This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.
Recently rediscovered results in the theory of partial differential equations show that for free fields, the properties of the field in an arbitrarily small volume of space, traced through eternity,
determine completely the field everywhere at all times. Over finite
times, the field is determined in the entire region spanned by the intersection of the future null cone of the earliest event and the past
null cone of the latest event. Thus this paradigm of classical field
Symmetric monoidal categories provide a convenient and enlightening framework within which to compare and contrast physical theories on a common mathematical footing. In this talk we consider two theories: stabiliser qubit quantum mechanics and the toy bit theory proposed by Rob Spekkens. Expressed in the categorical framework the two theories look very similar mathematically, reflecting their common physical features.
Quantum mechanics does not allow us to measure all possible combinations of observables on one system. Even in the simplest case of two observables we know, that measuring one of the observables changes the system in such way, that the other measurement will not give us desired precise information about the state of the system.
Nonlocality is arguably one of the most remarkable features of
quantum mechanics. On the other hand nature seems to forbid other
no-signaling correlations that cannot be generated by quantum systems.
Usual approaches to explain this limitation is based on information
theoretic properties of the correlations without any reference to
physical theories they might emerge from. However, as shown in [PRL 104,
140401 (2010)], it is the structure of local quantum systems that
A picture can be used to represent an experiment. In this talk we will consider such pictures and show how to turn them into pictures representing calculations (in the style of Penrose's diagrammatic tensor notation). In particular, we will consider circuits described probabilistically. A circuit represents an experiment where we act on various systems with boxes, these boxes being connected by the passage of systems between them. We will make two assumptions concerning such circuits.
I will review some recent advances on the line of deriving quantum field theory from pure quantum information processing. The general idea is that there is only Quantum Theory (without quantization rules), and the whole Physics---including space-time and relativity---is emergent from the processing. And, since Quantum Theory itself is made with purely informational principles, the whole Physics must be reformulated in information-theoretical terms.
Nonlocality is the most striking feature of quantum mechanics. It might even be considered its defining feature and understanding it may be the most important step towards understanding the whole theory. Yet for a long time it was impossible to pinpoint the reason behind the exact amount of nonlocality allowed by quantum mechanics expressed by Tsirelson bound. Recently information causality has been shown to be the principle from which this bound can be derived.
Landauer's erasure principle states that there is an inherent work cost associated with all irreversible operations, like the erasure of the data stored in a system. The necessary work is determined by our uncertainty: the more we know about the system, the less it costs to erase it.