28 citations · 124 across the 28 of their papers we have counts for
29 papers
A discrete Smorodinsky--Winternitz II superintegrable system
Pierre-Antoine Bernard, Vutha Vichhea Chea, Luc Vinet
We construct a discrete Smorodinsky--Winternitz II superintegrable system on a triangular region of the two-dimensional square lattice. The model is built from a pair of commuting…
Analytical Angle-Finding and Series Expansions for Quantum Signal Processing via Orthogonal Polynomial Theory
Pierre-Antoine Bernard, Nathan Wiebe
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials impl…
Exactly solvable inhomogeneous XY spin chain
Pierre-Antoine Bernard, Nicolas Crampé, Quentin Labriet +2
Analytical expressions for the eigenvalues of certain inhomogeneous XY spin chains are computed. These models are rewritten in terms of free-fermion models using a well-known Jorda…
Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
Pierre-Antoine Bernard, Rafael I. Nepomechie, Gilles Parez +3
In this paper, we investigate the ground-state entanglement entropy in inhomogeneous free-boson models in one spatial dimension. We develop a powerful method to extract the leading…
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…
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…
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…
m-distance-regular graphs and their relation to multivariate P-polynomial association schemes
Pierre-Antoine Bernard, Nicolas Crampe, Luc Vinet +2
An association scheme is -polynomial if and only if it consists of the distance matrices of a distance-regular graph. Recently, bivariate -polynomial association schemes of t…
Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes
Pierre-Antoine Bernard, Zachary Mann, Gilles Parez +1
This study investigates the scaling behavior of the ground-state entanglement entropy in a model of free fermions on folded cubes. An analytical expression is derived in the large-…
Computation of entanglement entropy in inhomogeneous free fermions chains by algebraic Bethe ansatz
Pierre-Antoine Bernard, Gauvain Carcone, Nicolas Crampe +1
The computation of the entanglement entropy for inhomogeneous free fermions chains based on q-Racah polynomials is considered. The eigenvalues of the truncated correlation matrix a…
Bivariate -polynomial association schemes
P. -A. Bernard, N. Crampe, L. Poulain d'Andecy +2
Bivariate P-polynomial association scheme of type are defined as a generalization of the P-polynomial association schemes. This generalization is shown to be equivalent to…
Multipartite information of free fermions on Hamming graphs
Gilles Parez, Pierre-Antoine Bernard, Nicolas Crampé +1
We investigate multipartite information and entanglement measures in the ground state of a free-fermion model defined on a Hamming graph. Using the known diagonalization of the adj…
Quantum State Transfer in Graphs with Tails
Pierre-Antoine Bernard, Christino Tamon, Luc Vinet +1
We consider quantum state transfer on finite graphs which are attached to infinite paths. The finite graph represents an operational quantum system for performing useful quantum in…
Bethe ansatz diagonalization of the Heun-Racah operator
Pierre-Antoine Bernard, Gauvain Carcone, Nicolas Crampe +1
The Heun-Racah operator is diagonalized with the help of the modified algebraic Bethe ansatz. This operator is the most general bilinear expression in two generators of the Racah a…
Entanglement of inhomogeneous free fermions on hyperplane lattices
Pierre-Antoine Bernard, Nicolas Crampé, Rafael I. Nepomechie +3
We introduce an inhomogeneous model of free fermions on a -dimensional lattice with continuous parameters that control the hopping strength between adjacent sites…
Time and band limiting operator and Bethe ansatz
P. -A. Bernard, N. Crampe, L. Vinet
The time and band limiting operator is introduced to optimize the reconstruction of a signal from only a partial part of its spectrum. In the discrete case, this operator commutes…
An explanation of the commuting operator "miracle" in time and band limiting
Pierre-Antoine Bernard, Nicolas Crampe, Luc Vinet
Time and band limiting operators are expressed as functions of the confluent Heun operator arising in the spheroidal wave equation. Explicit formulas are obtained when the bandwidt…
The Terwilliger algebra of symplectic dual polar graphs, the subspace lattices and
Pierre-Antoine Bernard, Nicolas Crampe, Luc Vinet
The adjacency matrix of a symplectic dual polar graph restricted to the eigenspaces of an abelian automorphism subgroup is shown to act as the adjacency matrix of a weighted subspa…