2024/12/12 by Zhai, Ke-Hong, Liu, Lei-Hua, Zhang, Hai-Qing · 3 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2412.08925
We extend the ``complexity=volume" (CV) conjecture in the wormhole to the quantum states in the framework of information geometry. In particular, we conjecture that Krylov complexity equals the volume of the Fubini-Study metric in the information geometry. In order to test our conjecture, we study the general Hermitian two-mode Hamiltonian according to the Weyl algebra both in the closed and open systems. By employing the displacement operator, we find that the wave function for a closed system corresponds to the well-known two-mode squeezed state. For an open system, we can create a wave function known as the open two-mode squeezed state by using the second kind of Meixner polynomials. Remarkably, in both cases, the resulting volume of the corresponding Fubini-Study metric provides strong evidence for the generalized CV conjecture.