Nathan Claudet
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View article: Local Equivalence of Stabilizer States: A Graphical Characterisation
Local Equivalence of Stabilizer States: A Graphical Characterisation Open
Stabilizer states form a ubiquitous family of quantum states that can be graphically represented through the graph state formalism. A fundamental property of graph states is that applying a local complementation - a well-known and extensiv…
View article: Deciding Local Unitary Equivalence of Graph States in Quasi-Polynomial Time
Deciding Local Unitary Equivalence of Graph States in Quasi-Polynomial Time Open
We describe an algorithm with quasi-polynomial runtime n^{log₂(n)+O(1)} for deciding local unitary (LU) equivalence of graph states. The algorithm builds on a recent graphical characterisation of LU-equivalence via generalised local comple…
View article: Covering a Graph with Minimal Local Sets
Covering a Graph with Minimal Local Sets Open
Local sets, a graph structure invariant under local complementation, have been originally introduced in the context of quantum computing for the study of quantum entanglement within the so-called graph state formalism. A local set in a gra…
View article: Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems
Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems Open
We study the notion of k-stabilizer universal quantum state, that is, an n-qubit quantum state, such that it is possible to induce any stabilizer state on any k qubits, by using only local operations and classical communications. These sta…
View article: Small k-pairable states
Small k-pairable states Open
A $k$-pairable $n$-qubit state is a resource state that allows Local Operations and Classical Communication (LOCC) protocols to generate EPR-pairs among any $k$-disjoint pairs of the $n$ qubits. Bravyi et al. introduced a family of $k$-pai…