Robustness of quantum Markov chains

If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum relative entropy) of the distribution to the nearest Markov chain distribution is precisely the conditional information. We prove here that this simple situation does not obtain for quantum conditional information. We show that for tri-partite quantum states the quantum conditional information is always a lower bound for the minimum relative entropy distance to a quantum Markov chain state, but the distance can be much greater; indeed the two quantities can be of different asymptotic order and may even differ by a dimensional factor.Comment: 14 pages, no figures; not for the feeble-minde

Quantum state merging and negative information

We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is the conditional entropy if classical communication is free. Since this quantity can be negative, and the state merging rate measures partial quantum information, we find that quantum information can be negative. The classical communication rate also has a minimum rate: a certain quantum mutual information. State merging enabled one to solve a number of open problems: distributed quantum data compression, quantum coding with side information at the decoder and sender, multi-party entanglement of assistance, and the capacity of the quantum multiple access channel. It also provides an operational proof of strong subadditivity. Here, we give precise definitions and prove these results rigorously.Comment: 23 pages, 3 figure

Inhomogeneously doped two-leg ladder systems

A chemical potential difference between the legs of a two-leg ladder is found to be harmful for Cooper pairing. The instability of superconductivity in such systems is analyzed by compairing results of various analytical and numerical methods. Within a strong coupling approach for the t-J model, supplemented by exact numerical diagonalization, hole binding is found unstable beyond a finite, critical chemical potential difference. The spinon-holon mean field theory for the t-J model shows a clear reduction of the the BCS gaps upon increasing the chemical potential difference leading to a breakdown of superconductivity. Based on a renormalization group approach and Abelian bosonization, the doping dependent phase diagram for the weakly interacting Hubbard model with different chemical potentials was determined.Comment: Revtex4, 11 pages, 7 figure

All Inequalities for the Relative Entropy

The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party to a smaller number $m$ of parties is always less than or equal to the relative entropy of the two original n-party states. This is the monotonicity of relative entropy. Using techniques from convex geometry, we prove that monotonicity under restrictions is the only general inequality satisfied by relative entropies. In doing so we make a connection to secret sharing schemes with general access structures. A suprising outcome is that the structure of allowed relative entropy values of subsets of multiparty states is much simpler than the structure of allowed entropy values. And the structure of allowed relative entropy values (unlike that of entropies) is the same for classical probability distributions and quantum states.Comment: 15 pages, 3 embedded eps figure

The Coupled Cluster Method in Hamiltonian Lattice Field Theory: SU(2) Glueballs

The glueball spectrum within the Hamiltonian formulation of lattice gauge theory (without fermions) is calculated for the gauge group SU(2) and for two spatial dimensions. The Hilbert space of gauge-invariant functions of the gauge field is generated by its parallel-transporters on closed paths along the links of the spatial lattice. The coupled cluster method is used to determine the spectrum of the Kogut-Susskind Hamiltonian in a truncated basis. The quality of the description is studied by computing results from various truncations, lattice regularisations and with an improved Hamiltonian. We find consistency for the mass ratio predictions within a scaling region where we obtain good agreement with standard lattice Monte Carlo results.Comment: 13 pages, 7 figure

Structure-function analysis reveals that the Pseudomonas aeruginosa Tps4 two-partner secretion system is involved in CupB5 translocation

Pseudomonas aeruginosa is a Gram-negative opportunistic bacterium, synonymous with cystic fibrosis patients, which can cause chronic infection of the lungs. This pathogen is a model organism to study biofilms: a bacterial population embedded in an extracellular matrix that provide protection from environmental pressures and lead to persistence. A number of Chaperone-Usher Pathways, namely CupA-CupE, play key roles in these processes by assembling adhesive pili on the bacterial surface. One of these, encoded by the cupB operon, is unique as it contains a nonchaperone-usher gene product, CupB5. Two-partner secretion (TPS) systems are comprised of a C-terminal integral membrane β-barrel pore with tandem N-terminal POTRA (POlypeptide TRansport Associated) domains located in the periplasm (TpsB) and a secreted substrate (TpsA). Using NMR we show that TpsB4 (LepB) interacts with CupB5 and its predicted cognate partner TpsA4 (LepA), an extracellular protease. Moreover, using cellular studies we confirm that TpsB4 can translocate CupB5 across the P. aeruginosa outer membrane, which contrasts a previous observation that suggested the CupB3 P-usher secretes CupB5. In support of our findings we also demonstrate that tps4/cupB operons are coregulated by the RocS1 sensor suggesting P. aeruginosa has developed synergy between these systems. Furthermore, we have determined the solution-structure of the TpsB4-POTRA1 domain and together with restraints from NMR chemical shift mapping and in vivo mutational analysis we have calculated models for the entire TpsB4 periplasmic region in complex with both TpsA4 and CupB5 secretion motifs. The data highlight specific residues for TpsA4/CupB5 recognition by TpsB4 in the periplasm and suggest distinct roles for each POTRA domain

