Project title: Order and disorder in quantum information science

Supervisors: David Jennings and Myungshik Kim

Project description:
Irreversible processes are ubiquitous in physics. The emergence of macroscopic irreversibility from microscopically reversible laws is typically attributed to the second law of thermodynamics, which roughly states that on average order is non-increasing in time. More recently, however, a wider notion of irreversibility is being developed which accounts for processes outside the remit of traditional thermodynamics. For instance, Nielsens’ majorization theorem in quantum information theory tells us that we may transform the state of two qubits from a Bell state to a product state under local operations and classical communication, but the reverse process under these restrictions is not permitted. On the other hand, many recent attempts have been made to extend thermodynamics itself to incorporate scenarios beyond which classical thermodynamic laws apply, such as to non-equilibrium settings or to quantum systems with ensemble sizes well below the thermodynamic limit. These lines of inquiry are beginning to shed light on the following question, which at a high-level we seek to address:

Q:  How do quantum mechanical forms of order differ from classical forms of order?

This is a broad question that applies to all so-called "quantum resources", such as quantum entanglement and quantum coherence. Recent results in quantum information theory have provided a range of non-trivial insights into this question, and this project will contribute to this line. Initial work will focus on the structure of ordered coherent systems, and will provide applications in thermodynamics, symmetry-constrained dynamics and quantum channel theory. Subsequent work will study how these resource-theoretic structures connect with on-going research in Quantum Technologies.