CIF: Small: Resource Theories of Quantum Channels

Quantum information science is based on the science of 'entanglement', where the quantum states of two or more objects have to be described with reference to each other, even though the individual objects are spatially separated. Despite being identified nearly a century ago, much is not understood regarding the relationship between the resources in a quantum system and the level of entanglement that can be achieved. This project seeks to answer some fundamental questions in the resource theory of entanglement for quantum channels. How much entanglement is required to prepare a quantum state or to simulate a quantum channel? How much entanglement can one distill from these same resources? How many "magic quantum states" are required to perform a given quantum computation? How much "non-Gaussianity" is required to achieve a quantum advantage in communication over quantum channels? How distinguishable are two quantum states or channels? The questions that this project addresses are of particular interest for the many applications of quantum information processing, such as solving computationally hard problems and enabling secure and covert communications. The project will also train an inter-disciplinary cadre of students in this domain through extensive education and curriculum development activities. This project will address foundational questions concerning resource theories of quantum channels. The traditional perspective in quantum resource theories concerns how to use free operations to convert one resourceful quantum state to another one. For example, a fundamental and well known question in entanglement theory is to determine the distillable entanglement of a bipartite state, which is equal to the maximum rate at which fresh Bell states can be distilled from many copies of a given bipartite state by employing local operations and classical communication for free. It is the aim of this research project to take this kind of question to the next level, with the main question being: What is the best way of using free channels to convert one resourceful quantum channel to another? The project seeks to identify measures of entanglement for quantum channels that allow for addressing the above questions while being efficiently computable, and also to understand dynamical processes in other resource theories, such as magic states and channels, distinguishability, purity, thermodynamics, non-Gaussianity, etc. 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.