quantum Shannon theory Research Papers (original) (raw)

The aim of this book is to develop "from the ground up" many of the major, exciting, pre- and post-millenium developments in the general area of study known as quantum Shannon theory. As such, we spend a significant amount of time on... more

The aim of this book is to develop "from the ground up" many of the major, exciting, pre- and post-millenium developments in the general area of study known as quantum Shannon theory. As such, we spend a significant amount of time on quantum mechanics for quantum information theory (Part II), we give a careful study of the important unit protocols of teleportation, super-dense coding, and entanglement distribution (Part III), and we develop many of the tools necessary for understanding information transmission or compression (Part IV). Parts V and VI are the culmination of this book, where all of the tools developed come into play for understanding many of the important results in quantum Shannon theory.

Quantum computers use the power of quantum physics to give rise to new types of security. For example, classical bits can be copied, but qubits generally cannot. With the recent introduction of quantum computers, there is an emerging need... more

Quantum computers use the power of quantum physics to give rise to new types of security. For example, classical bits can be copied, but qubits generally cannot. With the recent introduction of quantum computers, there is an emerging need to harness the power of quantum cryptography schemes to overshadow the computing force of counterfeiters. In this article, we will investigate 2 major questions in cryptography, namely (1) how to communicate a secret securely among multiple parties and (2) how to create a secure quantum currency that is sustainable to quantum attacks. We will rst investigate the No-cloning theorem and the errorcorrection schemes, and plug these notations into threshold schemes and quantum money schemes to analyze how quantum mechanisms work in encrypting data, as well as how interactive attacks can possibly break the schemes. We do not provide a concrete answer to either of the questions, as all the methods discussed in this article have been proven to be vulnerable to attackers with adequate computing ability. Regardless, they are important foundations to more recent development in cryptography and public-key quantum money.

The application of ecological concepts to ethnobotanical studies, in particular of diversity, is analyzed. Diversity indices are important tools that may help in understanding human-environment interactions. Those indices allow... more

The application of ecological concepts to ethnobotanical studies, in particular of diversity, is analyzed. Diversity indices are important tools that may help in understanding human-environment interactions. Those indices allow comparisons on the use of plants by different populations in different environments. A review on recent major ethnobotanical journals was carried out, and 10 studies (7 from Latin America, 2 from Asia and 1 from Europe) were selected based on available data to calculate diversity indices. The Shannon-Wiener indices and rarefaction curves were obtained. High diversity on plant uses were found for studies carried out at Peru, Mexico, Brazil and Thailand. A low diversity was found for Tonga, and island biogeography theory is used to discuss these results. Sampling effort is evaluated through rarefaction curves. The estimation of the diversity of resources used by native populations may be useful when planning conservation areas and their management. A aplicação de conceitos de ecologia em estudos etnobotânicos, em particular diversidade, é analisada. Os índices de diversidade são ferramentas importantes que nos ajudam a entender as interações humanas com o ambiente. Esses indices permitem comparar o uso de plantas por populações diferentes em ambientes diferentes. Foi realizada uma revisão nos principals periódicos recentes de etnobotânica e foram selecionados 10 estudos (7 da America Latina, 2 da Ásia e l da Europa), com base na disponibilidade de dados, para o cálculo dos indices de diversidade. Indices de Shannon-Wiener e curvas de rarefação foram obtidas. Foi encontrada uma alta diversidade de uso de plantas para Peru, México, Brazil e Tailândia. Uma baixa diversidade foi encontrada em Tonga, e a biogeografia de ilhas é usada para discutir os resultados. O esforço de amostragem é avaliado com base nos curvas de rarefação. A estimativa da diversidade dos recursos usados por populações nativas pode ser util no planejamento de áreas de conservação e em seu manejo.

