Yet another additivity conjecture

It is known that the additivity conjecture of Holevo capacity, output minimum entoropy, and the entanglement of formation (EoF), are equivalent with each other. Among them, the output minimum entropy is simplest, and hence many researchers are focusing on this quantity. Here, we suggest yet another entanglement measure, whose strong superadditivity and additivity are equivalent to the additivity of the quantities mentioned above. This quantity is as simple as the output minimum entropy, and in existing proofs of additivity conjecture of the output minimum entropy for the specific examples, they are essentially proving the strong superadditivity of this quantity.Comment: corrections of typo, etc. minor revisio

Thermal Abundances of Heavy Particles

Matsumoto and Yoshimura [hep-ph/9910393] have argued that there are loop corrections to the number density of heavy particles (in thermal equilibrium with a gas of light particles) that are not Boltzmann suppressed by a factor of e^(-M/T) at temperatures T well below the mass M of the heavy particle. We argue, however, that their definition of the number density does not correspond to a quantity that could be measured in a realistic experiment. We consider a model where the heavy particles carry a conserved U(1) charge, and the light particles do not. The fluctuations of the net charge in a given volume then provide a measure of the total number of heavy particles in that same volume. We show that these charge fluctuations are Boltzmann suppressed (to all orders in perturbation theory). Therefore, we argue, the number density of heavy particles is also Boltzmann suppressed.Comment: 9 pages, 1 figure; minor improvements in revised versio

A certain synchronizing property of subshifts and flow equivalence

We will study a certain synchronizing property of subshifts called $\lambda$-synchronization. The $\lambda$-synchronizing subshifts form a large class of irreducible subshifts containing irreducible sofic shifts. We prove that the $\lambda$-synchronization is invariant under flow equivalence of subshifts. The $\lambda$-synchronizing K-groups and the $\lambda$-synchronizing Bowen-Franks groups are studied and proved to be invariant under flow equivalence of $\lambda$-synchronizing subshifts. They are new flow equivalence invariants for $\lambda$-synchronizing subshifts.Comment: 28 page