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Chinese Physics B

Control Power of High-Dimensional Controlled Bidirectional Dense Coding

Yuan Tian, Zexin Yang, Chuqi Ye, Jian Li

Published Apr 24, 2026• 0 citations

Abstract

Abstract Controlled dense coding introduces a controller within the dense coding communication framework. The controller’s actions determine whether communication occurs at maximum channel capacity, enhancing both security and flexibility. Strengthen the controller’s power to ensure information security. To enhance the controller’s power in controlled bidirectional dense coding(CBDC) scheme, we designed two distinct schemes: (1) The decentralized CBDC scheme under the dimensionality reduction of Alice, which is called A-CBDC scheme; (2) The AB-CBDC scheme indicates that the decentralized CBDC scheme is under the dimensionality reduction of Alice and Bob. Through systematic calculations, we quantified the control power of these two schemes in a four-dimensional extended Greenberger-Horne-Zeilinger (GHZ) class state channel. The computational results obtained in noisy channels indicate that the A-CBDC scheme achieves a maximum enhancement in control power of 0.5454 bits compared to the original CBDC scheme. The AB-CBDC scheme achieves an even greater enhancement, with a maximum control power enhancement of 1.0908 bits-twice that of the A-CBDC scheme. The increased control power indicates that information obtained without the controller’s authorization is more incomplete and has a higher error rate.

DOI: 10.1088/1674-1056/ae6440

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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.

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.

A scheme of controlled dense coding was proposed by using non-symmetric quantum channel in3×2×2 dimensional entangled state.The collapse of the state and entanglement between Alice and Bob were controlled by Charlie's local measurement on his particle in two dimension.Then the 3×2 dimensional non-symmetric quantum channel was controlled.It can be seen that the average amount of transmitted information of dense coding was controlled by Charlie's measurement angle.One can find that the average amount of information is more than 2 bits by using maximally entangled state in the non-symmetric quantum channel.Thus,this scheme is high-efficiency.In the case the entanglement is non-maximally,the transmitted information is determined by the measurement angle 6 and the coefficient /3 of the entangled state.

Abstract Ensuring information security in quantum communication often requires a supervisory mechanism to regulate and authenticate information transmission. In this study, we investigate controlled quantum teleportation (CQT) and controlled dense coding (CDC) using parameterized three-particle pure states as quantum channels. We assess the authority of the controlling party through two key metrics: uncontrolled fidelity and minimal control power. Our analysis reveals that for single-parameter three-particle pure states, when no controlling party is involved, the average uncontrolled fidelity exceeds the classical fidelity threshold, rendering them unsuitable as arbitrary single-particle CQT channels. For multi-parameter three-particle pure states, we derive explicit parameter conditions under which non-trivial control power emerges and provide analytical expressions for several representative cases. Additionally, in the context of CDC, we quantify the minimal control power required when employing single-parameter three-particle states as quantum channels. Our findings establish rigorous criteria for controller authority in parameterized quantum communication, offering both theoretical guarantees and practical insights for secure quantum networks. This work lays the foundation for adaptive quantum protocols where control power and fidelity can be dynamically optimized to enhance security and performance in real-world implementations.