MC 6460
Candidate
Einar GabbassovÌý| University of À¶Ý®ÊÓƵ
Title
From Quantum Errors to Stochastic Dynamics: Unravelling Open Quantum Systems
Abstract
Open quantum systems are quantum systems that interact with an external environment and exhibit dynamics fundamentally distinct from those of isolated, unitary evolution. These interactions give rise to decoherence and dissipation, which are crucial for understanding quantum technologies and the limits of quantum information processing.
In this talk, I will introduce the mathematical framework used to describe such systems, with a focus on Lindblad master equations, which govern the averaged evolution of open quantum systems. I will then present their stochastic unravellings via stochastic Schrödinger equations, offering a trajectory-based perspective that connects the ensemble dynamics to individual realizations.
To make this connection intuitive, I will introduce the essentials of stochastic (Itô) calculus, which underpins the formulation of these stochastic differential equations. Along the way, we will examine basic quantum channels that model common errors such as dephasing, relaxation, and depolarization, and explore how these channels give rise to both deterministic and stochastic dynamical descriptions.
The talk is designed to be accessible to a general mathematics audience, with an emphasis on the interplay between operator theory, probability, and quantum physics.