Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination

We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is unambiguous, i. e. error-free, discrimination with a minimum probability of getting an inconclusive outcome, where the measurement fails to give a definite answer. For distinguishing between two mixed quantum states, we investigate the relation between the minimum error probability achievable in conclusive discrimination, and the minimum failure probability that can be reached in unambiguous discrimination of the same two states. The latter turns out to be at least twice as large as the former for any two given states. As an example, we treat the case that the state of the quantum system is known to be, with arbitrary prior probability, either a given pure state, or a uniform statistical mixture of any number of mutually orthogonal states. For this case we derive an analytical result for the minimum probability of error and perform a quantitative comparison to the minimum failure probability.Comment: Replaced by final version, accepted for publication in Phys. Rev. A. Revtex4, 6 pages, 3 figure

Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

Minimum-error discrimination between subsets of linearly dependent quantum states

A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal quantum states occurring with given a priori probabilities. A general analytical solution is obtained for N states that are restricted to a two-dimensional subspace of the Hilbert space of the system. The result for the special case of three arbitrary but linearly dependent states is applied to a variety of sets of three states that are symmetric and equally probable. It is found that, in this case, the minimum error probability for distinguishing one of the states from the other two is only about half as large as the minimum error probability for distinguishing all three states individually.Comment: Representation improved and generalized, references added. Accepted as a Rapid Communication in Phys. Rev.

Following Strain-Induced Mosaicity Changes of Ferroelectric Thin Films by Ultrafast Reciprocal Space Mapping

We investigate coherent phonon propagation in a thin film of ferroelectric PbZr0.2Ti0.8O3 (PZT) by ultrafast x-ray diffraction (UXRD) experiments, which are analyzed as time-resolved reciprocal space mapping (RSM) in order to observe the in- and out-of-plane structural dynamics simultaneously. The mosaic structure of the PZT leads to a coupling of the excited out-of-plane expansion to in-plane lattice dynamics on a picosecond timescale, which is not observed for out-of-plane compression.Comment: 5 pages, 4 figure

Spinning Dragging Strings

We use the AdS/CFT correspondence to compute the drag force experienced by a heavy quark moving through a maximally supersymmetric SU(N) super Yang-Mills plasma at nonzero temperature and R-charge chemical potential and at large 't Hooft coupling. We resolve a discrepancy in the literature between two earlier studies of such quarks. In addition, we consider small fluctuations of the spinning strings dual to these probe quarks and find no evidence of instabilities. We make some comments about suitable D7-brane boundary conditions for the dual strings.Comment: 25 pages, 4 figures; v2 refs added; v3 to appear in JHEP, clarifying comment

Development and fabrication of bismaleimide-graphite composites

The successful fabrication of high temperature resistant composites depends mainly on the processability of the resin binder matrix. For two new bismaleimide type resins the processing of graphite fabric prepregs to composites is described. One resin coded M 751 has to be processed from N-Methylpyrrolidone, the other resin evaluated is a so-called hot melt solvent-less system. Commercial T300/3000 Graphite fabrics were used as reinforcement. The M 751 - Resin is a press grade material and laminates are therefore moulded in high pressure conditions (400 N/sq cm). The solvent-less resin system H 795 is an autoclave grade material and can be cured at 40 N/sq cm. The cure cycles for both the press grade and the autoclave grade material (Fiberite W 143 fabric prepregs) are provided and the mechanical properties of laminates at low (23 C) and high (232 C) temperatures were measured. For comparison, the neat resin flexural properties are also presented. The water absorption for the neat resins and the graphite fabric laminates after a 1000 hour period was evaluated

A Holographic Prediction of the Deconfinement Temperature

We argue that deconfinement in AdS/QCD models occurs via a first order Hawking-Page type phase transition between a low temperature thermal AdS space and a high temperature black hole. Such a result is consistent with the expected temperature independence, to leading order in 1/N_c, of the meson spectrum and spatial Wilson loops below the deconfinement temperature. As a byproduct, we obtain model dependent deconfinement temperatures T_c in the hard and soft wall models of AdS/QCD. Our result for T_c in the soft wall model is close to a recent lattice prediction.Comment: 4 pages, 1 figure; v2 ref added, minor changes; v3 refs added, discussion modified, to appear in PR