Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry

Single-qubit channels are studied under two broad classes: amplitude damping channels and generalized depolarizing channels. A canonical derivation of the Kraus representation of the former, via the Choi isomorphism is presented for the general case of a system's interaction with a squeezed thermal bath. This isomorphism is also used to characterize the difference in the geometry and rank of these channel classes. Under the isomorphism, the degree of decoherence is quantified according to the mixedness or separability of the Choi matrix. Whereas the latter channels form a 3-simplex, the former channels do not form a convex set as seen from an ab initio perspective. Further, where the rank of generalized depolarizing channels can be any positive integer upto 4, that of amplitude damping ones is either 2 or 4. Various channel performance parameters are used to bring out the different influences of temperature and squeezing in dissipative channels. In particular, a noise range is identified where the distinguishability of states improves inspite of increasing decoherence due to environmental squeezing.Comment: 12 pages, 4 figure

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This chapter describes lasers and other sources of coherent light that operate in a wide wavelength range. First, the general principles for the generation of coherent continuous-wave and pulsed radiation are treated including the interaction of radiation with matter, the properties of optical resonators and their modes as well as such processes as Q-switching and mode-locking. The general introduction is followed by sections on numerous types of lasers, the emphasis being on todayʼs most important sources of coherent light, in particular on solid-state lasers and several types of gas lasers. An important part of the chapter is devoted to the generation of coherent radiation by nonlinear processes with optical parametric oscillators, difference- and sum-frequency generation, and high-order harmonics. Radiation in the extended ultraviolet (EUV) and x-ray ranges can be generated by free electron lasers (FEL) and advanced x-ray sources. Ultrahigh light intensities up to 1021 W/cm2 open the door to studies of relativistic laser–matter interaction and laser particle acceleration. The chapter closes with a section on laser stabilization