The optimality of attaching unlinked labels to unlinked meanings

Vocabulary learning by children can be characterized by many biases. When encountering a new word, children as well as adults, are biased towards assuming that it means something totally different from the words that they already know. To the best of our knowledge, the 1st mathematical proof of the optimality of this bias is presented here. First, it is shown that this bias is a particular case of the maximization of mutual information between words and meanings. Second, the optimality is proven within a more general information theoretic framework where mutual information maximization competes with other information theoretic principles. The bias is a prediction from modern information theory. The relationship between information theoretic principles and the principles of contrast and mutual exclusivity is also shown.Peer ReviewedPostprint (published version

Thermodynamic cost of creating correlations

We investigate the fundamental limitations imposed by thermodynamics for creating correlations. Considering a collection of initially uncorrelated thermal quantum systems, we ask how much classical and quantum correlations can be obtained via a cyclic Hamiltonian process. We derive bounds on both the mutual information and entanglement of formation, as a function of the temperature of the systems and the available energy. While for a finite number of systems there is a maximal temperature allowing for the creation of entanglement, we show that genuine multipartite entanglement---the strongest form of entanglement in multipartite systems---can be created at any temperature when sufficiently many systems are considered. This approach may find applications, e.g. in quantum information processing, for physical platforms in which thermodynamic considerations cannot be ignored.Comment: 17 pages, 3 figures, substantially rewritten with some new result