599 research outputs found
Weak randomness completely trounces the security of QKD
In usual security proofs of quantum protocols the adversary (Eve) is expected
to have full control over any quantum communication between any communicating
parties (Alice and Bob). Eve is also expected to have full access to an
authenticated classical channel between Alice and Bob. Unconditional security
against any attack by Eve can be proved even in the realistic setting of device
and channel imperfection. In this Letter we show that the security of QKD
protocols is ruined if one allows Eve to possess a very limited access to the
random sources used by Alice. Such knowledge should always be expected in
realistic experimental conditions via different side channels
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On the convex characterisation of the set of unital quantum channels
In this paper, we consider the convex structure of the set of unital quantum channels. To do this, we introduce a novel framework to construct and characterise different families of low-rank unital quantum maps. In this framework, unital quantum maps are represented as a set of complex parameters on which we impose a set of constraints. The different families of unital maps are obtained by mapping those parameters into the operator representation of a quantum map. For these families, we also introduce a scalar measuring their distance to the set of mixed-unitary maps. We consider the particular case of qutrit channels which is the smallest set of maps for which the existence of non-unitary extremal maps is known. In this setting, we show how our framework generalises the description of well-known maps such as the antisymmetric Werner-Holevo map but also novel families of qutrit maps
Quantum Sign Permutation Polytopes
Convex polytopes are convex hulls of point sets in the -dimensional space
\E^n that generalize 2-dimensional convex polygons and 3-dimensional convex
polyhedra. We concentrate on the class of -dimensional polytopes in \E^n
called sign permutation polytopes. We characterize sign permutation polytopes
before relating their construction to constructions over the space of quantum
density matrices. Finally, we consider the problem of state identification and
show how sign permutation polytopes may be useful in addressing issues of
robustness
The escape problem under stochastic volatility: the Heston model
We solve the escape problem for the Heston random diffusion model. We obtain
exact expressions for the survival probability (which ammounts to solving the
complete escape problem) as well as for the mean exit time. We also average the
volatility in order to work out the problem for the return alone regardless
volatility. We look over these results in terms of the dimensionless normal
level of volatility --a ratio of the three parameters that appear in the Heston
model-- and analyze their form in several assymptotic limits. Thus, for
instance, we show that the mean exit time grows quadratically with large spans
while for small spans the growth is systematically slower depending on the
value of the normal level. We compare our results with those of the Wiener
process and show that the assumption of stochastic volatility, in an apparent
paradoxical way, increases survival and prolongs the escape time.Comment: 29 pages, 12 figure
2D pattern evolution constrained by complex network dynamics
Complex networks have established themselves along the last years as being
particularly suitable and flexible for representing and modeling several
complex natural and human-made systems. At the same time in which the
structural intricacies of such networks are being revealed and understood,
efforts have also been directed at investigating how such connectivity
properties define and constrain the dynamics of systems unfolding on such
structures. However, lesser attention has been focused on hybrid systems,
\textit{i.e.} involving more than one type of network and/or dynamics. Because
several real systems present such an organization (\textit{e.g.} the dynamics
of a disease coexisting with the dynamics of the immune system), it becomes
important to address such hybrid systems. The current paper investigates a
specific system involving a diffusive (linear and non-linear) dynamics taking
place in a regular network while interacting with a complex network of
defensive agents following Erd\"os-R\'enyi and Barab\'asi-Albert graph models,
whose nodes can be displaced spatially. More specifically, the complex network
is expected to control, and if possible to extinguish, the diffusion of some
given unwanted process (\textit{e.g.} fire, oil spilling, pest dissemination,
and virus or bacteria reproduction during an infection). Two types of pattern
evolution are considered: Fick and Gray-Scott. The nodes of the defensive
network then interact with the diffusing patterns and communicate between
themselves in order to control the spreading. The main findings include the
identification of higher efficiency for the Barab\'asi-Albert control networks.Comment: 18 pages, 32 figures. A working manuscript, comments are welcome
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Fuzzy inference on quantum annealers
Quantum computers can potentially perform certain types of optimisation problems much more efficiently than classical computers, making them a promising tool for solving complex fuzzy logic problems. In two recent developments, based on solving Quadratic Unconstrained Binary Optimization (QUBO) problems on a type of quantum computers known as quantum annealers, we have introduced novel representations of a) fuzzy sets; b) implementations of some basic fuzzy logic operators (union, intersection, alpha-cut and maximum) and; c) the centroid defuzzification. In this paper, the previous works are further extended by presenting an implementation of Mamdani inference on the quantum annealer machines. We first present how the fuzzy rules can be formulated for such an implementation, then we present how to cascade different quantum-fuzzy operators in order to implement the quantum-fuzzy inference, and finally, a sample implementation of the inference on a real quantum computer is demonstrated. Having the main components of a rule-based fuzzy logic system implemented on quantum computers, this paper provides an integrated solution for implementing a whole fuzzy rule-based system on quantum computers
The Aerodynamics of Hummingbird Flight
Hummingbirds fly with their wings almost fully extended during their entire wingbeat. This pattern, associated with having proportionally short humeral bones, long distal wing elements, and assumed to be an adaptation for extended hovering flight, has lead to predictions that the aerodynamic mechanisms exploited by hummingbirds during hovering should be similar to those observed in insects. To test these predictions, we flew rufous hummingbirds (Selasphorus rufus, 3.3 g, n = 6) in a variable–speed wind tunnel (0-12 ms-1) and measured wake structure and dynamics using digital particle image velocimetry (DPIV). Unlike hovering insects, hummingbirds produced 75% of their weight support during downstroke and only 25% during upstroke, an asymmetry due to the inversion of their cambered wings during upstroke. Further, we have found no evidence of sustained, attached leading edge vorticity (LEV) during up or downstroke, as has been seen in similarly-sized insects - although a transient LEV is produced during the rapid change in angle of attack at the end of the downstroke. Finally, although an extended-wing upstroke during forward flight has long been thought to produce lift and negative thrust, we found circulation during downstroke alone to be sufficient to support body weight, and that some positive thrust was produced during upstroke, as evidenced by a vortex pair shed into the wake of all upstrokes at speeds of 4 – 12 m s-1
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