10 citations · 38 across the 24 of their papers we have counts for
11 papers · 1 filter
A dynamical algebra of protocol-induced transformations on Dicke states
Pierre-Antoine Bernard, Luc Vinet
Quantum -qubit states that are totally symmetric under the permutation of qubits are essential ingredients of important algorithms and applications in quantum information. Conse…
Entanglement Hamiltonian and orthogonal polynomials
Pierre-Antoine Bernard, Riccarda Bonsignori, Viktor Eisler +2
We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the singl…
Distinctive features of inhomogeneous spin chains
Pierre-Antoine Bernard, Gilles Parez, Luc Vinet
This review presents recent developments in the study of inhomogeneous XX spin chains, highlighting results on perfect state transfer, out-of-equilibrium stationary dynamics in ope…
Meta algebras and biorthogonal rational functions: the -Hahn case
Pierre-Antoine Bernard, Abderahmane Bouziane, Samuel Pellerin +5
A unified algebraic interpretation of both finite families of orthogonal polynomials and biorthogonal rational functions of -Hahn type is provided. The approach relies on the me…
A tale of two -deformations : connecting dual polar spaces and weighted hypercubes
Pierre-Antoine Bernard, Étienne Poliquin, Luc Vinet
Two -analogs of the hypercube graph are introduced and shown to be related through a graph quotient. The roles of the subspace lattice graph, of a twisted primitive elements of…
A -version of the relation between the hypercube, the Krawtchouk chain and Dicke states
Pierre-Antoine Bernard, Étienne Poliquin, Luc Vinet
It is shown how the spin chain based on the dual -Krawtchouk polynomials is connected to a weighted hypercube through the use of -Dicke states. The representation theoretic u…
Currents in non-equilibrium steady states of open inhomogeneous -spin chains
Pierre-Antoine Bernard, Ismaël Bussière, Roberto Floreanini +1
We investigate spin and heat currents in the non-equilibrium steady state of inhomogeneous -spin chains, which act as interfaces between two bosonic heat baths. Using special f…
Fermionic logarithmic negativity in the Krawtchouk chain
Gabrielle Blanchet, Gilles Parez, Luc Vinet
The entanglement of non-complementary regions is investigated in an inhomogeneous free-fermion chain through the lens of the fermionic logarithmic negativity. Focus is on the Krawt…
Bivariate - and -polynomial structures of the association schemes based on attenuated spaces
Pierre-Antoine Bernard, Nicolas Crampe, Luc Vinet +2
The bivariate - and -polynomial structures of association schemes based on attenuated spaces are examined using recurrence and difference relations of the bivariate polynomia…
Griffiths polynomials of Racah type
Nicolas Crampe, Luc Frappat, Julien Gaboriaud +3
Bivariate Griffiths polynomials of Racah type are constructed from univariate Racah polynomials. The bispectral properties of the former are deduced from simple properties of the l…
Entanglement of free-fermion systems, signal processing and algebraic combinatorics
Pierre-Antoine Bernard, Nicolas Crampé, Rafael I. Nepomechie +2
This paper offers a review of recent studies on the entanglement of free-fermion systems on graphs that take advantage of methods pertaining to signal processing and algebraic comb…