arXiv subjects

Jean Liénardy

Publications and source records attributed to Jean Liénardy.

7 recordsLinked to original sources

arXiv2026

Cryptanalysis of four arbitrated quantum signature schemes

Arbitrated quantum signature (AQS) schemes aim at ensuring the authenticity of a message with the help of an arbitrator. Moreover, they aim at preventing repudiation, both from a sender that denies the origin of a message, and from a receiver who disavows its reception. Such protocols use quantum communication and are often designed to protect quantum messages. In this paper, we study four recently submitted AQS schemes and propose attacks on their security. Firstly, we look at Zhang, Sun, Zhang and Jia's AQS scheme which aims at signing quantum messages with chained CNOT encryption. We show that the sender can repudiate her messages and make false allegation of reception. Moreover, we show that a dishonest receiver can forge signatures. Secondly, we analyse Ding, Xin, Yang and Sang's AQS protocol to sign classical messages based on GHZ states. We show that both the sender and the receiver have simple repudiation strategies. Thirdly, we study Lu, Li, Yu and Han's AQS scheme that uses controlled teleportation to protect quantum messages. We expose forgeries, false allegation attacks and the possibility of repudiation by both parties. Fourthly, we focus on the AQS scheme by Zhang, Xin, Sun, Li and Li designed to sign classical messages without entangled states. We show that one can disavow the reception of messages, and that information-theoretic security is not achieved for other security goals.

quant-ph↗

arXiv2025

The open XXZ chain at $Δ=-1/2$ and totally-symmetric alternating sign matrices

The open XXZ spin chain with the anisotropy parameter $Δ=-\frac12$, diagonal boundary fields that depend on a parameter $x$, and finite length $N$ is studied. In a natural normalisation, the components of its ground-state vector are polynomials in $x$ with integer coefficients. It is shown that their sum is given by a generating function for the weighted enumeration of totally-symmetric alternating sign matrices with weights depending on $x$.

math-ph↗

arXiv2022

The open XXZ chain at $Δ=-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations

The open XXZ spin chain with the anisotropy parameter $Δ=-\frac12$ and diagonal boundary magnetic fields that depend on a parameter $x$ is studied. For real $x>0$, the exact finite-size ground-state eigenvalue of the spin-chain Hamiltonian is explicitly computed. In a suitable normalisation, the ground-state components are characterised as polynomials in $x$ with integer coefficients. Linear sum rules and special components of this eigenvector are explicitly computed in terms of determinant formulas. These results follow from the construction of a contour-integral solution to the boundary quantum Knizhnik-Zamolodchikov equations associated with the $R$-matrix and diagonal $K$-matrices of the six-vertex model. A relation between this solution and a weighted enumeration of totally-symmetric alternating sign matrices is conjectured.

math-ph↗

arXiv2021

Bipartite fidelity for models with periodic boundary conditions

For a given statistical model, the bipartite fidelity $\mathcal F$ is computed from the overlap between the groundstate of a system of size $N$ and the tensor product of the groundstates of the same model defined on two subsystems $A$ and $B$, of respective sizes $N_A$ and $N_B$ with $N = N_A + N_B$. In this paper, we study $\mathcal F$ for critical lattice models in the case where the full system has periodic boundary conditions. We consider two possible choices of boundary conditions for the subsystems $A$ and $B$, namely periodic and open. For these two cases, we derive the conformal field theory prediction for the leading terms in the $1/N$ expansion of $\mathcal F$, in a most general case that corresponds to the insertion of four and five fields, respectively. We provide lattice calculations of $\mathcal F$, both exact and numerical, for two free-fermionic lattice models: the XX spin chain and the model of critical dense polymers. We study the asymptotic behaviour of the lattice results for these two models and find an agreement with the predictions of conformal field theory.

cond-mat.stat-mech↗

arXiv2020

On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions

The transfer matrix of the square-lattice eight-vertex model on a strip with $L\geqslant 1$ vertical lines and open boundary conditions is investigated. It is shown that for vertex weights $a,b,c,d$ that obey the relation $(a^2+ab)(b^2+ab)=(c^2+ab)(d^2+ab)$ and appropriately chosen $K$-matrices $K^\pm$ this transfer matrix possesses the remarkably simple, non-degenerate eigenvalue $Λ_L = (a+b)^{2L}\,\text{tr}(K^+K^-)$. For positive vertex weights, $Λ_L$ is shown to be the largest transfer-matrix eigenvalue. The corresponding eigenspace is equal to the space of the ground states of the Hamiltonian of a related XYZ spin chain. An essential ingredient in the proofs is the supersymmetry of this Hamiltonian.

math-ph↗

arXiv2017

On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions

The square-lattice eight-vertex model with vertex weights $a,b,c,d$ obeying the relation $(a^2+ab)(b^2+ab) = (c^2+ab)(d^2+ab)$ and periodic boundary conditions is considered. It is shown that the transfer matrix of the model for $L=2n+1$ vertical lines and periodic boundary conditions along the horizontal direction possesses the doubly degenerate eigenvalue $Θ_n = (a+b)^{2n+1}$. This proves a conjecture by Stroganov from 2001. The proof uses the supersymmetry of a related XYZ spin-chain Hamiltonian. The eigenstates of the transfer matrix corresponding to $Θ_n$ are shown to be the ground states of the spin-chain Hamiltonian. Moreover, for positive vertex weights $Θ_n$ is the largest eigenvalue of the transfer matrix.

math-ph↗

arXiv2016

Open spin chains with dynamic lattice supersymmetry

The quantum spin $1/2$ XXZ chain with anisotropy parameter $Δ=-1/2$ possesses a dynamic supersymmetry on the lattice. This supersymmetry and a generalisation to higher spin are investigated in the case of open spin chains. A family of non-diagonal boundary interactions that are compatible with the lattice supersymmetry and depend on several parameters is constructed. The cohomology of the corresponding supercharges is explicitly computed as a function of the parameters and the length of the chain. For certain specific values of the parameters, this cohomology is shown to be non-trivial. This implies that the spin-chain ground states are supersymmetry singlets. Special scalar products involving an arbitrary number of these supersymmetry singlets for chains of different lengths are exactly computed. As a physical application, the logarithmic bipartite fidelity of the open quantum spin $1/2$ XXZ chain with $Δ=-1/2$ and special diagonal boundary interactions is determined.

math-ph↗