Measurable entanglement

Universal and measurable entanglement entropy in the spin-boson model.

We study the entanglement between a qubit and its environment from the spin-boson model with Ohmic dissipation. Through a mapping to the anisotropic Kondo model, we derive the entropy of entanglement of the spin E(alpha,Delta,h), where alpha is the dissipation strength, Delta is the tunneling amplitude between qubit states, and h is the level asymmetry. For 1-alpha>>Delta/omegac and (Delta,h)<<...

Measurable Utility and the Measurable Choice Theorem

Measurable Transformations

Measurable Sensitivity

We introduce the notions of measurable and strong measurable sensitivity, which are measure-theoretic versions of the conditions of sensitive dependence on initial conditions and strong sensitive dependence on initial conditions, respectively. Strong measurable sensitivity is a consequence of light mixing, implies that a transformation has only finitely many eigenvalues, and does not exist in t...

Measurable Categories

We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a rigorous construction for the bicategory used in [4] and [3] as the basis for a representation theory of (Lie) 2-groups. Two important technical results are establishe...