35 citations · 87 across the 12 of their papers we have counts for
12 papers
A Topos Theoretic Notion of Entropy
Carmen-Maria Constantin, Andreas Doering
In the topos approach to quantum theory, the spectral presheaf plays the role of the state space of a quantum system. We show how a notion of entropy can be defined within the topo…
Two New Complete Invariants of von Neumann Algebras
Andreas Doering
We show that the oriented context category and the oriented spectral presheaf are complete invariants of a von Neumann algebra not isomorphic to and wi…
Flows on Generalised Gelfand Spectra of Nonabelian Unital C*-Algebras and Time Evolution of Quantum Systems
Andreas Doering
In arXiv:1212.2613, we associated a presheaf Σ^A with each unital C*-algebra A. The spectral presheaf Σ^A generalises the Gelfand spectrum of an abelian unital C*-algebra. In the p…
Generalised Gelfand Spectra of Nonabelian Unital C*-Algebras
Andreas Doering
To each unital C*-algebra A we associate a presheaf Σ^A, called the spectral presheaf of A, which can be regarded as a generalised Gelfand spectrum. We develop a categorical notion…
Self-adjoint Operators as Functions II: Quantum Probability
Andreas Doering, Barry Dewitt
In "Self-adjoint Operators as Functions I: Lattices, Galois Connections, and the Spectral Order" [arXiv:1208.4724], it was shown that self-adjoint operators affiliated with a von N…
Contextual Entropy and Reconstruction of Quantum States
Carmen Maria Constantin, Andreas Doering
We introduce a new notion of entropy for quantum states, called contextual entropy, and show how it unifies Shannon and von Neumann entropy. The main result is that from the knowle…