paper

Generalized CV Conjecture and Krylov Complexity in Two-Mode Hermitian Systems via Information Geometry

arXiv:2412.08925 · doi:10.1016/j.aop.2026.170534

Abstract

We extend the CV conjecture to quantum states of two-mode Hermitian systems using the framework of information geometry. Specifically, we conjecture that the Krylov complexity of a quantum state equals the volume of the Fubini-Study metric. To test this conjecture, we construct the wave functions for both closed and open two-mode systems. For the closed system, the wave function corresponds to the well-known two-mode squeezed state, while for the open system, we employ the second kind of Meixner polynomials to generate an open two-mode squeezed state. Remarkably, in both cases, the calculated Fubini-Study volume matches the Krylov complexity, providing analytic evidence for the generalized CV relation in this controlled two-mode setting. Our results establish a direct link between operator growth in Krylov space and geometric properties of quantum states, highlighting the potential applications of this framework in quantum information and quantum optics.

References in corpus (25)