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Entropy

Control Power in Continuous Variable Controlled Quantum Teleportation

Yuehan Tian, Dunbo Cai, Nengfei Gong, Yining Li, Ling Qian, Runqing Zhang, Zhiguo Huang, Tiejun Wang

Published Nov 25, 2024• 2 citations
Publisher

Abstract

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.

DOI
10.3390/e26121017

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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.
Quantum nonlocality is an important resource for ensuring the security of quantum communication, which plays an indispensable role in building quantum networks. From bipartite to multipartite quantum systems, various inequalities are constructed as tools to unearth the quantum nonlocality. Control power is a crucial indicator for evaluating supervision, control, and collaboration in quantum networks. However, there is currently no exploration of the relevance between the control power and the quantum nonlocality in continuous variable quantum networks. In this work, based on the Mermin−Klyshko (MK) inequality with rotated quantum-number parity operators, we reveal the quantum nonlocality of general Greenberger−Horne−Zeilinger-type (GHZ-type) entangled coherent states, which can be extended to arbitrary multi-mode states. And then, we evaluate the control power through quantum nonlocality in continuous variable controlled quantum teleportation via a 3-mode GHZ-type entangled coherent state as channel. The results show that the control power of continuous variable quantum networks is a monotonically increasing function of genuine tripartite nonlocality. This quantitative dependence of control power on quantum nonlocality remains robust even with decoherence. The advantages of the MK inequality are simplicity in computation and scalability into arbitrary multi-mode channels. In addition, maximal violation of the MK inequality can be achieved more easily in the experiment. Our work proves that, compared with the Bell−Mermin inequality, the MK inequality performs better in experimental measurements of complete control power; compared with the Svetlichny inequality, the MK inequality avoids negative and unreasonable control power when inequalities exceed the classical upper bound. Therefore, the MK inequality is found to be a more reliable tool to reveal the quantum nonlocality in multipartite systems. This work illuminates the important application of nonlocality in multipartite continuous variable quantum communications and is of significance for the construction of practical quantum protocols.
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.
A controlled quantum teleportation of continuous variable using a tripartite Greenberger–Horne–Zeilinger (GHZ) state is proposed. The protocol enables controlling the fidelity of bipartite teleportation by shifting the phase of one of the three modes involved in the teleportation. This method reduces the quality of the tripartite entanglement and by quadrature measurements of the changed mode, bipartite entanglement can be distilled from the original entanglement. Because of the phase shift, the quality of the bipartite entanglement is inferior to the entanglement distilled from the original GHZ-state. By controlling the quality of the entanglement we realize the controlled teleportation.
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.
Hybrid entanglement between discrete-variable (DV) and continuous-variable (CV) quantum systems is an essential resource for heterogeneous quantum networks. Our previous work showed that in lossy channels the teleportation of DV qubits, via CV-entangled states, can be significantly improved by a new protocol defined by a modified Bell state measurement at the sender. This work explores whether a new, similarly modified, CV-based teleportation protocol can lead to improvement in the transfer of hybrid entangled states. To set the scene, we first determine the performance of such a modified protocol in teleporting CV-only qubits, showing that significant improvement over traditional CV-based teleportation is obtained. We then explore similar modifications in the teleportation of a specific hybrid entangled state showing that significant improvement over traditional CV-based teleportation is again found. For a given channel loss, we find teleporting the DV qubit of the hybrid entangled state can always achieve higher fidelity than teleporting the CV qubit. We then explore the use of various non-Gaussian operations in our modified teleportation protocol, finding that, at a cost of lower success probability, quantum scissors provides the most improvement in the loss tolerance. Our new results emphasize that in lossy conditions, the quantum measurements undertaken at the sender can have a surprising and dramatic impact on CV-based teleportation.
Quantum teleportation protocols of continuous variable (CV) Greeberger–Horne–Zeilinger (GHZ) and Einstein–Podolsky–Rosen (EPR) entangled states are proposed, and are generalized to teleportation of arbitrary multimode GHZ entangled states described by Van Loock and Braunstein (2000 Phys. Rev. Lett. 84 3482). Each mode of a multimode entangled state is teleported using a CV EPR entangled pair and classical communication. The analytical expression of fidelity for the multimode Gaussian states which evaluates the teleportation quality is presented. The analytical results show that the fidelity is a function of both the squeezing parameter r, which characterizes the multimode entangled state to be teleported, and the channel parameter p, which characterizes the EPR pairs shared by Alice and Bob. The fidelity increases with increasing p, but decreases with increasing r, i.e., it is more difficult to teleport the more perfect multimode entangled states. The entanglement degree of the teleported multimode entangled states increases with increasing both r and p. In addition, the fact is proved that our teleportation protocol of EPR entangled states using parallel EPR pairs as quantum channels is the best case of the protocol using four-mode entangled states (Adhikari et al 2008 Phys. Rev. A 77 012337).