The Jamio{\l}kowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt number kk and kk-positive maps

Positive maps which are not completely positive are used in quantum information theory as witnesses for convex sets of states, in particular as entanglement witnesses and more generally as witnesses for states having Schmidt number not greater than k. It is known that such witnesses are related to k-positive maps. In this article we propose a new proof for the correspondence between vectors having Schmidt number k and k-positive maps using Jamiolkowski's criterion for positivity of linear maps; to this aim, we also investigate the precise notion of the term "Jamiolkowski isomorphism". As consequences of our proof we get the Jamiolkowski criterion for complete positivity, and we find a special case of a result by Choi, namely that k-positivity implies complete positivity, if k is the dimension of the smaller one of the Hilbert spaces on which the operators act.Comment: 9 page

Liquid phase hydrogenation of crotonaldehyde over Pt/SiO2 catalysts

The dependence of the catalytic properties of Pt/SiO2 catalysts for the hydrogenation of crotonaldehyde on the hydrogen pressure, the reaction temperature, the nature of the solvent and the presence of several additives were investigated. Strong deactivation of the catalysts mainly caused by decarbonylation of crotonaldehyde and irreversible adsorption of CO was observed. The initial activity of the deactivated catalysts is regained by oxidation of the adsorbed CO to CO2 by purging with air. The selectivity to crotylalcohol increased with increasing number of turnovers per metal site. This is explained with preferential blocking of the nonselective sites on the metal crystallites by CO and by a slow surface modification of the aging catalyst with organic deposits. The overall rate and the selectivity to the saturated aldehyde are markedly enhanced by an increase in hydrogen pressure and by a decrease in reaction temperature. The addition of modifiers such as potassium acetate, triphenylphosphine and thiophene had only little influence on the activity and the selectivity of the catalysts

Complete sets of cyclic mutually unbiased bases in even prime power dimensions

We present a construction method for complete sets of cyclic mutually unbiased bases (MUBs) in Hilbert spaces of even prime power dimensions. In comparison to usual complete sets of MUBs, complete cyclic sets possess the additional property of being generated by a single unitary operator. The construction method is based on the idea of obtaining a partition of multi-qubit Pauli operators into maximal commuting sets of orthogonal operators with the help of a suitable element of the Clifford group. As a consequence, we explicitly obtain complete sets of cyclic MUBs generated by a single element of the Clifford group in dimensions $2^m$ for $m=1,2,...,24$.Comment: 10 page

Asymptotic correctability of Bell-diagonal qudit states and lower bounds on tolerable error probabilities in quantum cryptography

The concept of asymptotic correctability of Bell-diagonal quantum states is generalised to elementary quantum systems of higher dimensions. Based on these results basic properties of quantum state purification protocols are investigated which are capable of purifying tensor products of Bell-diagonal states and which are based on $B$-steps of the Gottesman-Lo-type with the subsequent application of a Calderbank-Shor-Steane quantum code. Consequences for maximum tolerable error rates of quantum cryptographic protocols are discussed

Error tolerance of two-basis quantum key-distribution protocols using qudits and two-way classical communication

We investigate the error tolerance of quantum cryptographic protocols using $d$-level systems. In particular, we focus on prepare-and-measure schemes that use two mutually unbiased bases and a key-distillation procedure with two-way classical communication. For arbitrary quantum channels, we obtain a sufficient condition for secret-key distillation which, in the case of isotropic quantum channels, yields an analytic expression for the maximally tolerable error rate of the cryptographic protocols under consideration. The difference between the tolerable error rate and its theoretical upper bound tends slowly to zero for sufficiently large dimensions of the information carriers.Comment: 10 pages, 1 figur

