3,206 research outputs found
A qutrit Quantum Key Distribution protocol with better noise resistance
The Ekert quantum key distribution protocol uses pairs of entangled qubits
and performs checks based on a Bell inequality to detect eavesdropping. The
3DEB protocol uses instead pairs of entangled qutrits to achieve better noise
resistance than the Ekert protocol. It performs checks based on a Bell
inequality for qutrits named CHSH-3. In this paper, we present a new protocol,
which also uses pairs of entangled qutrits, but achieves even better noise
resistance than 3DEB. This gain of performance is obtained by using another
inequality called here hCHSH-3. As the hCHSH3 inequality involve products of
observables which become incompatible when using quantum states, we show how
the parties running the protocol can measure the violation of hCHSH3 in the
presence of noise, to ensure the secrecy of the key.Comment: 11 page
A Primer on Reproducing Kernel Hilbert Spaces
Reproducing kernel Hilbert spaces are elucidated without assuming prior
familiarity with Hilbert spaces. Compared with extant pedagogic material,
greater care is placed on motivating the definition of reproducing kernel
Hilbert spaces and explaining when and why these spaces are efficacious. The
novel viewpoint is that reproducing kernel Hilbert space theory studies
extrinsic geometry, associating with each geometric configuration a canonical
overdetermined coordinate system. This coordinate system varies continuously
with changing geometric configurations, making it well-suited for studying
problems whose solutions also vary continuously with changing geometry. This
primer can also serve as an introduction to infinite-dimensional linear algebra
because reproducing kernel Hilbert spaces have more properties in common with
Euclidean spaces than do more general Hilbert spaces.Comment: Revised version submitted to Foundations and Trends in Signal
Processin
Bivariate copulas defined from matrices
We propose a semiparametric family of copulas based on a set of orthonormal
functions and a matrix. This new copula permits to reach values of Spearman's
Rho arbitrarily close to one without introducing a singular component.
Moreover, it encompasses several extensions of FGM copulas as well as copulas
based on partition of unity such as Bernstein or checkerboard copulas. Finally,
it is also shown that projection of arbitrary densities of copulas onto tensor
product bases can enter our framework
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