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International Conference on Electronics, Communications and Computing (IC|ECCO)

Superdense Coding of Information in Quantum Computer in the Paired Bosons Representation

Ion I. Geru

Published Apr 1, 2022• 0 citations
Publisher

Abstract

An alternative approach to superdense coding of information in quantum computing is proposed on the basis of Schwinger’s two-boson representation of angular momentum. Since the effective spin S = 2n-1 - ½ corresponds to the n-qubit system, this representation can be used in the quantum computing. Operators of the logical elements of the quantum circuit were found, performing superdense coding of information in the paired bosons representation. It is shown that for superdense coding of information, the results obtained in the spinor representation and in the representation of paired bosons coincide. For one-qubit systems, one of the two representations cannot be favored. In the case of n-qubit systems for n >> 1, the representation of paired bosons is probably more convenient for applications, since in this representation the explicit form of the Pauli operators X, Y, and Z does not depend on n.

DOI
10.52326/ic-ecco.2021/tap.04

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An alternative approach to superdense coding of information in quantum computing is proposed on the basis of Schwinger’s two-boson representation of angular momentum. Since the effective spin S = 2n-1 - ½ corresponds to the n-qubit system, this representation can be used in the quantum computing. Operators of the logical elements of the quantum circuit were found, performing superdense coding of information in the paired bosons representation. It is shown that for superdense coding of information, the results obtained in the spinor representation and in the representation of paired bosons coincide. For one-qubit systems, one of the two representations cannot be favored. In the case of n-qubit systems for n >> 1, the representation of paired bosons is probably more convenient for applications, since in this representation the explicit form of the Pauli operators X, Y, and Z does not depend on n.
This paper deals with the features of quantum computing for a system containing a relatively large number of qubits n, which is characterized by a half-integer effective spin S in the Schwinger representation of paired bosons. It was shown that for n = 70, the number of boson states corresponding to lowest 2S + 1 excited energy levels of each of the two harmonic oscillators implementing the two-boson representation of the effective spin S is N = 1070 = 1.18 x 1021. Under such conditions, it can be assumed with great precision that for n ≥ 70 all boson states of both harmonic oscillators participate in the implementation of the two-boson representation of the effective spin S. This allows one to apply the quantum field theory methods when performing quantum computations for multi-qubit systems. Another advantage of the Schwinger representation of paired bosons compared to the spinor representation when performing quantum computations for multi-qubit systems is that in the first case the form of the spin projection operators of the effective spin S does not depend on the number of qubits n.
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.