Complex conjugation supermap of unitary quantum maps and its universal implementation protocol

A complex conjugation of unitary quantum map is a second-order map (supermap) that maps a unitary operator $U$ to its complex conjugate $U^*$. First, we present a deterministic quantum protocol that universally implements the complex conjugation supermap when we are given a blackbox quantum circuit, guaranteed to implement some unitary operation, whose only known description is its dimension. We then discuss the complex conjugation supermap in the context of entanglement theory and derive a conjugation-based expression of the $G$-concurrence. Finally, we present a physical process involving identical fermions from which the complex conjugation protocol is derived as a simulation of the process using qudits.Comment: ver.5: published version, 5 pages, 2 figures, double-colum

Optimization of 5-axis milling processes using process models

Productivity and part quality are extremely important for all machining operations, but particularly for 5-axis milling where the machine tool cost is relatively higher, and most parts have complex geometries and high quality requirements with tight tolerances. 5- axis milling, presents additional challenges in modeling due to more complex tool and workpiece interface geometry, and process mechanics. In this paper, modeling and optimization of 5-axis processes with cutting strategy selection are presented. The developed process models are used for cutting force predictions using a part-tool interface identification method which is also presented. Based on the model predictions and simulations, best cutting conditions are identified. Also, for finish process of a complex surface, machining time is estimated using three machining strategy alternatives. Results are demonstrated by example applications, and verified by experiments

Support and injective resolutions of complexes over commutative rings

Examples are given to show that the support of a complex of modules over a commutative noetherian ring may not be read off the minimal semi-injective resolution of the complex. The same examples also show that a localization of a semi-injective complex need not be semi-injective.Comment: 5 pages; major revisions; to appear in Homology, Homotopy and application