3,064 research outputs found
Entanglement and quantum combinatorial designs
We introduce several classes of quantum combinatorial designs, namely quantum
Latin squares, cubes, hypercubes and a notion of orthogonality between them. A
further introduced notion, quantum orthogonal arrays, generalizes all previous
classes of designs. We show that mutually orthogonal quantum Latin arrangements
can be entangled in the same way than quantum states are entangled.
Furthermore, we show that such designs naturally define a remarkable class of
genuinely multipartite highly entangled states called -uniform, i.e.
multipartite pure states such that every reduction to parties is maximally
mixed. We derive infinitely many classes of mutually orthogonal quantum Latin
arrangements and quantum orthogonal arrays having an arbitrary large number of
columns. The corresponding multipartite -uniform states exhibit a high
persistency of entanglement, which makes them ideal candidates to develop
multipartite quantum information protocols.Comment: 14 pages, 3 figures. Comments are very welcome
Genuinely multipartite entangled states and orthogonal arrays
A pure quantum state of N subsystems with d levels each is called
k-multipartite maximally entangled state, written k-uniform, if all its
reductions to k qudits are maximally mixed. These states form a natural
generalization of N-qudits GHZ states which belong to the class 1-uniform
states. We establish a link between the combinatorial notion of orthogonal
arrays and k-uniform states and prove the existence of several new classes of
such states for N-qudit systems. In particular, known Hadamard matrices allow
us to explicitly construct 2-uniform states for an arbitrary number of N>5
qubits. We show that finding a different class of 2-uniform states would imply
the Hadamard conjecture, so the full classification of 2-uniform states seems
to be currently out of reach. Additionally, single vectors of another class of
2-uniform states are one-to-one related to maximal sets of mutually unbiased
bases. Furthermore, we establish links between existence of k-uniform states,
classical and quantum error correction codes and provide a novel graph
representation for such states.Comment: 24 pages, 7 figures. Comments are very welcome
Quantum correlations in nanostructured two-impurity Kondo systems
We study the ground-state entanglement properties of nanostructured Kondo
systems consisting of a pair of impurity spins coupled to a background of
confined electrons. The competition between the RKKY-like coupling and the
Kondo effect determines the development of quantum correlations between the
different parts of the system. A key element is the electronic filling due to
confinement. An even electronic filling leads to results similar to those found
previously for extended systems, where the properties of the reduced
impurity-spin subsystem are uniquely determined by the spin correlation
function defining a one-dimensional phase space. An odd filling, instead,
breaks spin-rotation symmetry unfolding a two-dimensional phase space showing
rich entanglement characteristics as, e.g., the requirement of a larger amount
of entanglement for the development of non-local correlations between impurity
spins. We check these results by numerical simulations of elliptic quantum
corrals with magnetic impurities at the foci as a case study.Comment: Submitted for publication. 8 pages, 4 figures. Revised versio
A reduced basis method for frictional contact problems formulated with Nitsche's method
We develop an efficient reduced basis method for the frictional contact
problem formulated using Nitsche's method. We focus on the regime of small
deformations and on Tresca friction. The key idea ensuring the computational
efficiency of the method is to treat the nonlinearity resulting from the
contact and friction conditions by means of the Empirical Interpolation Method.
The proposed algorithm is applied to the Hertz contact problem between two
half-disks with parameter-dependent radius. We also highlight the benefits of
the present approach with respect to the mixed (primal-dual) formulation
Commutative association schemes
Association schemes were originally introduced by Bose and his co-workers in
the design of statistical experiments. Since that point of inception, the
concept has proved useful in the study of group actions, in algebraic graph
theory, in algebraic coding theory, and in areas as far afield as knot theory
and numerical integration. This branch of the theory, viewed in this collection
of surveys as the "commutative case," has seen significant activity in the last
few decades. The goal of the present survey is to discuss the most important
new developments in several directions, including Gelfand pairs, cometric
association schemes, Delsarte Theory, spin models and the semidefinite
programming technique. The narrative follows a thread through this list of
topics, this being the contrast between combinatorial symmetry and
group-theoretic symmetry, culminating in Schrijver's SDP bound for binary codes
(based on group actions) and its connection to the Terwilliger algebra (based
on combinatorial symmetry). We propose this new role of the Terwilliger algebra
in Delsarte Theory as a central topic for future work.Comment: 36 page
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