Comparison of 16S rRNA gene sequences of genus Methanobrevibacter

BACKGROUND: The phylogeny of the genus Methanobrevibacter was established almost 25 years ago on the basis of the similarities of the 16S rRNA oligonucleotide catalogs. Since then, many 16S rRNA gene sequences of newly isolated strains or clones representing the genus Methanobrevibacter have been deposited. We tried to reorganize the 16S rRNA gene sequences of this genus and revise the taxonomic affiliation of the isolates and clones representing the genus Methanobrevibacter. RESULTS: The phylogenetic analysis of the genus based on 786 bp aligned region from fifty-four representative sequences of the 120 available sequences for the genus revealed seven multi-member groups namely, Ruminantium, Smithii, Woesei, Curvatus, Arboriphilicus, Filiformis, and the Termite gut symbionts along with three separate lineages represented by Mbr. wolinii, Mbr. acididurans, and termite gut flagellate symbiont LHD12. The cophenetic correlation coefficient, a test for the ultrametric properties of the 16S rRNA gene sequences used for the tree was found to be 0.913 indicating the high degree of goodness of fit of the tree topology. A significant relationship was found between the 16S rRNA sequence similarity (S) and the extent of DNA hybridization (D) for the genus with the correlation coefficient (r) for logD and logS, and for [ln(-lnD) and ln(-lnS)] being 0.73 and 0.796 respectively. Our analysis revealed that for this genus, when S = 0.984, D would be <70% at least 99% of the times, and with 70% D as the species "cutoff", any 16S rRNA gene sequence showing <98% sequence similarity can be considered as a separate species. In addition, we deduced group specific signature positions that have remained conserved in evolution of the genus. CONCLUSIONS: A very significant relationship between D and S was found to exist for the genus Methanobrevibacter, implying that it is possible to predict D from S with a known precision for the genus. We propose to include the termite gut flagellate symbiont LHD12, the methanogenic endosymbionts of the ciliate Nyctotherus ovalis, and rat feces isolate RT reported earlier, as separate species of the genus Methanobrevibacter

Semi-Insulating Polysilicon Hetero- and Isotype Junctions on Silicon

The effects of nitrogen trifluorideinthe gas stream during deposition of semi-insulating polysilicon (SIPOS) on the electrical characteristics of undoped (SIPSO)/p-Si, and n+-SIPOS/n-Si isotype junctions were investigated. The current-voltage characteristics of undoped SIPOS/p-Si heterojunctions exhibit a strong dependence on the oxygen content of the SIPOS film and depart from a hyperbolic sine behavior as the refractive index of the SIPOS increases.. The addition of nitrogen trifluoride decreases the current density of these undoped SIPOS/p-Si heterojunctions due presumably to the oxidation/hydrolysis of SiF species intoSiO2. The n+-SIPOS formed a rectifying isotype junction o n-Si. The forward current voltage characteristics exhibit two distinct activation energies separated by a kink in the forward semi-logarithmic characteristics; one below the cut-in voltage and one above the cut-in voltage. The two activation energies result from the presence of interface states in the structures. However, the forward current-voltage characteristics of the fluorinated SIPOS isotype junctions exhibit no kink and only a single activation energy due, presumably, to hydrogen passivating the interfacial traps during the hydrolysis process

Multiple Modes of Phase Locking between Sniffing and Whisking during Active Exploration

Sense organs are often actively controlled by motor processes and such active sensing profoundly shapes the timing of sensory information flow. The temporal coordination between different active sensing processes is less well understood but is essential for multisensory integration, coordination between brain regions, and energetically optimal sampling strategies. Here we studied the coordination between sniffing and whisking, the motor processes in rodents that control the acquisition of smell and touch information, respectively. Sniffing, high-frequency respiratory bouts, and whisking, rapid back and forth movements of mystacial whiskers, occur in the same theta frequency range (4-12 Hz) leading to a hypothesis that these sensorimotor rhythms are phase locked. To test this, we monitored sniffing using a thermocouple in the nasal cavity and whisking with an electromyogram of the mystacial pad in rats engaged in an open field reward foraging behavior. During bouts of exploration, sniffing and whisking showed strong one-to-one phase locking within the theta frequency range (4-12 Hz). Interestingly, we also observed multimode phase locking with multiple whisks within a sniff cycle or multiple sniffs within a whisk cycle-always at the same preferred phase. This specific phase relationship coupled the acquisition phases of the two sensorimotor rhythms, inhalation and whisker protraction. Our results suggest that sniffing and whisking may be under the control of interdependent rhythm generators that dynamically coordinate active acquisition of olfactory and somatosensory information

Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture

We relate the construction of a complete set of cyclic mutually unbiased bases, i. e., mutually unbiased bases generated by a single unitary operator, in power-of-two dimensions to the problem of finding a symmetric matrix over F_2 with an irreducible characteristic polynomial that has a given Fibonacci index. For dimensions of the form 2^(2^k) we present a solution that shows an analogy to an open conjecture of Wiedemann in finite field theory. Finally, we discuss the equivalence of mutually unbiased bases.Comment: 11 pages, added chapter on equivalenc