17,325 research outputs found
Singular value decomposition and matrix reorderings in quantum information theory
We review Schmidt and Kraus decompositions in the form of singular value
decomposition using operations of reshaping, vectorization and reshuffling. We
use the introduced notation to analyse the correspondence between quantum
states and operations with the help of Jamiolkowski isomorphism. The presented
matrix reorderings allow us to obtain simple formulae for the composition of
quantum channels and partial operations used in quantum information theory. To
provide examples of the discussed operations we utilize a package for the
Mathematica computing system implementing basic functions used in the
calculations related to quantum information theory.Comment: 11 pages, no figures, see
http://zksi.iitis.pl/wiki/projects:mathematica-qi for related softwar
Structural and electronic properties of the graphene/Al/Ni(111) intercalation-like system
Decoupling of the graphene layer from the ferromagnetic substrate via
intercalation of sp metal has recently been proposed as an effective way to
realize single-layer graphene-based spin-filter. Here, the structural and
electronic properties of the prototype system, graphene/Al/Ni(111), are
investigated via combination of electron diffraction and spectroscopic methods.
These studies are accompanied by state-of-the-art electronic structure
calculations. The properties of this prospective Al-intercalation-like system
and its possible implementations in future graphene-based devices are
discussed.Comment: 20 pages, 8 figures, and supplementary materia
Single-qubit optical quantum fingerprinting
We analyze and demonstrate the feasibility and superiority of linear optical
single-qubit fingerprinting over its classical counterpart. For one-qubit
fingerprinting of two-bit messages, we prepare `tetrahedral' qubit states
experimentally and show that they meet the requirements for quantum
fingerprinting to exceed the classical capability. We prove that shared
entanglement permits 100% reliable quantum fingerprinting, which will
outperform classical fingerprinting even with arbitrary amounts of shared
randomness.Comment: 4 pages, one figur
The optimal unitary dilation for bosonic Gaussian channels
A generic quantum channel can be represented in terms of a unitary
interaction between the information-carrying system and a noisy environment.
Here, the minimal number of quantum Gaussian environmental modes required to
provide a unitary dilation of a multi-mode bosonic Gaussian channel is analyzed
both for mixed and pure environment corresponding to the Stinespring
representation. In particular, for the case of pure environment we compute this
quantity and present an explicit unitary dilation for arbitrary bosonic
Gaussian channel. These results considerably simplify the characterization of
these continuous-variable maps and can be applied to address some open issues
concerning the transmission of information encoded in bosonic systems.Comment: 9 page
Vacuum entanglement governs the bosonic character of magnons
It is well known that magnons, elementary excitations in a magnetic material,
behave as bosons when their density is low. We study how the bosonic character
of magnons is governed by the amount of a multipartite entanglement in the
vacuum state on which magnons are excited. We show that if the multipartite
entanglement is strong, magnons cease to be bosons. We also consider some
examples, such as ground states of the Heisenberg ferromagnet and the
transverse Ising model, the condensation of magnons, the one-way quantum
computer, and Kitaev's toric code. Our result provides insights into the
quantum statistics of elementary excitations in these models, and into the
reason why a non-local transformation, such as the Jordan-Wigner
transformation, is necessary for some many-body systems.Comment: 4 pages, no figur
Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities
Quantum theory imposes a strict limit on the strength of non-local
correlations. It only allows for a violation of the CHSH inequality up to the
value 2 sqrt(2), known as Tsirelson's bound. In this note, we consider
generalized CHSH inequalities based on many measurement settings with two
possible measurement outcomes each. We demonstrate how to prove Tsirelson
bounds for any such generalized CHSH inequality using semidefinite programming.
As an example, we show that for any shared entangled state and observables
X_1,...,X_n and Y_1,...,Y_n with eigenvalues +/- 1 we have | + <X_2
Y_1> + + + ... + - | <= 2 n
cos(pi/(2n)). It is well known that there exist observables such that equality
can be achieved. However, we show that these are indeed optimal. Our approach
can easily be generalized to other inequalities for such observables.Comment: 9 pages, LateX, V2: Updated reference [3]. To appear in Physical
Review
Transport in time-dependent dynamical systems: Finite-time coherent sets
We study the transport properties of nonautonomous chaotic dynamical systems
over a finite time duration. We are particularly interested in those regions
that remain coherent and relatively non-dispersive over finite periods of time,
despite the chaotic nature of the system. We develop a novel probabilistic
methodology based upon transfer operators that automatically detects maximally
coherent sets. The approach is very simple to implement, requiring only
singular vector computations of a matrix of transitions induced by the
dynamics. We illustrate our new methodology on an idealized stratospheric flow
and in two and three dimensional analyses of European Centre for Medium Range
Weather Forecasting (ECMWF) reanalysis data
The effect of size and type upon the efficiency of milk and beef production in cattle
International audienc
Maximal utilization of heterosis in milk and beef production
International audienc
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