The Shannon entropy in the atomic, molecular and chemical physics context is presented by using as test cases the hydrogenic-like atoms H c , He + c and Li 2+ c confined by an impenetrable spherical box. Novel expressions for entropic... more

The Shannon entropy in the atomic, molecular and chemical physics context is presented by using as test cases the hydrogenic-like atoms H c , He + c and Li 2+ c confined by an impenetrable spherical box. Novel expressions for entropic uncertainty relation and Shannon entropies S r and S p are proposed to ensure their physical dimensionless characteristic. The electronic ground state energy and the quantities S r , S p and S t are calculated for the hydrogenic-like atoms to different confinement radii by using a variational method. The global behavior of these quantities and different conjectures are analyzed. The results are compared, when available, with those previously published.

In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon's R(D) theory in the case of Gaussian stationary processes, which says that transforming into a... more

In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon's R(D) theory in the case of Gaussian stationary processes, which says that transforming into a Fourier basis followed by block coding gives an optimal lossy compression technique; practical developments like transform-based image compression have been inspired by this result. In this paper we also discuss connections perhaps less familiar to the information theory community, growing out of the field of harmonic analysis. Recent harmonic analysis constructions, such as wavelet transforms and Gabor transforms, are essentially optimal transforms for transform coding in certain settings. Some of these transforms are under consideration for future compression standards. We discuss some of the lessons of harmonic analysis in this century. Typically, the problems and achievements of this field have involved goals that were not obviously related to practical data compression, and have used a language not immediately accessible to outsiders. Nevertheless, through an extensive generalization of what Shannon called the “sampling theorem”, harmonic analysis has succeeded in developing new forms of functional representation which turn out to have significant data compression interpretations. We explain why harmonic analysis has interacted with data compression, and we describe some interesting recent ideas in the field that may affect data compression in the future

1 16 16 15 15 2 12 11 11 12 3 . 8 5 7 10 4 . 6 5 7 - ~- For the dual of a Goppa code we could get very similar results as Theorem 4 and its corollary (for the minimum distancc of that code, see [12]). Since the dual distance of a... more

1 16 16 15 15 2 12 11 11 12 3 . 8 5 7 10 4 . 6 5 7 - ~- For the dual of a Goppa code we could get very similar results as Theorem 4 and its corollary (for the minimum distancc of that code, see [12]). Since the dual distance of a quadratic residue code of length n is at least &, we ...

This paper provides Shannon theoretic coding theorems on the impersonation attack and the substitution attack against authentication systems constructed by secret key cryptography. Though several lower bounds on the success probability of... more

This paper provides Shannon theoretic coding theorems on the impersonation attack and the substitution attack against authentication systems constructed by secret key cryptography. Though several lower bounds on the success probability of the impersonation attack and the substitution attack have been developed, their upper bounds are rarely discussed. This paper treats an extended authentication system including blocklength K and permits the decoding error probability tending to zero as K→∞. It is shown that 2-KI(W:E) is the smallest attainable upper bound of the success probability of the impersonation attack, where I(W;E) denotes the mutual information between cryptogram W and key E. A relationship between the success probability of the substitution attack and H(E|W) is also characterized, where H(E|W) denotes the conditional entropy of E given W

International Journal on Information Theory (IJIT) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of Information Theory. Authors are solicited to contribute to the... more

International Journal on Information Theory (IJIT) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of Information Theory. Authors are solicited to contribute to the journals by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the areas of Information Theory and applications.

O seminário discute uma possível articulação entre a Teoria Matemática da Comunicação e a Teoria Quântica, mais especificamente, tal conexão é feita por meio da entropia da informação que passa a ser representada nos espaços das posições... more

O seminário discute uma possível articulação entre a Teoria Matemática da Comunicação e a Teoria Quântica, mais especificamente, tal conexão é feita por meio da entropia da informação que passa a ser representada nos espaços das posições e dos momentos. Além disto, essas duas últimas quantidades são essenciais para a composição da chamada soma entrópica e da relação de incerteza entrópica. Os sistemas físicos tratados no presente estudo são o oscilador harmônico confinado e determinados átomos hidrogenoides confinados.