Parts and Composites of Quantum Systems

We consider three types of entities for quantum measurements. In order of generality, these types are observables, instruments and measurement models. If α and β are entities, we define what it means for α to be a part of β. This relationship is essentially equivalent to α being a function of β and in this case β can be employed to measure α. We then use the concept to define the coexistence of entities and study its properties. A crucial role is played by a map α^ which takes an entity of a certain type to one of a lower type. For example, if I is an instrument, then I^ is the unique observable measured by I. Composite systems are discussed next. These are constructed by taking the tensor product of the Hilbert spaces of the systems being combined. Composites of the three types of measurements and their parts are studied. Reductions in types to their local components are discussed. We also consider sequential products of measurements. Specific examples of Lüders, Kraus and trivial instruments are used to illustrate various concepts. We only consider finite-dimensional systems in this article. Finally, we mention the role of symmetry representations for groups using quantum channels.

Melamine Deaminase and Atrazine Chlorohydrolase: 98 Percent Identical but Functionally Different

ABSTRACT The gene encoding melamine deaminase (TriA) fromPseudomonas sp. strain NRRL B-12227 was identified, cloned into Escherichia coli, sequenced, and expressed for in vitro study of enzyme activity. Melamine deaminase displaced two of the three amino groups from melamine, producing ammeline and ammelide as sequential products. The first deamination reaction occurred more than 10 times faster than the second. Ammelide did not inhibit the first or second deamination reaction, suggesting that the lower rate of ammeline hydrolysis was due to differential substrate turnover rather than product inhibition. Remarkably, melamine deaminase is 98% identical to the enzyme atrazine chlorohydrolase (AtzA) fromPseudomonas sp. strain ADP. Each enzyme consists of 475 amino acids and differs by only 9 amino acids. AtzA was shown to exclusively catalyze dehalogenation of halo-substituted triazine ring compounds and had no activity with melamine and ammeline. Similarly, melamine deaminase had no detectable activity with the halo-triazine substrates. Melamine deaminase was active in deamination of a substrate that was structurally identical to atrazine, except for the substitution of an amino group for the chlorine atom. Moreover, melamine deaminase and AtzA are found in bacteria that grow on melamine and atrazine compounds, respectively. These data strongly suggest that the 9 amino acid differences between melamine deaminase and AtzA represent a short evolutionary pathway connecting enzymes catalyzing physiologically relevant deamination and dehalogenation reactions, respectively.