Quantum Foundations

I will give a general method for producing a process theory of local spacetime events and higher-order transformations from any base process theory of first-order maps. This process theory models events as intervention-context pairs, uniting the local actions by agents with the structure of the spacetime around them. I will show how this theory is richer than a standard process theory by permitting additional ways of composing agents beyond the usual tensor product, thereby capturing various strengths of possible spatio-temporal correlations. I will also explain the connection between these compositions and the logic "system BV".

Recent efforts to formulate a unified, causally neutral approach to quantum theory have highlighted the need for a framework treating spatial and temporal correlations on an equal footing. Building on this motivation, we propose operationally inspired axioms for quantum states over time, demonstrating that, unlike earlier approaches, these axioms yield a unique quantum state over time that is valid across both bipartite and multipartite spacetime scenarios. In particular, we show that the Fullwood-Parzygnat state over time uniquely satisfies these axioms, thus unifying bipartite temporal correlations and extending seamlessly to any number of temporal points. In particular, we identify two simple assumptions—linearity in the initial state and a quantum analog of conditionability—that single out a multipartite extension of bipartite quantum states over time, giving rise to a canonical generalization of Kirkwood-Dirac type quasi-probability distributions. This result provides a new characterization of quantum Markovianity, advancing our understanding of quantum correlations across both space and time.

the no-cloning theorem is an essential result in quantum information on top of which many quantum cryptography protocols are built. In this talk we examine the cloning question in the context of classical mechanics/Hamiltonian mechanics. We find the answer is quite subtle: whether a mechanical system can be cloned depends on the topological structure of its phase space. In particular, for a system to be clonable, its phase space must be contractible. This means certain systems (e.g. particle moving on a line) is clonable, while others (e.g. the simple pendulum) cannot be cloned. We explain the idea of the proof, which uses tools from algebraic topology (homotopy groups and Whitehead’s theorem). Finally we discuss the physical interpretations of this result: how do we reconcile this theorem with the experience that generally speaking, classical information is clonable? Can we use this no-cloning theorem to build secure communication protocols in classical systems instead of quantum ones?