Renormalization algorithm with graph enhancement

We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underly the density-matrix renormalization group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) may be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This new variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement (RAGE) and present numerical examples demonstrating that improvements over density-matrix renormalization group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.Comment: 4 pages, 1 figur

Quantum communication cost of preparing multipartite entanglement

We study the preparation and distribution of high-fidelity multi-party entangled states via noisy channels and operations. In the particular case of GHZ and cluster states, we study different strategies using bipartite or multipartite purification protocols. The most efficient strategy depends on the target fidelity one wishes to achieve and on the quality of transmission channel and local operations. We show the existence of a crossing point beyond which the strategy making use of the purification of the state as a whole is more efficient than a strategy in which pairs are purified before they are connected to the final state. We also study the efficiency of intermediate strategies, including sequences of purification and connection. We show that a multipartite strategy is to be used if one wishes to achieve high fidelity, whereas a bipartite strategy gives a better yield for low target fidelity.Comment: 21 pages, 17 figures; accepted for publication in Phys. Rev. A; v2: corrections in figure

Carotid artery stiffness in metabolic syndrome: Sex differences

Introduction: The effect of metabolic syndrome (MS) on carotid stiffness (CS) in the context of gender is under research. Objective: We examined the relationship between the MS and CS in men (M) and women (W) and investigated if the impact of cardiovascular risk factors on CS is modulated by gender. Patients and Methods: The study included 419 subjects (mean age 54.3 years): 215 (51%) with MS (109 W and 106 M) and 204 (49%) without MS (98 W and 106 M). Carotid intima-media thickness (IMT) and CS parameters (beta stiffness index (beta), Peterson’s elastic modulus (Ep), arterial compliance (AC) and one-point pulse wave velocity (PWV-beta)) were measured with the echo-tracking (eT) system. Results: ANCOVA demonstrated that MS was associated with elevated CS indices (p = 0.003 for beta and 0.025 for PWV-beta), although further sex-specific analysis revealed that this relationship was significant only in W (p = 0.021 for beta). Age was associated with CS in both M and W, pulse pressure (PP) and body mass index turned out to be determinants of CS solely in W, while the effect of mean arterial pressure (MAP) and heart rate was more pronounced in M. MANOVA performed in subjects with MS revealed that age and diabetes mellitus type 2 were determinants of CS in both sexes, diastolic blood pressure and MAP – solely in M and systolic blood pressure, PP and waist circumference – solely in W (the relationship between the waist circumference and AC was paradoxical). Conclusion: The relationship between MS and CS is stronger in W than in M. In subjects with MS, various components of arterial pressure exert different sex-specific effects on CS – with the impact of the pulsative component of arterial pressure (PP) observed in W and the impact of the steady component (MAP) observed in M

Optimal purification of thermal graph states

In this paper, a purification protocol is presented and its performance is proven to be optimal when applied to a particular subset of graph states that are subject to local Z-noise. Such mixed states can be produced by bringing a system into thermal equilibrium, when it is described by a Hamiltonian which has a particular graph state as its unique ground state. From this protocol, we derive the exact value of the critical temperature above which purification is impossible, as well as the related optimal purification rates. A possible simulation of graph Hamiltonians is proposed, which requires only bipartite interactions and local magnetic fields, enabling the tuning of the system temperature.Comment: 5 pages, 4 figures v2: published versio

Entanglement entropy of two disjoint intervals in c=1 theories

We study the scaling of the Renyi entanglement entropy of two disjoint blocks of critical lattice models described by conformal field theories with central charge c=1. We provide the analytic conformal field theory result for the second order Renyi entropy for a free boson compactified on an orbifold describing the scaling limit of the Ashkin-Teller (AT) model on the self-dual line. We have checked this prediction in cluster Monte Carlo simulations of the classical two dimensional AT model. We have also performed extensive numerical simulations of the anisotropic Heisenberg quantum spin-chain with tree-tensor network techniques that allowed to obtain the reduced density matrices of disjoint blocks of the spin-chain and to check the correctness of the predictions for Renyi and entanglement entropies from conformal field theory. In order to match these predictions, we have extrapolated the numerical results by properly taking into account the corrections induced by the finite length of the blocks to the leading scaling behavior.Comment: 37 pages, 23 figure

Urinary C-Peptide of Insulin as a Non-Invasive Marker of Nutritional Status: Some Practicalities

Nutritional status is a critical element of many aspects of animal ecology, but has proven difficult to measure non-invasively in studies of free-ranging animals. Urinary C-peptide of insulin (UCP), a small polypeptide cleaved in an equimolar ratio from proinsulin when the body converts it to insulin, offers great promise in this regard, and recent studies of several non-human primate species have utilized it with encouraging results. Despite this, there are a number of unresolved issues related to the collection, processing, storage and transport of samples. These include: contamination of samples on collection (most commonly by dirt or faeces), short-term storage before returning to a field station, differences in processing and long-term storage methods (blotting onto filter paper, freezing, lyophilizing), and for frozen samples, transportation while keeping samples frozen. Such issues have been investigated for urine samples in particular with respect to their effects on steroid hormone metabolites, but there has been little investigation of their effects on UCP measurement. We collected samples from captive macaques, and undertook a series of experiments where we systematically manipulated samples and tested the effects on subsequent UCP measurements. We show that contamination of urine samples by faeces led to a decrease in UCP levels by >90%, but that contamination with dirt did not have substantial effects. Short-term storage (up to 12 hours) of samples on ice did not affect UCP levels significantly, but medium-term storage (up to 78 hours) did. Freezing and lyophilization for long-term storage did not affect UCP levels, but blotting onto filter paper did. A transportation simulation showed that transporting frozen samples packed in ice and insulated should be acceptable, but only if it can be completed within a period of a few days and if freeze-thaw can be avoided. We use our data to make practical recommendations for fieldworkers

Concatenated tensor network states

We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise entanglement and long-ranged correlations. We illustrate the approach for the enhancement of matrix product states, i.e. 1D tensor networks, where we replace each of the matrices of the original matrix product state with another 1D tensor network. This procedure yields a 2D tensor network, which includes -- already for tensor dimension two -- all states that can be prepared by circuits of polynomially many (possibly non-unitary) two-qubit quantum operations, as well as states resulting from time evolution with respect to Hamiltonians with short-ranged interactions. We investigate the possibility to efficiently extract information from these states, which serves as the basic step in a variational optimization procedure. To this aim we utilize known exact and approximate methods for 2D tensor networks and demonstrate some improvements thereof, which are also applicable e.g. in the context of 2D projected entangled pair states. We generalize the approach to higher dimensional- and tree tensor networks.Comment: 16 pages, 4 figure