Quantum Physics

I will first present a theorem based on the Decoupling Theorem of [1] which gives sufficient and necessary conditions for a quantum channel (CPTPM) being such that it yields the same output for almost all possible inputs. This theorem allows us to reproduce and generalize results oft [2,3], in which cornerstones of statistical physics are derived from first principles of quantum mechanics, in a very natural and easy way. Specifically, we express them in a way which allows to apply results about random 2-qubit interactions [4]. Furthermore, we apply this theorem to provide a criterion for whether different initial states of some subspace of a quantum mechanical system in contact with an environment have at some given time already evolved to the same state or not. As it turns out, this question can be answered by examining a simple entropic inequality evaluated for just one particular state [5]. Applying this criterion to realistic Hamiltonians with local interactions may lead to improved bounds on the thermalization times of quantum mechanical systems.

I will present a new approach to information theoretic foundations of quantum theory, developed in order to encompass quantum field theory and curved space-times. Its kinematics is based on the geometry of spaces of integrals on W*-algebras, and is independent of probability theory and Hilbert spaces. It allows to recover ordinary quantum mechanical kinematics as well as emergent curved space-times. Unlike the approaches based on lattices of projections, this kinematics provides a direct mathematical generalisation of the ordinary probability theory to the regime of non-commutative algebras. The new quantum information dynamics is provided by the constrained maximisation of quantum relative entropy. The von Neumann-Lueders rule and several other rules of that type, including Bayes' rule in commutative case, are the special cases of it. Using Favretti's generalisation of the Jaynes-Mitchell source theory, I will show how this dynamics allows one to derive `interacting QFT'-like correlation functions and perturbation expansions in geometric terms of experimental control-and-response parameters, without using Hilbert spaces or measure spaces. Finally, I will present a new bayesian interpretation of quantum theory, aimed at dealing with the intersubjective experimental verifiability, but without providing any ontological claims. Quite noticeably, this interpretation leads to a concrete category theoretic formulation of the new foundations.

We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particle's arrival at the counter is identified with the loss of normalization for an initial wave packet. The result is obtained under the sole assumption that the absorbing term vanishes on the initial wave function. Nearly minimal uncertainty can be achieved in a two-level system.