Abstract
Information-theoretical quantities such as statistical distinguishability typically result from optimisations over all conceivable observables. Physical theories, however, are not generally considered valid for all mathematically allowed measurements. For instance, quantum field theories are not meant to be correct or even consistent at arbitrarily small lengthscales. A general way of limiting such an optimisation to certain observables is to first coarse-grain the states by a quantum channel. We show how to calculate contractive quantum information metrics on coarse-grained equilibrium states of free bosonic systems (Gaussian states), in directions generated by arbitrary perturbations of the Hamiltonian. As an example, we study the Klein-Gordon field. If the phase-space resolution is coarse compared to h-bar, the various metrics become equal and the calculations simplify. In that context, we compute the scale dependence of the distinguishability of the quartic interaction.
Highlights
Information-theoretical quantities such as statistical distinguishability typically result from optimisations over all conceivable observables
We show how to calculate contractive quantum information metrics on coarse-grained equilibrium states of free bosonic systems (Gaussian states), in directions generated by arbitrary perturbations of the Hamiltonian
We focus on the calculation of quantum information metrics which directly generalise the classical Fisher information metric
Summary
We focus on the calculation of quantum information metrics which directly generalise the classical Fisher information metric. A metric associates to every ρ a positive linear operator Ω−1 ρ on Tρ defining the scalar product. Its geodesic distance has a closed analytical form as the Bures distance [11] It gives a tight bound on the variance of parameter estimation [8, 16], and is as such usually called the quantum Fisher information. We are interested in the case where E is a unital completely positive map, that is, E(1) = 1, and (E ⊗ idn )(A) ≥ 0 for all A ≥ 0 and all finite extra dimension n These conditions guarantee that ρ ◦ (E ⊗ idn ) (with density matrix (E∗ ⊗ id)(ρ)) is a valid state whenever ρ is. Given the metric Ω−1 ρ which gives rise to the geodesic distance d, and given the channel E, and the Hamiltonian H, we want to compute the coarse-grained distance d E∗ (ρλ1 ), E∗ (ρλ2 )
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
