Nonclassicality Criteria from Phase-Space Representations and Information-Theoretical Constraints Are Maximally Inequivalent

We consider two celebrated criteria for defining the nonclassicality of bipartite bosonic quantum systems, the first stemming from information theoretic concepts and the second from physical constraints on the quantum phase space. Consequently, two sets of allegedly classical states are singled out: (i) the set C composed of the so-called classical-classical (CC) states—separable states that are locally distinguishable and do not possess quantum discord; (ii) the set P of states endowed with a positive P representation (P-classical states)—mixtures of Glauber coherent states that, e.g., fail to show negativity of their Wigner function. By showing that C and P are almost disjoint, we prove that the two defining criteria are maximally inequivalent. Thus, the notions of classicality that they put forward are radically different. In particular, generic CC states show quantumness in their P representation, and vice versa, almost all P-classical states have positive quantum discord and, hence, are not CC. This inequivalence is further elucidated considering different applications of P-classical and CC states. Our results suggest that there are other quantum correlations in nature than those revealed by entanglement and quantum discord.

Documents and Dependencies: an Exploration of Vector Space Models for Semantic Composition

In most previous research on distributional semantics, Vector Space Models (VSMs) of words are built either from topical information (e.g., documents in which a word is present), or from syntactic/semantic types of words (e.g., dependency parse links of a word in sentences), but not both. In this paper, we explore the utility of combining these two representations to build VSM for the task of semantic composition of adjective-noun phrases. Through extensive experiments on benchmark datasets, we find that even though a type-based VSM is effective for semantic composition, it is often outperformed by a VSM built using a combination of topic- and type-based statistics. We also introduce a new evaluation task wherein we predict the composed vector representation of a phrase from the brain activity of a human subject reading that phrase. We exploit a large syntactically parsed corpus of 16 billion tokens to build our VSMs, with vectors for both phrases and words, and make them publicly available.