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Oxford Quantum Talks Archive

The power of epistemic restrictions in axiomatizing quantum theory: from trits to qutrits

Rob Spekkens, University of Cambridge
Seminars, October 2008, University of Oxford

It is common to assert that the discovery of quantum theory overthrew our classical conception of nature. But what, precisely, was overthrown? Providing a rigorous answer to this question is of practical concern, as it helps to identify and analyze quantum technologies that outperform their classical counterparts. It is also of significance for modern physics, where the challenge of applying quantum theory in new realms or moving beyond quantum theory necessitates a deep understanding of the principles upon which it is based. In this talk, I demonstrate that a large part of quantum theory can be obtained from a single innovation relative to classical theories, namely, that there is a fundamental restriction on the sorts of statistical distributions over classical states that can be prepared. This restriction implies a fundamental limit on the amount of knowledge that any observer can have about the classical state. I will consider in particular the case of an arbitrary number of 3-state classical systems, or trits, and I will show that using a particular sort of statistical restriction that appeals to the symplectic structure of the classical state space, one can reproduce the predictions of the stabilizer formalism for qutrits. I will end with a few speculations about the conceptual innovations that might underlie phenomena that can't be derived from a statistical restriction and what might be the origin of the restriction.

[video] [streaming video]