Phase Diagram of the quadrumerized Shastry-Sutherland Model

We determine the phase diagram of a generalized Shastry-Sutherland model, using a combination of dimer- and quadrumer-boson methods and numerical exact diagonalization techniques. Along special lines in the parameter space the model reduces to the standard Shastry-Sutherland model, the 1/5-th depleted square lattice and the two-dimensional plaquette square lattice model. We study the evolution of the ordered phases found in the latter two unfrustrated models under the effect of frustration. Furthermore we present new exact diagonalization results for the Shastry-Sutherland model on clusters with up to 32 sites, supporting the existence of an intermediate gapped valence bond crystal phase with plaquette long-ranged order.Comment: Replaced with final version, added journal-re

Dynamics of Entanglement in One-Dimensional Spin Systems

We study the dynamics of quantum correlations in a class of exactly solvable Ising-type models. We analyze in particular the time evolution of initial Bell states created in a fully polarized background and on the ground state. We find that the pairwise entanglement propagates with a velocity proportional to the reduced interaction for all the four Bell states. Singlet-like states are favored during the propagation, in the sense that triplet-like states change their character during the propagation under certain circumstances. Characteristic for the anisotropic models is the instantaneous creation of pairwise entanglement from a fully polarized state; furthermore, the propagation of pairwise entanglement is suppressed in favor of a creation of different types of entanglement. The ``entanglement wave'' evolving from a Bell state on the ground state turns out to be very localized in space-time. Further support to a recently formulated conjecture on entanglement sharing is given.Comment: 25 pages, 21 figures; revte

Thinning leads to calving-style changes at Bowdoin Glacier, Greenland

This research has been supported by the Alfred and Flora Spälti Fund and the ETH Zurich Foundation (Sun2ice; grant no. ETH-12 16-2); the Swiss National Science Foundation (grant nos. 200021-153179/1 and PP00P2_183719); the SPI Exploratory Grants 2018 awarded to Fabian Walter and Guillaume Jouvet; the Japanese Ministry of Education, Culture, Sports, Science and Technology through the GRENE Arctic Climate Research Project and the Arctic Challenge for Sustainability (ArCS) project; and by NERC (CALISMO: Calving Laws for Ice Sheet Models; grant no. NE/P011365/1).Ice mass loss from the Greenland ice sheet is the largest single contributor to sea level rise in the 21st century. The mass loss rate has accelerated in recent decades mainly due to thinning and retreat of its outlet glaciers. The diverse calving mechanisms responsible for tidewater glacier retreat are not fully understood yet. Since a tidewater glacier's sensitivity to external forcings depends on its calving style, detailed insight into calving processes is necessary to improve projections of ice sheet mass loss by calving. As tidewater glaciers are mostly thinning, their calving styles are expected to change. Here, we study calving behaviour changes under a thinning regime at Bowdoin Glacier, north-western Greenland, by combining field and remote-sensing data from 2015 to 2019. Previous studies showed that major calving events in 2015 and 2017 were driven by hydro-fracturing and melt-undercutting. New observations from uncrewed aerial vehicle (UAV) imagery and a GPS network installed at the calving front in 2019 suggest ungrounding and buoyant calving have recently occurred as they show (1) increasing tidal modulation of vertical motion compared to previous years, (2) absence of a surface crevasse prior to calving, and (3) uplift and horizontal surface compression prior to calving. Furthermore, an inventory of calving events from 2015 to 2019 based on satellite imagery provides additional support for a change towards buoyant calving since it shows an increasing occurrence of calving events outside of the melt season. The observed change in calving style could lead to a possible retreat of the terminus, which has been stable since 2013. We therefore highlight the need for high-resolution monitoring to detect changing calving styles and numerical models that cover the full spectrum of calving mechanisms to improve projections of ice sheet mass loss by calving.Publisher PDFPeer reviewe