Quantum Information Measures of a Dirichlet Waveguide with Neumann Window(s)

ABSTRACT Engineering boundary conditions in low‐dimensional structures provides a simple yet powerful way of shaping how quantum information is stored and transported. We investigate a flat 2D Dirichlet waveguide containing one or two finite Neumann windows and compute the bound states in both position and momentum space as functions of the window length. From these wavefunctions, we evaluate three complementary quantum‐information measures ‐Shannon entropy, Onicescu informational energy, and Fisher information in real and reciprocal space, and we analyze the associated entropic and Fisher uncertainty relations. Special attention is paid to the behavior near the critical window lengths at which excited bound states emerge from the continuum, where we derive analytic limiting expressions for the wavefunctions and all information measures. In this regime, we show that the particle effectively inherits the properties of the ground state of a 1D Dirichlet quantum well, independently of the detailed window boundary condition. A systematic comparison between single‐ and double‐window geometries highlights how boundary engineering can be used to tailor localization, sensitivity, and information‐theoretic characteristics of waveguide modes relevant for quantum transport, waveguide‐based qubits, and quantum sensing architectures.