A Fundamental Limit of Measurement Imposed by the Elementary Interactions

Quantum information theory is closely related to quantum measurement theory because one must perform measurement to obtain information on a quantum system. Among many possible limits of quantum measurement, the simplest ones were derived directly from the uncertainty principles. However, such simple limits are not the only limits. I here suggest a new limit which comes from the forms and the strengths of the elementary interactions. Namely, there are only four types of elementary interactions in nature; their forms are determined by the gauge invariance (and symmetry breaking), and their coupling constants (in the low-energy regime) have definite values. I point out that this leads to a new fundamental limit of quantum measurements. Furthermore, this fundamental limit imposes the fundamental limits of getting information on, preparing, and controlling quantum systems.Comment: 10 pages including 1 figure. Proc. 3rd Tohwa Univ. Int. Conf. Statistical Physics (Fukuoka, Japan, 1999) to be published from AI

Landauer Conductance and Nonequilibrium Noise of One-Dimensional Interacting Electron Systems

The conductance of one-dimensional interacting electron systems is calculated in a manner similar to Landauer's argument for non-interacting systems. Unlike in previous studies in which the Kubo formula was used, the conductance is directly evaluated as the ratio of current $J$ to the chemical potential difference $\Delta \mu$ between right-going and left-going particles. It is shown that both $J$ and $\Delta \mu$ are renormalized by electron-electron (e-e) interactions, but their ratio, the conductance, is not renormalized at all if the e-e interactions are the only scattering mechanism. It is also shown that nonequilibrium current fluctuation at low frequency is absent in such a case. These conclusions are drawn for both Fermi liquids (in which quasi-particles are accompanied with the backflow) and Tomonaga-Luttinger liquids.Comment: 4 pages, No figure