherent states. Its upper bound is 1/2, which exceeds the upper bound in discrete variable controlled quantum teleportation (1/3). The robustness of the protocol is analyzed with photon absorption. The results show that the improving ability of the control power will descend by the increasing photon loss, with the upper bound unchanged and robust. Our results illuminate the role of control power in multipartite continuous variable quantum information processing and provide a criterion for evaluating the quality of quantum communication networks.
In this paper a scheme for controlled teleportation of arbitrary high-dimensional unknown quantum states is proposed by using the generalized Bell-basis measurement and the generalized Hadamard transformation. As two special cases, two schemes of controlled teleportation of an unknown single-qutrit state and an unknown two-qutrit state are investigated in detail. In the first scheme, a maximally entangled three-qutrit state is used as the quantum channel, while in the second scheme, an entangled two-qutrit state and an entangled three-qutrit state are employed as the quantum channels. In these schemes, an unknown qutrit state can be teleported to either one of two receivers, but only one of them can reconstruct the qutrit state with the help of the other. Based on the case of qutrits, a scheme of controlled teleportation of an unknown qudit state is presented.