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IEEE SoutheastCon

Quantum Authentication Protocol for Secure Quantum Superdense Coding

Teo Kim, Jinsuk Baek, John T. Yi

Published Mar 15, 2024• 3 citations
Publisher

Abstract

In quantum information theory, superdense coding allows two network entities to exchange two classical bits via a quantum channel using a single quantum bit (qubit) transmission, provided they have pre-shared an entangled qubit. An attacker intercepting the qubit during transmission cannot extract meaningful data without the other entangled qubit from the pair. However, an attacker can disrupt the communication by introducing its own qubit to the receiver. To enhance the security of superdense coding, we propose an authentication mechanism through a classical communication channel.

DOI
10.1109/southeastcon52093.2024.10500244

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In quantum information theory, superdense coding allows two network entities to exchange two classical bits via a quantum channel using a single quantum bit (qubit) transmission, provided they have pre-shared an entangled qubit. An attacker intercepting the qubit during transmission cannot extract meaningful data without the other entangled qubit from the pair. However, an attacker can disrupt the communication by introducing its own qubit to the receiver. To enhance the security of superdense coding, we propose an authentication mechanism through a classical communication channel.
Superdense coding proved that entanglement-assisted quantum communications can improve the data transmission rates compared to classical systems. It allows sending 2 classical bits between the parties in exchange of 1 quantum bit and a pre-shared entangled Bell pair. This paper introduces a new protocol which is intended for distributed communication. Using a pre-shared entangled Bell pair and 1 classical bit 2,5 classical bits can be transmitted in average. This means not only valuable increase in capacity but the two-way distributed operation opens new fields of investigation.
We are now ready to look at our first protocols for quantum information. In this section, we examine two communication protocols which can be implemented using the tools we have developed in the preceding sections. These protocols are known as superdense coding and quantum teleportation. Both are inherently quantum: there are no classical protocols which behave in the same way. Both involve two parties who wish to perform some communication task between them. In descriptions of such communication protocols (especially in cryptography), it is very common to name the two parties ‘Alice’ and ‘Bob’, for convenience. We will follow this tradition. We will repeatedly refer to communication channels. A quantum communication channel refers to a communication line (e.g. a fiberoptic cable), which can carry qubits between two remote locations. A classical communication channel is one which can carry classical bits (but not qubits).1 The protocols (like many in quantum communication) require that Alice and Bob initially share an entangled pair of qubits in the Bell state The above Bell state is sometimes referred to as an EPR pair. Such a state would have to be created ahead of time, when the qubits are in a lab together and can be made to interact in a way which will give rise to the entanglement between them. After the state is created, Alice and Bob each take one of the two qubits away with them. Alternatively, a third party could create the EPR pair and give one particle to Alice and the other to Bob. If they are careful not to let them interact with the environment, or any other quantum system, Alice and Bob’s joint state will remain entangled. This entanglement becomes a resource which Alice and Bob can use to achieve protocols such as the following. Suppose Alice wishes to send Bob two classical bits of information. Superdense coding is a way of achieving this task over a quantum channel, requiring only that Alice send one qubit to Bob. Alice and Bob must initially share the Bell state Suppose Alice is in possession of the first qubit and Bob the second qubit.
Superdense coding is a quantum communication protocol that enables the transmission of more than one classical bit of information per qubit, using entangled states. While superdense coding with 2-qubits is well understood and directly maps to the Bell states, the same cannot be said for higher numbers of qubits. This project aims to develop an algorithm for superdense coding using a larger number of qubits, while analyzing how the capacity for information transmission scales with qubit count. Additionally, we will determine the error thresholds for accurately reconstructing the encoded information and investigate how error scales as the number of qubits increases. Gaining a deeper understanding of superdense coding has significant applications in quantum cryptography, as superdense coding schemes can be used to set up quantum secure direct communication (QSDC) protocols.
The aim of the research is the mathematical analysis of quantum superdense coding based on quantum entanglement to increase the efficiency and reliability of information transmission in quantum communication systems. The essence of quantum superdense coding is the ability to transmit two classical bits of information using one qubit, which is part of an entangled pair. The fundamental principles of the superdense quantum coding method are considered. The relevance of the research in the context of the development of secure quantum communications and optimization of information transmission in quantum networks is substantiated. A review of modern scientific publications devoted to the theoretical principles of superdense coding is conducted, which indicate the development potential and practical prospects of this direction of quantum informatics. The analysis of mathematical modeling of quantum superdense encoding and decoding is performed using two alternative approaches – projective measurement in the Bell basis and the inverse Bell transform. It is shown that both approaches allow for the complete recovery of classical information transmitted using entangled quantum states. The advantage of the inverse Bell transform is the simplicity of implementation on quantum devices, the flexibility and accuracy of information processing, and the possibility of scaling, which makes it a reasonable choice in many practical applications. The influence of noise and decoherence on the efficiency of superdense coding has been studied, which is a critical factor in the practical implementation of this method in real quantum systems. A mathematical model of data transmission through a quantum channel under the action of additive white noise has been constructed. An analytical dependence of the probability of correct information recovery on the noise level has been established, which allows us to estimate the limits of reliability of superdense coding in noisy environments. Based on the research, the prospects for the practical application of superdense coding in quantum communication networks, in particular the quantum Internet, as well as in quantum computing and information security systems, have been outlined. The results obtained contribute to the further development of quantum technologies and can be used to create new protocols for highly efficient quantum data transmission.
We introduce a generalization of one-way superdense coding to two-way communication protocols for transmitting classical bits by using entangled quantum pairs. The proposed protocol jointly addresses the provision of entangled pairs and superdense coding, introducing an integrated approach for managing entanglement within the communication protocol. To assess the performance of the proposed protocol, we consider its data rate and resource usage, and we analyse this both in an ideal setting with no decoherence, and in a more realistic setting where decoherence must be taken into account. In the ideal case, the proposal offers a 50% increase in both data rate and resource usage efficiency compared to conventional protocols. Even when decoherence is taken into consideration, the quantum protocol performs better as long as the decoherence time is not extremely short. Finally, we present the results of implementing the protocol in a computer simulation based on the Netsquid framework. We compare the simulation results with the theoretical values.
Quantum superdense coding protocol is addressed in the literature as a promising approach for efficient quantum communication. It allows two parties, to transmit classical bits using quantum bits. However, its security is threatened by a scrambling attack that involves modifying the automated gate specification to effectively scramble the final measurement, and by a bijection attack that performs a bijective transformation on the final measured strings. In this paper, we propose a novel approach to preventing such attacks by introducing decoy qubits into the superdense coding protocol, which act as a source of randomness that can detect any tampering with the entangled states and enable the detection of an eavesdropper. To strategize the selection and sending of these decoy qubits and address the interaction between the sender, receiver, and eavesdropper, we propose a dynamic non-cooperative game-based approach evaluated with a Q-learning algorithm to model and analyze this problem as a benefit-cost model. The utility functions of the proposed game are based on the concepts of return on protection, which illustrates the gain of selecting and sending a decoy qubit, and return on attack, which illustrates the reward of the eavesdropper for performing an attack to compromise the communication. Moreover, we discuss and analyze the Nash equilibrium convergence of this attack-defense model. Finally, we perform simulation work using a Q-learning algorithm to show the effectiveness of the proposed model in assessing the behavior of the players and its ability to reach equilibrium within a finite number of steps.