Riemannian Quantum Circuit

Number theory is an abstract mathematical field that has found a fertile environment for development in theoretical physics. In particular, several physical systems were related to the zeros of the Riemann-zeta function. In this work we present the theory of a quantum circuit related to a finite number of zeros of the Riemann-zeta function. The existence of such circuit will permit in the future the solution of some number theory problems through the realization of quantum algorithms based on those zeros.Comment: 7 page

Quantum-Chaotic Cryptography

In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.Comment: 7 pages and 5 figure

Quantum and Classical Information Theory with Disentropy

Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication to medical image processing, for example. Now, entropy meets its dual, the disentropy. As such, the disentropy can be used everywhere entropy is used, offering a different point of view: since entropy is a measure of disorder or uncertainty, disentropy is a measure of order or certainty. Thus, important concepts of physics can be rewritten using disentropy instead of entropy. Although there is a large range of problems that can be solved using entropy or disentropy, there are situations where only the disentropy can be used. This happens because the disentropy can provide a real output value when its argument is negative, while the entropy cannot. Thus, it is possible to calculate, for example, the disentropy of quasi-probability distributions like the Wigner function of highly quantum states. In this direction, the present work shows applications of the disentropy in a small list of problems: quantum and classical information theory, black hole thermodynamics, image processing and number theory.Comment: 37 pages, new equations, graphs and example

The zeros of the Riemann-zeta function and the transition from pseudo-random to harmonic behavior

In this work, it is introduced a new function based on the non-trivial zeros of the Riemann-zeta function. Such function shows an interesting behavior: when the argument of the function grows, it changes from a pseudo-random behavior to a harmonic behavior with decreasing frequency.Comment: 6 pages and 9 figure

On the role of the basis of measurement in quantum gate teleportation

Quantum teleportation is a powerful protocol with applications in several schemes of quantum communication, quantum cryptography and quantum computing. The present work shows the required conditions for a two-qubit quantum gate to be deterministically and probabilistically teleported by a quantum gate teleportation scheme using different basis of measurement. Additionally, we present examples of teleportation of two-qubit gates that do not belong to Clifford group as well the limitations of the quantum gate teleportation scheme employing a four-qubit state with genuine four-way entanglement.Comment: 12 pages and 2 figure

Riemann Hypothesis as an Uncertainty Relation

Physics is a fertile environment for trying to solve some number theory problems. In particular, several tentative of linking the zeros of the Riemann-zeta function with physical phenomena were reported. In this work, the Riemann operator is introduced and used to transform the Riemann's hypothesis in a Heisenberg-type uncertainty relation, offering a new way for studying the zeros of Riemann's functionComment: 3 page

Considerations about the randomness of bit strings originated from sequences of integer numbers according to a simple quantum computer model

This work uses a simple quantum computer model to discuss the randomness of bit strings originated from integer sequences. The considered quantum computer model has three elements: a processing unit responsible for a mathematical operation, an initial equally weighted superposition and a quantum state used as resource. The randomness depends on the last.Comment: 4 page

Quantum Physics, Algorithmic Information Theory and the Riemanns Hypothesis

In the present work the Riemanns hypothesis (RH) is discussed from four different perspectives. In the first case, coherent states and the Stengers approximation to Riemann-zeta function are used to show that RH avoids an indeterminacy of the type 0/0 in the inner product of two coherent states. In the second case, the Hilber-Polya conjecture with a quantum circuit is considered. In the third case, randomness, entanglement and the Moebius function are used to discuss the RH. At last, in the fourth case, the RH is discussed by inverting the first derivative of the Chebyshev function. The results obtained reinforce the belief that the RH is true.Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1505.0074

Quantum search followed by classical search versus quantum search alone

In this work, we show that the usage of a quantum gate that gives extra information about the solution searched permits to improve the performance of the search algorithm by switching from quantum to classical search in the appropriated moment. A comparison to the case where only quantum search is used is also realized.Comment: 3 page

An SDN-based approach to enhance BGP security

BGP is vulnerable to a series of attacks. Many solutions have been proposed in the past two decades, but the most effective remain largely undeployed. This is due to three fundamental reasons: the solutions are too computationally expensive for current routers, they require changes to BGP, and/or they do not give the right incentives to promote deployment. In this abstract we propose a Software-Defined Networking (SDN) architecture to secure BGP routing. Our solution, BGPSecX, targets an IXP and it includes techniques to allow different IXPs to collaborate. With SDN we remove the computational burden from routers and do not make changes to BGP. Targeting IXPs and promoting inter-IXP collaboration enables the creation of incentives to foster adoption of BGP security services