Nonlinear stochastic Schrödinger equations in terms of quantum Bernoulli noise

This paper develops a theoretical framework for nonlinear stochastic Schrödinger equations (SSEs) driven by quantum Bernoulli noise (QBN), providing mathematical foundations for modeling open quantum systems in quantum information processing. We establish the well-posedness of [Formula: see text]-strong solutions for linear SSEs and construct solutions for the nonlinear equations via Girsanov transformations. Our approach utilizes operator lifting techniques on the Hilbert space [Formula: see text] and validates the framework through numerical simulations of qubit-reservoir systems. The results demonstrate higher state fidelity compared to Lindblad models under strong coupling, with applications to quantum error correction and real-time control in near-term quantum devices.