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.
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.
A method of generating superdense coding based on quantum hyper-entanglement and facilitated by quantum networks is discussed. Superdense coding refers to the coding of more than one classical bit into each qubit. Quantum hyperentanglement refers to quantum entanglement in more than one degree of freedom, e.g. polarization, energy-time, and orbital angular momentum (OAM). The new superdense coding scheme permits 2L bits to be encoded into each qubit where L is the number of degrees of freedom used for quantum hyper-entanglement. The superdense coding procedure is based on a generalization of the Bell state for L degrees of freedom. Theory describing the structure, generation/transmission, and detection of the generalized Bell state is developed. Circuit models are provided describing the generation/transmission process and detection process. Detection processes are represented mathematically as projection operators. A mathematical proof that that the detection scheme permits the generalized Bell states to be distinguished with 100% probability is provided. Measures of effectiveness (MOEs) are derived for the superdense coding scheme based on open systems theory represented in terms of density operators. Noise and loss related to generation/transmission, detection and propagation are included. The MOEs include various probabilities, quantum Chernoff bound, a measure of the number of message photons that must be transmitted to successfully send and receive a message, SNR and the quantum Cramer Rao’ lower bound. Quantum networks with quantum memory are used to increase the efficiency of the superdense coding scheme.
Abstract The superdense coding protocol is essential for quantum communication, allowing more efficient data transmission. This protocol facilitates the transfer of two bits of classical information using just one qubit by leveraging a pre-existing pair of Bell states. To achieve this capability, traditional implementations of superdense coding depend on entangled states, such as Bell states. This paper introduces a novel circuit that utilizes Bell diagonal states to implement the superdense coding protocol. We provide detailed instructions for the procedure using IBM’s Quantum Computing Lab, enabling practical applications in real-world contexts. Furthermore, the paper highlights the security features of this protocol, emphasizing its significance for secure communication in quantum networks. The combination of efficiency and security represents a notable advancement in quantum information science. We implemented and tested the proposed superdense coding circuit on the IBM Q quantum computing platform using Qiskit. Through extensive simulations on IBM’s Statevector and QASM simulators, we assessed the performance of the circuit based on Bell diagonal states (BDS)in terms of accuracy, noise resilience, and resource efficiency. Our findings indicate that, while Bell diagonal states pose challenges related to noise and decoherence, they also provide potential advantages in reducing qubit usage and enhancing error correction. This research contributes to the exploration of alternative techniques for superdense coding, which may have applications in quantum communication and future quantum networks. However, additional theoretical and experimental investigations are necessary to fully evaluate the scalability and practicality of this approach.
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.
This study presents a generalized n--bit superdense coding protocol that enables the transmission of n classical bits of information using an entangled n--qubit quantum system and the transmission of n−1 qubits. The protocol involves creating a maximally entangled n--qubit GHZ state, encoding the classical message with Pauli--Z and Pauli--X gates, and then transmitting and decoding the message via quantum communication, quantum operations, and measurements. The key novelty of this work is an explicit, scalable n--bit encoding routine, realized on the GHZ channel with a low--depth encoding layer using only single--qubit Pauli--X and Pauli--Z operations.
The protocol was tested on real quantum hardware using Qiskit 2.0 and the IBM--Fez quantum computer for message lengths of 4, 6, 8, and 10 bits, as a circuit--level proof of concept on a single processor; the physical transmission of qubits between the parties was not implemented. Results show that success rates decrease as message length, transpiled circuit depth and gate count increase; the latter two are set mainly by transpilation rather than by the encoding itself. A mutual information analysis shows that the transmitted information exceeds the classical bound of n−1 bits only for short messages. Strategies to improve performance include sending messages in shorter segments and advances in qubit coherence and gate fidelity. This work offers a practical and easily scalable quantum communication protocol with potential applications in quantum networks and communication systems.
Quantum communication allows us to share information by using the quantum states of qubits. Superdense coding is a very popular protocol or scheme for quantum communication, which uses entangled qubits. Entangled qubits can also be used to share information using an ALOHA based protocol. Performance evaluation of these protocols is essential for their implementation in quantum communication. In this paper, we calculate the bit error rates (BERs) of these two entanglement-based quantum communication schemes. It has been noticed that the BER performance is improved in an ALOHA based scheme compared to the Superdense coding scheme. However, without using any error correction schemes, the BERs are still very high in both the cases compared to the classical communication methods. The BER performance can be further improved by using the appropriate error correction schemes, which are under investigation.