Quantum Theory Derived from Information Principles
This lecture will be given by Professor Wegewijs.
A central theme in modern physics is its connection to information. The slogan "IT from BIT" (J. Wheeler) suggests that physics is ultimately grounded in something of information theoretical nature. In other words, if you know what quantum theory does in terms of information (i.e., operationally, what can be done in the lab), then it should be 100% clear how it does it (i.e., why the mathematical formalism is the way it is). This begs the question how you can talk about quantum theory at all since it is formulated in terms of mathematical axioms "that just work" and not through physical principles as, for example, relativity.
In the present course we will show that quantum theory can, however, be formulated directly as an information theory in terms of just 6 operational principles, i.e., by stating only what an experimenter can do in the lab and what (classical) information can acquired this way.
* If you are interested in quantum information science, then this course provides a concise and clear derivation of its essential results without going into computation, algorithms etc. However, in contrast to standard courses all these results are derived entirely in terms of "operations you can do in the lab" providing insights quite different from traditional mathematical derivations.
* If you don't care about quantum computing at all, but are interested in quantum theory of open systems / statistical physics, then this course may still be interesting for you. In that language, we show how you can do quantum theory entirely in Liouville space, i.e., on the level of (a generalization of) density operators. The underlying Hilbert space - including the superposition principle ! - comes out as a consequence of clear physical principles.
To be 100% sure: this course will NOT discuss any (re-re-)interpretation of quantum theory. It will also not imply or require any "modification" of quantum theory. The main goal is a clearer understanding of the standard, well-tested theory which can be exploited in calculations using operational (quantum-)circuits.
Course outline in blocks:
(I) Introduction: Classical & quantum theory (the usual way)
By way of introduction I will show how the standard formulation of classical and quantum theory indeed imply information principles and differing only regarding 1 principle.
(II) Operational probabilistic theories
In the remainder of the course we will turn this around and instead start from principles. This requires a very general probabilistic approach to physical theories which is based on experimental capabilities (e.g. tomography plays a key role).
(III) Quantum theory from information principles
We start from scratch by setting up quantum theory based on 6 principles and show how one can discuss information processing tasks without ever writing down a state vector, density matrix, or even introducing a Hilbert space.
(IV) Hilbert space from information principles
At the end of the course we derive as a result the traditional mathematical axioms of quantum theory by considering constraints on elementary information processing tasks.
The course is self-contained: I provide prerecorded video lectures + typeset PDF slides suitable for detailed study which are based on (and sometimes complement) the book. Prior knowledge of quantum information theory is not necessary but may be helpful.
G. M. D’Ariano, G. Chiribella, and P. Perinotti, Quantum theory from first principles: An informational approach, 2017
This book is electronically available via the RWTH library.
|Fri 12:30pm - 2pm||MBP2 116 (4273)||15.10.2021 - 28.01.2022|