Non-disturbing quantum measurements

We consider pairs of quantum observables (POVMs) and analyze the relation between the notions of non-disturbance, joint measurability and commutativity. We specify conditions under which these properties coincide or differ---depending for instance on the interplay between the number of outcomes and the Hilbert space dimension or on algebraic properties of the effect operators. We also show that (non-)disturbance is in general not a symmetric relation and that it can be decided and quantified by means of a semidefinite program.Comment: Minor corrections in v

Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons

In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model solitons to generic scalar-field solitons for an infinitely stiff potential. The static k-lump moduli space C^k/S_k features a natural K"ahler metric induced from an embedding Grassmannian. The moduli-space dynamics is blind against adding a WZW-like term to the sigma-model action and thus also applies to the integrable U(1) Ward model. For the latter's two-soliton motion we compare the exact field configurations with their supposed moduli-space approximations. Surprisingly, the two do not match, which questions the adiabatic method for noncommutative solitons.Comment: 1+15 pages, 2 figures; v2: reference added, to appear in JHE

Optimal Location of Sources in Transportation Networks

We consider the problem of optimizing the locations of source nodes in transportation networks. A reduction of the fraction of surplus nodes induces a glassy transition. In contrast to most constraint satisfaction problems involving discrete variables, our problem involves continuous variables which lead to cavity fields in the form of functions. The one-step replica symmetry breaking (1RSB) solution involves solving a stable distribution of functionals, which is in general infeasible. In this paper, we obtain small closed sets of functional cavity fields and demonstrate how functional recursions are converted to simple recursions of probabilities, which make the 1RSB solution feasible. The physical results in the replica symmetric (RS) and the 1RSB frameworks are thus derived and the stability of the RS and 1RSB solutions are examined.Comment: 38 pages, 18 figure

Total Neoadjuvant Therapy for Rectal Cancer in the CAO/ARO/AIO-12 Randomized Phase 2 Trial: Early Surrogate Endpoints Revisited

Background: Early efficacy outcome measures in rectal cancer after total neoadjuvant treatment are increasingly investigated. We examined the prognostic role of pathological complete response (pCR), tumor regression grading (TRG) and neoadjuvant rectal (NAR) score for disease-free survival (DFS) in patients with rectal carcinoma treated within the CAO/ARO/AIO-12 randomized phase 2 trial. Methods: Distribution of pCR, TRG and NAR score was analyzed using the Pearson’s chi-squared test. Univariable analyses were performed using the log-rank test, stratified by treatment arm. Discrimination ability of non-pCR for DFS was assessed by analyzing the ROC curve as a function of time. Results: Of the 311 patients enrolled, 306 patients were evaluable (Arm A:156, ArmB:150). After a median follow-up of 43 months, the 3-year DFS was 73% in both groups (HR, 0.95, 95% CI, 0.63–1.45, p = 0.82). pCR tended to be higher in Arm B (17% vs. 25%, p = 0.086). In both treatment arms, pCR, TRG and NAR were significant prognostic factors for DFS, whereas survival in subgroups defined by pCR, TRG or NAR did not significantly differ between the treatment arms. The discrimination ability of non-pCR for DFS remained constant over time (C-Index 0.58) but was slightly better in Arm B (0.61 vs. 0.56). Conclusion: Although pCR, TRG and NAR were strong prognostic factors for DFS in the CAO/ARO/AIO-12 trial, their value in selecting one TNT approach over another could not be confirmed. Hence, the conclusion of a long-term survival benefit of one treatment arm based on early surrogate endpoints should be stated with caution

Fermions and Loops on Graphs. I. Loop Calculus for Determinant

This paper is the first in the series devoted to evaluation of the partition function in statistical models on graphs with loops in terms of the Berezin/fermion integrals. The paper focuses on a representation of the determinant of a square matrix in terms of a finite series, where each term corresponds to a loop on the graph. The representation is based on a fermion version of the Loop Calculus, previously introduced by the authors for graphical models with finite alphabets. Our construction contains two levels. First, we represent the determinant in terms of an integral over anti-commuting Grassman variables, with some reparametrization/gauge freedom hidden in the formulation. Second, we show that a special choice of the gauge, called BP (Bethe-Peierls or Belief Propagation) gauge, yields the desired loop representation. The set of gauge-fixing BP conditions is equivalent to the Gaussian BP equations, discussed in the past as efficient (linear scaling) heuristics for estimating the covariance of a sparse positive matrix.Comment: 11 pages, 1 figure; misprints correcte

Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem

The set of doubly-stochastic quantum channels and its subset of mixtures of unitaries are investigated. We provide a detailed analysis of their structure together with computable criteria for the separation of the two sets. When applied to O(d)-covariant channels this leads to a complete characterization and reveals a remarkable feature: instances of channels which are not in the convex hull of unitaries can return to it when either taking finitely many copies of them or supplementing with a completely depolarizing channel. In these scenarios this implies that a channel whose noise initially resists any environment-assisted attempt of correction can become perfectly correctable.Comment: 31 page

Energy gap in superconducting fullerides: optical and tunneling studies

Tunneling and optical transmission studies have been performed on superconducting samples of Rb3C60. At temperatures much below the superconducting transition temperature Tc the energy gap is 2 Delta=5.2 +- 0.2meV, corresponding to 2 Delta/kB Tc = 4.2. The low temperature density of states, and the temperature dependence of the optical conductivity resembles the BCS behavior, although there is an enhanced ``normal state" contribution. The results indicate that this fulleride material is an s-wave superconductor, but the superconductivity cannot be described in the weak coupling limit.Comment: RevTex file with four .EPS figures. Prints to four pages. Also available at http://buckminster.physics.sunysb.edu/papers/pubrece.htm