arXiv subjects
Publications and source records attributed to Sejong Kim.
In this article we consider the extended version of a real counterpart of qubit density matrices, called the Möbius matrix, and we see that it is a normalized Lorentz boost. Using the isomorphic gyrogroup structures between the set $\PP$ of all Lorentz boosts and the Einstein gyrogroup on the open unit ball $\B$ of $\R^n$ we give an explicit formula of the fidelity for Möbius matrices in terms of Lorentz gamma factors.
In this letter, we show that for all the so-called path-symmetric states, the measurement of parity of photon number at the output of an optical interferometer achieves maximal phase sensitivity at the quantum Cramer-Rao bound. Such optimal phase sensitivity with parity is attained at a suitable bias phase, which can be determined a priori. Our scheme is applicable for local phase estimation.
We recall the Einstein velocity addition on the open unit ball $\B$ of $\R^{3}$ and its algebraic structure, called the Einstein gyrogroup. We establish an isomorphism between the Einstein gyrogroup on $\B$ and the set of all qubit density matrices representing mixed states endowed with an appropriate addition. Our main result establishes a relation between the trace metric for the qubit density matrices and the rapidity metric on the Einstein gyrogroup $\B$.
Based on electron-beam direct writing on the SiOx/Si substrates, favorable absorption sites for ferric cations (Fe3+ ions) were created on the surface oxide layer. This allowed Fe3+-assisted self-assembled arrays of single-wall carbon nanotube (SWNT) probes to be produced. Auger investigation indicated that the incident energetic electrons depleted oxygen, creating more dangling bonds around Si atoms at the surface of the SiOx layer. This resulted in a distinct difference in the friction forces from unexposed regions as measured by lateral force microscopy (LFM). Atomic force microscopy (AFM) affirmed that the irradiated domains absorbed considerably more Fe3+ ions upon immersion into pH 2.2 aqueous FeCl3 solution. This rendered a greater yield of FeO(OH)/FeOCl precipitates, primarily FeO(OH), upon subsequent washing with lightly basic dimethylformamide (DMF) solution. Such selective metalfunctionalization established the basis for the subsequent patterned forest-assembly of SWNTs as demonstrated by resonance Raman spectroscopy.