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International Journal of Pure and Apllied Mathematics

ENTROPY EFFECT IN QUANTUM COMPUTING AND INFORMATION: AN OPEN-SOURCE ENVIRONMENT SIMULATION

R.H. Moretti, M.F. Borges, Jose-Luis Machado, Camila Andrade Brandão

Published Dec 23, 2014• 1 citation
Publisher

Abstract

The technologies are rapidly developing, but some of them present in the computers, as for instance their processing capacity, are reaching their physical limits.It is up to quantum computation offer solutions to these limitations and issues that may arise.In the field of information security, encryption is of paramount importance, being then the development of quantum methods instead of the classics, given the computational power offered by quantum computing.In the quantum world, the physical states are interrelated, thus occurring phenomenon called entanglement.This study presents both a theoretical essay on the merits of quantum mechanics, computing, information, cryptography and quantum entropy, and some simulations, implementing in C language the effects of entropy of entanglement of photons in a data transmission, using Von Neumann entropy and Tsallis entropy.

DOI
10.12732/ijpam.v97i4.1

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The technologies are rapidly developing, but some of them present in the computers, as for instance their processing capacity, are reaching their physical limits.It is up to quantum computation offer solutions to these limitations and issues that may arise.In the field of information security, encryption is of paramount importance, being then the development of quantum methods instead of the classics, given the computational power offered by quantum computing.In the quantum world, the physical states are interrelated, thus occurring phenomenon called entanglement.This study presents both a theoretical essay on the merits of quantum mechanics, computing, information, cryptography and quantum entropy, and some simulations, implementing in C language the effects of entropy of entanglement of photons in a data transmission, using Von Neumann entropy and Tsallis entropy.
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Quantum entanglement, a fundamental phenomenon in quantum mechanics, holds immense potential for secure information transfer. This research explores the concept of utilizing quantum entanglement to encode information with enhanced security, surpassing traditional encryption methods. We propose a novel approach, termed "Quantum Information Entropy Encoding," that leverages the unique properties of entangled states to establish a secure communication channel. This method aims to achieve information security beyond the capabilities of classical cryptography through the application of entanglement-based data encoding. The core mechanism centers around creating a quantum state representation of information, exploiting entanglement for enhanced security, and integrating this encoding into quantum computation for information entropy assessment. We detail the proposed algorithm, its underlying principles, and preliminary experimental results demonstrating the potential of this approach. This work explores the theoretical foundations and practical implementation challenges related to this new approach to quantum information security.
Nowadays quantum information science is in a state of theoretic completeness; much is invested to research quality physical solution for quantum computer and applications, so the field is led by physicists and information science and technology professionals. This field proved its potential and many (including us) believe it is in the right direction to go. In this paper we'll try to present and analyze the philosophy and nature of quantum information science and discuss hot topics around them. Although there is plenty of space for discussion around this field, we will concentrate on some important issues, such as quantum communication, algorithms and cryptography. Communication promises to be one of the directions where huge breakthroughs will be observed (entanglement as communication), algorithms have already shown exponential advantage (Shor's factoring) over classical counterparts and different paradigm of information processing. Cryptography seems to utilize general achievements in quantum information science and make encryption protocols very secure. Quantum computation can be understood as a generalization of classical computation: The possible states of a quantum computer are superpositions of bit strings, where the tensor factor is called a quantum bit or qubit. To evaluate the computational complexity of an algorithm, either classical or quantum, it is necessary to specify a set of elementary operations, the number of which used during the computation quantities the complexity. If we allow arbitrary permutations classically, or arbitrary unitary transformations quantum mechanically, any state can be reached from any other state in a single step. The general kind of quantum computer should be programmed to perform distinctively quantum operations such as generating two bits in a superposition state. An appropriate measurement on the final superposed state of the computer produces a probabilistic behavior of the output, and because of this quantum parallelization does not reduce the average time required for parallelizable computation completion. The development of quantum computing science and technology as well as quantum computers as thinking machines is very dependent on different achievements of modern research in fundamental and applied physics as well as novel mathematical methods and tools.
