VC-dimension of short Presburger formulas

We study VC-dimension of short formulas in Presburger Arithmetic, defined to have a bounded number of variables, quantifiers and atoms. We give both lower and upper bounds, which are tight up to a polynomial factor in the bit length of the formula

Are there phase transitions in information space?

The interplay between two basic quantities -- quantum communication and information -- is investigated. Quantum communication is an important resource for quantum states shared by two parties and is directly related to entanglement. Recently, the amount of local information that can be drawn from a state has been shown to be closely related to the non-local properties of the state. Here we consider both formation and extraction processes, and analyze informational resources as a function of quantum communication. The resulting diagrams in information space allow us to observe phase-like transitions when correlations become classical.Comment: 4 pages, 3 epsi figures, to appear in Phys. Rev. Let

Probing the atmosphere of a sub-Jovian planet orbiting a cool dwarf

We derive the 0.01 $\mu$m binned transmission spectrum, between 0.74 and 1.0 $\mu$m, of WASP-80b from low resolution spectra obtained with the FORS2 instrument attached to ESO's Very Large Telescope. The combination of the fact that WASP-80 is an active star, together with instrumental and telluric factors, introduces correlated noise in the observed transit light curves, which we treat quantitatively using Gaussian Processes. Comparison of our results together with those from previous studies, to theoretically calculated models reveals an equilibrium temperature in agreement with the previously measured value of 825K, and a sub-solar metallicity, as well as an atmosphere depleted of molecular species with absorption bands in the IR ($\gg 5\sigma$). Our transmission spectrum alone shows evidence for additional absorption from the potassium core and wing, whereby its presence is detected from analysis of narrow 0.003 $\mu$m bin light curves ($\gg 5\sigma$). Further observations with visible and near-UV filters will be required to expand this spectrum and provide more in-depth knowledge of the atmosphere. These detections are only made possible through an instrument-dependent baseline model and a careful analysis of systematics in the data.Comment: 13 pages, 11 figures, 3 tables. Accepted for publication in MNRA

A Thermodynamical Approach to Quantifying Quantum Correlations

We consider the amount of work which can be extracted from a heat bath using a bipartite state shared by two parties. In general it is less then the amount of work extractable when one party is in possession of the entire state. We derive bounds for this "work deficit" and calculate it explicitly for a number of different cases. For pure states the work deficit is exactly equal to the distillable entanglement of the state, and this is also achievable for maximally correlated states. In these cases a form of complementarity exists between physical work which can be extracted and distillable entanglement. The work deficit is a good measure of the quantum correlations in a state and provides a new paradigm for understanding quantum non-locality.Comment: 4 pages, Revtex4, title changed, caveat added to theore

Designing optimal discrete-feedback thermodynamic engines

Feedback can be utilized to convert information into useful work, making it an effective tool for increasing the performance of thermodynamic engines. Using feedback reversibility as a guiding principle, we devise a method for designing optimal feedback protocols for thermodynamic engines that extract all the information gained during feedback as work. Our method is based on the observation that in a feedback-reversible process the measurement and the time-reversal of the ensuing protocol both prepare the system in the same probabilistic state. We illustrate the utility of our method with two examples of the multi-particle Szilard engine.Comment: 15 pages, 5 figures, submitted to New J. Phy