23,404 research outputs found
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
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
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
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
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
Asymptotic Quantum Search and a Quantum Algorithm for Calculation of a Lower Bound of the Probability of Finding a Diophantine Equation That Accepts Integer Solutions
Several mathematical problems can be modeled as a search in a database. An
example is the problem of finding the minimum of a function. Quantum algorithms
for solving this problem have been proposed and all of them use the quantum
search algorithm as a subroutine and several intermediate measurements are
realized. In this work, it is proposed a new quantum algorithm for finding the
minimum of a function in which quantum search is not used as a subroutine and
only one measurement is needed. This is also named asymptotic quantum search.
As an example, we propose a quantum algorithm based on asymptotic quantum
search and quantum counting able to calculate a lower bound of the probability
of finding a Diophantine equation with integer solution.Comment: Eleven pages, two figures. A complexity analysis is include
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