No-local-broadcasting theorem for quantum correlations

We prove that the correlations present in a multipartite quantum state have an \emph{operational} quantum character as soon as the state does not simply encode a multipartite classical probability distribution, i.e. does not describe the joint state of many classical registers. Even unentangled states may exhibit such \emph{quantumness}, that is pointed out by the new task of \emph{local broadcasting}, i.e. of locally sharing pre-established correlations: this task is feasible if and only if correlations are classical and derive a no-local-broadcasting theorem for quantum correlations. Thus, local broadcasting is able to point out the quantumness of correlations, as standard broadcasting points out the quantum character of single system states. Further, we argue that our theorem implies the standard no-broadcasting theorem for single systems, and that our operative approach leads in a natural way to the definition of measures for quantumness of correlations.Comment: 5 pages, various changes (title, shortened, references added, corrected typos,...), submitte

Randomness, Nonlocality and information in entagled correlations

It is shown that the Einstein, Podolsky and Rosen (EPR) correlations for arbitrary spin-s and the Greenberger, Horne and Zeilinger (GHZ) correlations for three particles can be described by nonlocal joint and conditional quantum probabilities. The nonlocality of these probabilities makes the Bell's inequalities void. A description that exhibits the relation between the randomness and the nonlocality of entangled correlations is introduced. Entangled EPR and GHZ correlations are studied using the Gibbs-Shannon entropy. The nonlocal character of the EPR correlations is tested using the information Bell's inequalities. Relations between the randomness, the nonlocality and the entropic information for the EPR and the GHZ correlations are established and discussed.Comment: 19 pages, REVTEX, 8 figures included in the uuencoded postscript fil

Quantifying origin and character of long-range correlations in narrative texts

In natural language using short sentences is considered efficient for communication. However, a text composed exclusively of such sentences looks technical and reads boring. A text composed of long ones, on the other hand, demands significantly more effort for comprehension. Studying characteristics of the sentence length variability (SLV) in a large corpus of world-famous literary texts shows that an appealing and aesthetic optimum appears somewhere in between and involves selfsimilar, cascade-like alternation of various lengths sentences. A related quantitative observation is that the power spectra S(f) of thus characterized SLV universally develop a convincing `1/f^beta' scaling with the average exponent beta =~ 1/2, close to what has been identified before in musical compositions or in the brain waves. An overwhelming majority of the studied texts simply obeys such fractal attributes but especially spectacular in this respect are hypertext-like, "stream of consciousness" novels. In addition, they appear to develop structures characteristic of irreducibly interwoven sets of fractals called multifractals. Scaling of S(f) in the present context implies existence of the long-range correlations in texts and appearance of multifractality indicates that they carry even a nonlinear component. A distinct role of the full stops in inducing the long-range correlations in texts is evidenced by the fact that the above quantitative characteristics on the long-range correlations manifest themselves in variation of the full stops recurrence times along texts, thus in SLV, but to a much lesser degree in the recurrence times of the most frequent words. In this latter case the nonlinear correlations, thus multifractality, disappear even completely for all the texts considered. Treated as one extra word, the full stops at the same time appear to obey the Zipfian rank-frequency distribution, however.Comment: 28 pages, 8 figures, accepted for publication in Information Science

Orbital Symmetry and Electron Correlation in Na_{x}CoO_2

Measurements of polarization-dependent soft x-ray absorption reveal that the electronic states determining the low-energy excitations of Na$_{x}$CoO$_2$ have predominantly $a_{1g}$ symmetry with significant O $2p$ character. A large transfer of spectral weight observed in O $1s$ x-ray absorption provides spectral evidence for strong electron correlations in the layered cobaltates. Comparing Co $2p$ x-ray absorption with calculations based on a cluster model, we conclude that Na$_{x}$CoO$_2$ exhibits a charge-transfer electronic character rather than a Mott-Hubbard character

Spin nematics in the bilinear-biquadratic S=1 spin chain

We report the existence of an extended critical, nondimerized region in the phase diagram of the bilinear-biquadratic spin-one chain. The dominant power law correlations are ferroquadrupolar, i.e. spin nematic in character. Another known critical region is also characterized by dominant quadrupolar correlations, although with a different wave vector. Our results show that spin nematic correlations play an important role in quantum magnets with spin S >= 1 in regions between antiferromagnetic and ferromagnetic phases.Comment: 4 pages, 7 figure

Effective bosonic hamiltonian for excitons : a too naive concept

Excitons, being made of two fermions, may appear from far as bosons. Their close-to-boson character is however quite tricky to handle properly. Using our commutation technique especially designed to deal with interacting close-to-boson particles, we here calculate the exact expansion in Coulomb interaction of theexciton-exciton correlations, and show that a naive effective bosonic hamiltonian for excitons cannot produce these X-X correlations correctly

Bath-induced correlations in an infinite-dimensional Hilbert space

Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T > 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.Comment: 13 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1512.0870