Noise robustness in the detection of non separable random unitary maps

We briefly review a recently proposed method to detect properties of quantum noise processes and quantum channels. We illustrate in detail the method for detecting non separable random unitary channels and consider in particular the explicit examples of the CNOT and CZ gates. We analyse their robustness in the presence of noise for several quantum noise models.Comment: 10 pages, 1 figur

Lectures on Duflo isomorphisms in Lie algebra and complex geometry

International audienceDuflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Later on, Duflo’s result was refound by Kontsevich in the framework of deformation quantization, who also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. The present book, which arose from a series of lectures by the first author at ETH, derives these two isomorphisms from a Duflo-type result for Q-manifolds.All notions mentioned above are introduced and explained in the book, the only prerequisites being basic linear algebra and differential geometry. In addition to standard notions such as Lie (super)algebras, complex manifolds, Hochschild and Chevalley–Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in details.The book is well-suited for graduate students in mathematics and mathematical physics as well as for researchers working in Lie theory, algebraic geometry and deformation theory

3C 345: the historical light curve (1967-1990) from the digitized plates of the Asiago Observatory

In the frame of a large project to digitize the plate archives of the Italian and Vatican Astronomical Observatories, we have already performed the digitization of all available plates of the field of the quasar 3C345. The plates, approximately 100, were taken with the three telescopes of the Asiago Observatory (122 cm, 182 cm, 67/90 cm Schmidt Telescope) in the period from 1967 to 1990. We present here essentially new data, mostly in the B band, about the variability of 3C 345 and also of other four objects (3 quasars and the active galaxy NGC 6212) in the same field, in that period. Beyond the well known 3C 345 itself, also the other three quasars show variability, with a range of 2.0 mag for Q1 and Q2, 1 mag for Q3. The low level variability detected for the nucleus of NGC 6212 is more suspicious, and should be confirmed by linear detector data.Comment: 8 pages, 9 figures, 7 tables, submitted to MNRA