A fundamental concept in quantum mechanics, quantum entanglement describes a one-of-a-kind occurrence in which two particles, separated by physical distance, become physically connected so that the states of one particle can instantly affect the states of the other. Quantum entanglement has both theoretical and practical consequences for communication and information processing, which are explored in this study. This article explores the latest developments in quantum cryptography, quantum teleportation, and quantum computing, focusing on how these technologies have the ability to transform communication networks, computational speed, and data security. While outlining potential future research directions, the report delves into issues including scalability and decoherence. This manuscript uses entanglement to highlight its revolutionary impact on the development of scientific and technological frontiers.
The rapid progress made in the domain of quantum computing has presented a number of opportunities as well as challenges in numerous domains, particularly in the domain of cryptography and security. The extraordinary computational capacity of quantum computing can be used to conduct computations at a much faster rate than classical computing, which makes quantum computing a potential threat to many cryptography systems. This paper presents a focused analysis of quantum computing’s influence on a cryptographic system and the digital data protection. This paper examines the basic concepts of quantum physics and discusses the challenges of classical cryptography protocols, along with the analysis of post-quantum solutions, focusing on the issues of secrecy, verification, and quantum security of these protocols. The evidence collected from various sources proves that quantum algorithms pose a threat to classical public-key cryptosystems; on the other hand, ML-KEM, ML-DSA, and SLH-DSA are the post-quantum solutions. It is imperative that a move to quantum-resistant encryption entails appropriate migration policies and standards alongside technological advancements. Such conclusions suggest that adequate preparedness can help in enhancing the security of encrypted information with advancing quantum technology. This study emphasizes the significance of hybrid cryptographic implementations and cryptographic agility in the changeover from classical cryptography to quantum cryptography security frameworks. Real-world implementation should strike a balance between security power and efficiency of computation among other considerations.
Information and computation theory have undergone a spurt of new growth, and a renewal of their historic connection to basic physics, as they have expanded to treat the intact transmission and processing of quantum states, and the interaction of such 'quantum information' with traditional forms of information. We may wonder why this did not happen earlier, as quantum principles have long been accepted as fundamental to all of physics. Perhaps the founders of information and computation theory, such as Shannon, Turing and von Neumann, were too accustomed to thinking of information processing in macroscopic terms, not yet having before them the powerful examples of the genetic code and ever-shrinking microelectronics. Be that as it may, information until recently has largely been thought of in classical terms, with quantum mechanics playing a supporting role in the design of the equipment to process it, and setting limits on the rate at which it could be sent through certain channels. Now we know that a fully quantum theory of information and information processing offers, among other benefits, a brand of cryptography whose security rests on fundamental physics, and a reasonable hope of constructing quan- tum computers that could dramatically speed up the solution of certain mathematical problems. These benefits depend on distinc- tively quantum properties such as uncertainty, interference and entanglement. At a more fundamental level, it has become clear that an information theory based on quantum principles extends and completes classical information theory, just as complex numbers extend and complete the reals. Besides quantum generalizations of classical notions such as sources, channels and codes, the new theory includes two complementary, quantifiable kinds of information— classical information and quantum entanglement. Classical infor- mation can be copied at will, but can only be transmitted forward in time, to a receiver in the sender's forward light cone. Entanglement in contrast, cannot be copied, but can connect any two points in space-time. Conventional data processing operations destroy entanglement, but quantum operations can create it and use it for various purposes, such as speeding up certain classical computa- tions and assisting in the transmission of classical information or intact quantum states. Part of the new quantum information theory is the qualitative and quantitative study of entanglement, and its interactions with classical information. Any means, such as an optical fibre, of delivering quantum systems more or less intact from one place to another, may be viewed as a quantum channel. Unlike classical channels, which are well characterized by a single capacity, quantum channels have several distinct capacities, depending on what one is trying to use them for, and what auxiliary resources are brought into play. New effects involving quantum information continue to be discovered, not only in the traditional areas of computation, channel capacity, and cryptography, but in areas such as commu- nication complexity and game theory.