FET: Small: NSF-NSERC: Fundamental limits on quantum communications

Quantum information theory studies how quantum-mechanical systems process information. A central goal is to understand how much information can be preserved when the information-carrying systems are affected by noise, which is modeled as a quantum channel. The capacity of a channel quantifies the optimal rates of faithful information-processing.

However, solving the optimization problems characterizing these capacities is challenging due to the complicated structure of correlations in large quantum systems. This project aims to contribute to our understanding of quantum channel capacities. It will develop flexible methods to construct simple testbed channels with interesting yet tractable information-theoretic properties; devise methods to efficiently approximate quantum channel capacities of general channels; and study new ways of transmitting information through channels based on insights from classical network information theory.

As a collaborative project between the US and Canada, it will strengthen international collaboration and communication. Visits between the two investigators' institutions will benefit workforce training. There will also be workshops and review articles, which will greatly benefit the research community and students in particular.

Quantum channel capacities can be expressed in terms of an optimization problem involving entropic quantities. These entropic quantities are generally non-additive due to non-trivial interactions of the channel with the quantum correlations in many-body quantum systems. As a result, the entropic optimization problems determining quantum channel capacities become intractable to solve exactly.

This project aims to address this challenge from different angles. First, it proposes a method of constructing quantum channels with rich information-theoretic properties but for which the corresponding optimization problems are solvable. Second, it will develop new methods to estimate channel capacities of general unstructured quantum channels.

The chosen approach relies on a channel capacity bound that is additive but involves auxiliary systems of unbounded dimension. The main technical focus is to further develop an existing method of handling such unbounded optimizations through a converging hierarchy of bounded convex optimization problems. Third, it will study new coding techniques for quantum information transmission that are inspired by broadcast channel coding, the classical analogue of quantum channel coding.

Novel coding techniques based on this correspondence will provide new insights into the limitations of faithful quantum information transmission.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.