math.OA
2 postsarXiv:2501.06520v1 Announce Type: new Abstract: In this paper, by using the core EP inverse and the Drazin inverse which are two well known generalized inverses, a new class of matrices entitled core EP Drazin matrices (shortly, CEPD matrices) is introduced. This class contains the set of all EP matrices and also the set of normal matrices. Some algebraic properties of these matrices are also investigated. Moreover, some results about the Drazin inverse and the core EP inverse of partial isometries are derived, and using them, some conditions for which partial isometries are CEPD, are obtained. To illustrate the main results, some numerical examples are given.
arXiv:2412.17909v1 Announce Type: cross Abstract: We investigate state designs for continuous-variable quantum systems using the aid of lattice-like quantum states. These are code states of Gottesman-Kitaev-Preskill (GKP) codes. We show that for an n-mode system, the set of all GKP states forms a rigged continuous-variable state 2-design. We use these lattice state designs to construct a continuous variable shadow tomography protocol, derive sample complexity bounds for both global- and local GKP shadows under reasonable physical assumptions, and provide the physical gadgets needed to implement this protocol.