Duality of privacy amplification against quantum adversaries and data compression with quantum side information

We show that the tasks of privacy amplification against quantum adversaries and data compression with quantum side information are dual in the sense that the ability to perform one implies the ability to perform the other. These are two of the most important primitives in classical information theory, and are shown to be connected by complementarity and the uncertainty principle in the quantum setting. Applications include a new uncertainty principle formulated in terms of smooth min- and max-entropies, as well as new conditions for approximate quantum error correction.Comment: v2: Includes a derivation of an entropic uncertainty principle for smooth min- and max-entropies. Discussion of the Holevo-Schumacher-Westmoreland theorem remove

Hybridization, polyploidy, and evolutionary transitions between monoecy and dioecy in Bryonia (Cucurbitaceae)

Correns’s 1903 (Berichte der Deutschen Botanischen Gesellschaft 21: 133 – 147) crosses between a monoecious and a dioecious species of Bryonia revealed the simple Mendelian inheritance of dioecy and provided the first instance of an XY sex determination system in any organism. Bryonia ranges from the Canary Islands to Central Asia and comprises seven dioecious and three monoecious species; its closest relative, Ecballium elaterium, has dioecious and monoecious populations. We used chloroplast (cp) and nuclear (nr) gene phylogenies to infer sexual system evolution in Bryonia. We also tested for associations between sexual system and ploidy level, based on published and original chromosome counts. Conflicts between cp and nr topologies imply that the dioecious hexaploid B. cretica arose from hybridization(s), probably involving the dioecious diploids B. dioica, B. syriaca, and/or B. multiflora. A tetraploid dioecious endemic on Corsica and Sardinia probably originated from B. dioica via autopolyploidy. While the cp phylogeny resolves few species relationships, the nr tree implies at least two evolutionary changes in sexual system. There is no correlation between sexual system and ploidy level. Molecular clocks suggest that the deepest divergence, between a species on the Canary Islands and the ancestor of all remaining species, occurred ca. 10 million years ago

Comment on "Indispensable Finite Time Correlations for Fokker-Planck Equations from Time Series Data"

Comment on "Indispensable Finite Time Correlations for Fokker-Planck Equations from Time Series Data"Comment: 2 pages, 1 figur

Linear flavour violation and anomalies in B physics

We propose renormalizable models of new physics that can explain various anomalies observed in decays of B-mesons to electron and muon pairs. The new physics states couple to linear combinations of Standard Model fermions, yielding a pattern of flavour violation that gives a consistent fit to the gamut of flavour data. Accidental symmetries prevent contributions to baryon- and lepton-number-violating processes, as well as enforcing a loop suppression of new physics contributions to flavour violating processes. Data require that the new flavour-breaking couplings are largely aligned with the Yukawa couplings of the SM and so we also explore patterns of flavour symmetry breaking giving rise to this structure.Comment: v2: 28 pages, 10 figures. Added two appendices to make the SU(2) structure of the model clearer, and to discuss Z/photon penguin contributions. Updated a bound on Bs mixing, and added references. Conclusions unchanged. Version to appear in JHE

Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way post-processing

We derive a bound for the security of QKD with finite resources under one-way post-processing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols like Bennett-Brassard 1984 and six-states. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N\sim 10^5 signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained using the exponential de Finetti theorem, but the additional overhead leads to very pessimistic estimates

One-shot lossy quantum data compression

We provide a framework for one-shot quantum rate distortion coding, in which the goal is to determine the minimum number of qubits required to compress quantum information as a function of the probability that the distortion incurred upon decompression exceeds some specified level. We obtain a one-shot characterization of the minimum qubit compression size for an entanglement-assisted quantum rate-distortion code in terms of the smooth max-information, a quantity previously employed in the one-shot quantum reverse Shannon theorem. Next, we show how this characterization converges to the known expression for the entanglement-assisted quantum rate distortion function for asymptotically many copies of a memoryless quantum information source. Finally, we give a tight, finite blocklength characterization for the entanglement-assisted minimum qubit compression size of a memoryless isotropic qubit source subject to an average symbol-wise distortion constraint.Comment: 36 page