Zenith Grant Awardee
Dr. Bob Coecke
Oxford University
Project Title
The Road to a New Quantum Formalism: Categories as a Canvas for Quantum Foundations
Project Summary
When watching television, we don't observe the `low-level' matrices of tiny pixels the screen is made up from, but rather `high-level' Gestalts of each of the figuring entities making up the story that the images convey. These entities and their story is the essence of the images; the matrix of pixels is just a technologically convenient representation. Similarly, in modern computer programming, one does not `speak' in terms of 0s and 1s, but rather relies on high-level concepts about information flow. The way we reason nowadays about quantum theory is still very `low-level', in terms of matices of so-called complex numbers. Recent work identified a high-level formal framework for quantum theory, resulting in purely diagrammatic languages for reason and compution, and also corresponding logics, that is, languages which a computer `understands'. By not making explicit the underlying `low-level pixels' there is still plenty of freedom to articulate the ideas behind other important foundational work on quantum theory. Therefore our approach can act as a canvas on which we can paint a variety of theories of physical reality. This would provide us with a true image of nature, rather than its pixels.
Technical Abstract
Monoidal categories have recently proven to be an excellent high-level framework for reasoning about quantum information and computation. Features are an intuitive purely diagrammatic calculus, which enables pictorial derivation of several protocols as well as computing the quantum Fourier transform, and comprehension of quantum, classical and mixed data types. The corresponding categorical logic enables automation.
Important operational features, not present in the usual quantum formalism, are types and compositionality. The approach moreover reveals those high-level concepts, which are key to quantum phenomena, and still leaves a large degree of axiomatic freedom. It therefore has the potential to become a unifying framework for a variety of existing approaches in quantum foundations. Compelling evidence for this is provided by our recent presentations of Spekkens' Toy Theory and C*-algebras within this approach, as well as promising developments towards describing BBLW convex theories, algebraic QFTs and Doering-Isham-Butterfield topoi, to name a few. We expect to obtain important insights on all of these approaches as well as to blend the key features of these within new models and axiom systems for quantum reasoning, and possibly make important steps towards quantum gravity.
QSpace Latest
PressRelease: Shining a light on the roots of plant “intelligence”
All living organisms emit a low level of light radiation, but the origin and function of these ‘biophotons’ are not yet fully understood. An international team of physicists, funded by the Foundational Questions Institute, FQxI, has proposed a new approach for investigating this phenomenon based on statistical analyses of this emission. Their aim is to test whether biophotons can play a role in the transport of information within and between living organisms, and whether monitoring biophotons could contribute to the development of medical techniques for the early diagnosis of various diseases. Their analyses of the measurements of the faint glow emitted by lentil seeds support models for the emergence of a kind of plant ‘intelligence,’ in which the biophotonic emission carries information and may thus be used by plants as a means to communicate. The team reported this and reviewed the history of biophotons in an article in the journal Applied Sciences in June 2024.