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arXiv · 2412.08925

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

Ke-Hong Zhai·Lei-Hua Liu·Hai-Qing Zhang
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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.

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Ke-Hong Zhai, Lei-Hua Liu, Hai-Qing Zhang. 2024-12-12. Generalized CV Conjecture and Krylov Complexity in Two-Mode Hermitian Systems via Information Geometry. https://doi.org/10.1016/j.aop.2026.170534

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