Quantum Cryptography

Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.Comment: 55 pages, 32 figures; to appear in Reviews of Modern Physic

Minimizing Decoherence in Optical Fiber for Long Distance Quantum Communication

In this research work, I have derived analytical models for decoherence of quantum states of light and developed techniques based on Dynamical Decoupling (DD) to preserve the quantum state of polarization qubit and Orbital Angular Momentum (OAM) qudit in single-mode, multi-mode and specialized optical fibers. In subsequent work, I have derived the analytical model for decoherence of an entangled state in an optical fiber to show that such a decoherence causes loss of entanglement. I also showed that such states can be preserved with DD. In Chapter 1, I have introduced the subject of a quantum computer and its relation to quantum communication. I give a brief overview of fundamental concepts and tools required to understand the subject matter. In Chapter 2, I discuss optical fibers from the perspective of the electromagnetic wave in a waveguide and explain the modes in an optical fiber. Later, I explain about the sources of noise or refractive index fluctuation in an optical fiber and show how to numerically reproduce a model of an optical fiber. In Chapter 3, I introduce the topic of quantum decoherence and discuss in detail an open-loop control technique called Dynamical Decoupling, that is applied to the system to minimize decoherence. I discuss ideal and nonideal pulse sequences used for suppressing decoherence. In Chapter 4, I derive the analytical model for decoherence of a polarization qubit in a single-mode, multi-mode fiber, and decoherence OAM qudit in specialized multi-mode fiber. In Chapter 5, I introduce the topic of entanglement for the bipartite system and multi-partite system, and a measure called concurrence to quantify the entanglement. I then derive the analytic model for decoherence of a pure entangled state and show that decoherence causes loss of entanglement for the case of a pure and mixed Werner-like state. \break In Chapter 6, I discuss the method of numerical simulation and show by numerical simulation that polarization qubit, OAM qudit and entanglement of polarization qudit can be preserved with dynamical decoupling in an optical fiber. In Chapter 7, I have summarized the results and discuss the scope of future work. In the appendix, I have included additional research work not directly related to the current topic of decoherence in an optical fiber. To summarize my research, I have derived a model for decoherence and then numerically showed that a polarization qubit can be preserved in a single mode and multi-mode optical fiber. I also show that an OAM qudit can be preserved for a certain maximum value of quantum number l . Finally, I show that entanglement of pure and Werner mixed states can be preserved

Análisis de algoritmos criptográficos clásicos vs algoritmos cuánticos.

En este trabajo de investigación se realizó una comparación de los algoritmos criptográficos cuánticos vs clásicos con respecto a la seguridad en la obtención de la clave, en base a una revisión sistemática de donde se definió parámetros medibles de comparación, entre estos algoritmos como: la unidad estructural de la información, base de su seguridad, origen de la clave, tamaño de la clave, si el atacante copia la información, detección de intrusos y tecnología aplicada en el mercado, es de importancia conocer el algoritmo criptográfico más fuerte para la seguridad de la información debido a que la tecnología va en incremento y al mismo tiempo la información se convierte en un activo de gran valor a proteger ya que los hackers al interceptar información pueden realizar denegación de servicios, falta de integridad en datos, daños físicos a estructuras, robos millonarios de dólares e información. También se desarrolló el estudio técnico-económico para la de implementar un sistema cuántico en una infraestructura gubernamental del Consejo Nacional Electoral (CNE). Del estudio se determinó que los algoritmos criptográficos cuánticos son más apropiados para este propósito, esto se demostró con el método estadístico CHI cuadrado, para la comprobación de hipótesis. Se concluye que es técnicamente factible la propuesta de implementar criptografía cuántica con el algoritmo BB84 en la estructura nacional gubernamental CNE, con una inversión aproximada al 0.022% del gasto público de 2017. Se recomienda implementar la propuesta técnica económica planteada en la presente investigación para en la infraestructura de CNE en función de garantizar la seguridad de la información.In this research work, a comparison of quantum vs classical cryptographic algorithms was made with regard to the security in obtaining the key, it was based on a systematic review where measurable parameters of comparison were defined, among these algorithms as: the structural unit of information, base of its security, key origin, key size, if the attacker copies the information, intrusion detection and technology applied in the market, it is important to know the strongest cryptographic algorithm for the security of the information because the technology is increasing and at the same time the information becomes a valuable asset to protect since the hackers when intercepting information can perform denial of services, lack of data integrity, physical damage to structures, thefts of millions of dollars and information. Also the technical-economic study was developed to implement a quantum system in a governmental infrastructure of the National Electoral Council (NEC). From the study, it was determined that the quantum cryptographic algorithms are more appropriate for this purpose; this was demonstrated with the CHI square statistical method, for the verification of the hypothesis. It is concluded that the proposal to implement quantum cryptography with the BB84 algorithm in the national government structure NEC is technically feasible, with an approximate investment of 0.022% of public expenditure in 2017. It is recommended to implement the economic technical proposal raised in this research for the infrastructure of NEC in order to guarantee the security of the information

Análisis de algoritmos criptográficos clásicos vs algoritmos cuánticos.

En este trabajo de investigación se realizó una comparación de los algoritmos criptográficos cuánticos vs clásicos con respecto a la seguridad en la obtención de la clave, en base a una revisión sistemática de donde se definió parámetros medibles de comparación, entre estos algoritmos como: la unidad estructural de la información, base de su seguridad, origen de la clave, tamaño de la clave, si el atacante copia la información, detección de intrusos y tecnología aplicada en el mercado, es de importancia conocer el algoritmo criptográfico más fuerte para la seguridad de la información debido a que la tecnología va en incremento y al mismo tiempo la información se convierte en un activo de gran valor a proteger ya que los hackers al interceptar información pueden realizar denegación de servicios, falta de integridad en datos, daños físicos a estructuras, robos millonarios de dólares e información. También se desarrolló el estudio técnico-económico para la de implementar un sistema cuántico en una infraestructura gubernamental del Consejo Nacional Electoral (CNE). Del estudio se determinó que los algoritmos criptográficos cuánticos son más apropiados para este propósito, esto se demostró con el método estadístico CHI cuadrado, para la comprobación de hipótesis. Se concluye que es técnicamente factible la propuesta de implementar criptografía cuántica con el algoritmo BB84 en la estructura nacional gubernamental CNE, con una inversión aproximada al 0.022% del gasto público de 2017. Se recomienda implementar la propuesta técnica económica planteada en la presente investigación para en la infraestructura de CNE en función de garantizar la seguridad de la información.In this research work, a comparison of quantum vs classical cryptographic algorithms was made with regard to the security in obtaining the key, it was based on a systematic review where measurable parameters of comparison were defined, among these algorithms as: the structural unit of information, base of its security, key origin, key size, if the attacker copies the information, intrusion detection and technology applied in the market, it is important to know the strongest cryptographic algorithm for the security of the information because the technology is increasing and at the same time the information becomes a valuable asset to protect since the hackers when intercepting information can perform denial of services, lack of data integrity, physical damage to structures, thefts of millions of dollars and information. Also the technical-economic study was developed to implement a quantum system in a governmental infrastructure of the National Electoral Council (NEC). From the study, it was determined that the quantum cryptographic algorithms are more appropriate for this purpose; this was demonstrated with the CHI square statistical method, for the verification of the hypothesis. It is concluded that the proposal to implement quantum cryptography with the BB84 algorithm in the national government structure NEC is technically feasible, with an approximate investment of 0.022% of public expenditure in 2017. It is recommended to implement the economic technical proposal raised in this research for the infrastructure of NEC in order to guarantee the security of the information