Reconciliation of Quantum and Relativistic Causality

Brief description of the project and impact:
This project falls within the EPSRC ''Quantum Information'' Research area. The main aim of this project is to identify a new way of reconciling quantum and relativistic causality. We intend to formulate our framework using tools from category theory and algebraic quantum field theory. Category theory is a branch of mathematics that recently admits significant applications in quantum information. Algebraic quantum field theory (AQFT) on the other hand, assigns the algebra of observables to spacetime regions. The motivation for exploiting AQFT is that a physical experiment takes place in a specific region of spacetime. Thus, the physical quantities determined from the experiment are localised in that specific region.
Traditionally, in AQFT observables are assigned to Minkowski spacetime regions. Here, we intend to adopt a discrete spacetime approach, namely define our regions as finite partial orders. The motivation for adopting a discrete spacetime is the growing belief in the field of theoretical physics that spacetime is discrete at the very fundamental level. The impact of this project will be two-fold: We hope to pave the way for a quantum information theoretic generalization of AQFT and provide insight towards quantum foundations.

Aims and objectives:
It is a well-established fact in quantum theory that one can acquire a complete description of a physical system under study, if the corresponding states and observables are provided together with a probability distribution of values. In the realm of AQFT however, there is another property that affects its conceptual structure. This property is locality which is a combination of two other properties, i.e. localisation and causality. The fact that an experiment takes place in a specific spacetime region is associated with the notion of localization. The concept of causality is related to no-faster than light communication. Thus, observables associated with spacelike separated regions commute.
In this context, we aim at defining a mapping that associates discrete spacetime regions with algebras of quantum observables. Traditionally, in quantum theory states and observables possess a ``realization'' in terms of lab instruments. In the relativistic realm, we can distinguish instruments by how they are placed relative to a reference frame in our lab. There are ten parameters all in all, that could specify the placement of the apparatus in the lab and correspond to ten parameters of the Poincare group. The laws of nature are Poincare invariant which translates as the result of the experiment should not depend in the different ways with which an apparatus can be placed in a lab. This is a general assertion related to Minkowski spacetime and the reconciliation with the discrete case is not obvious. Thus, we intend to specify suitable mappings that maintain the algebraic structure when a transformation is performed in the discrete spacetime. Finally, we aim at designing toy models associating qubit algebras to discrete spacetime regions and figure out how one can perform quantum information tasks, such as quantum teleportation in this context.

Novelty of the research methodology:
The mathematical language that we intend to use, has already provided us with new insights regarding the foundations of quantum information theory. It defines a unifying language for a wide variety of phenomena drawn from areas including quantum theory, quantum information, logic, topology and even linguistics. Algebraic quantum field theory on the other hand provides a mathematically precise description of the quantum field theory structure which is a great advantage when performing research in quantum information within a relativistic context.

Quantum technologies promise a transformation of the fields of measurement, communication and information processing. They present a particular opportunity since they are disruptive technologies: not only do they offer a chance for rapid growth but they also allow lesser participants in a field (such as the UK in IT) to become major players through appropriate risk-taking and manpower development. Students graduating from the InQuBATE Skills Hub will have the right mindset to work in the industries where quantum technologies will be applied, and help to break down the traditional barriers between those sectors to make this transformation happen. They will have all the necessary technical and transferable skills, plus a network of contacts with our partners, their fellow cohort members and the academic supervisors.

Our commercial partners are keen to help our students realise their potential and achieve the impact we expect of them, through the training they offer and their contributions to the centre's research. They include companies who have already developed quantum technologies to products in quantum communication (Toshiba) and optimization (D-Wave), large corporates who are investing in quantum technology because they see its potential to transform their businesses in aerospace, defence, instrumentation and internet services (Lockheed Martin, Google,) and government agencies with key national responsibilities (NPL). We want to see the best communication of our students' research, so our students will benefit from the existing training programme set up with a leading scientific publisher (Nature Publishing Group); we also want to see more of the future companies that lead this field based the UK, so we have partnered with venture capital group DFJ Esprit to judge and mentor the acceleration of our students' innovations toward the market.