Information Theory Based Methods for the Reconstruction of Quantum Wave Functions

N. Canosa, R. Rossignoli, Angelo Plastino

yonghang lu, Junfan Zhu, Fuhua Gao +1 more

The wave function is the cornerstone of quantum theory, and various techniques have been proposed for its direct measurement. The reconstruction of the wave function can be achieved by utilizing the real and imaginary components of momentum weak value, which correspond to amplitude and phase differentiation, respectively. However, these methods are limited in their applicability to wave functions with large phase gradients due to the weak coupling condition, which is a fundamental constraint. In this paper, we propose a method for reconstructing wave functions with large phase gradients based on optical differentiation through weak measurement. We have developed a more generalized theory of phase differentiation and implemented a common optical path and fast measurement for wave functions with large phase gradients. The experimental detection of wave functions with varying phase gradients has validated the reliability of our method. This work expands the range of applications for weak measurement while retaining its high resolution and sensitivity advantages, particularly in the field of wavefront sensing.

Lev B. Levitin

Zhen Luo, Yingjin Ma, Chungen Liu +1 more

We improve the methodology to construct a complete active space-configuration interaction (CAS-CI) expansion for density-matrix renormalization group (DMRG) wave functions using a matrix-product state representation, inspired by the sampling-reconstructed CAS [SR-CAS; Boguslawski , K. ; J. Chem. Phys. 2011 , 134 , 224101 ] algorithm. In our scheme, the genetic algorithm, in which the "crossover" and "mutation" processes can be optimized based on quantum information theory, is employed when reconstructing a CAS-CI-type wave function in the Hilbert space. Analysis of results for ground and excited state wave functions of conjugated molecules, transition metal compounds, and a lanthanide complex illustrate that our scheme is very efficient for searching the most important CI expansions in large active spaces.

Yi Zheng, Mu Yang, Yu-Wei Liao +3 more

The quantum wave function of multiple particles provides additional information which is inaccessible to detectors working alone. Here, we introduce the coincidence wave-front sensing (CWS) method to reconstruct the phase of the multiphoton transverse spatial wave function. The spatially resolved coincidence photon counting is involved. Numerical simulations of two-photon cases using the weak measurement wave-front sensor are performed to test its correctness, and the phase information hidden in the correlation is revealed. Our work provides a direct spatial way to characterize multipartite quantum systems and leads to fundamental studies like experimental Bohmian mechanics and applications in quantum optical technologies.

Peter Mittelstaedt