1,721,049 research outputs found
The local functors of points of supermanifolds
No full textWe study the functor of points and the local functor of points
(here called the Weil-Berezin functor of points) for smooth
and holomorphic supermanifolds, providing characterization
theorems and fully discussing the representability issues.
In the end we examine applications to differential calculus
including the transitivity theorems
HIGHEST WEIGHT HARISH-CHANDRA SUPERMODULES AND THEIR GEOMETRIC REALIZATIONS
No full textIn this paper we discuss the highest weight kr-finite representations of the pair (r, kr) consisting of r, a real form of a complex basic Lie superalgebra of classical type ( ≠ A(n, n)), and the maximal compact subalgebra kr of r,0, together with their geometric global realizations. These representations occur, as in the ordinary setting, in the superspaces of sections of holomorphic super vector bundles on the associated Hermitian superspaces Gr/Kr
Constructing Extremal Compatible Quantum Observables by Means of Two Mutually Unbiased Bases
No full textWe describe a particular class of pairs of quantum observables which are extremal in the convex set of all pairs of compatible quantum observables. The pairs in this class are constructed as uniformly noisy versions of two mutually unbiased bases (MUB) with possibly different noise intensities affecting each basis. We show that not all pairs of MUB can be used in this construction, and we provide a criterion for determining those MUB that actually do yield extremal compatible observables. We apply our criterion to all pairs of Fourier conjugate MUB, and we prove that in this case extremality is achieved if and only if the quantum system Hilbert space is odd-dimensional. Remarkably, this fact is no longer true for general non-Fourier conjugate MUB, as we show in an example. Therefore, the presence or the absence of extremality is a concrete geometric manifestation of MUB inequivalence, that already materializes by comparing sets of no more than two bases at a time
Quotients in supergeometry
No full textThe purpose of this paper is to present the notion of
quotient of supergroups in different categories using the
unified treatment of the functor of points and to
examine some physically interesting examples
The Exponential of Nilpotent Supergroups in the Theory of Harish-Chandra Representations
Get PDFIn this paper we discuss the exponential map in the case of nilpotent superalgebras. This provides global coordinates for nilpotent analytic supergroups, which are useful in the applications
HIGHEST WEIGHT HARISH-CHANDRA SUPERMODULES AND THEIR GEOMETRIC REALIZATIONS
Get PDFIn this paper we discuss the highest weight kr-finite representations of the pair (r, kr) consisting of r, a real form of a complex basic Lie superalgebra of classical type ( ≠ A(n, n)), and the maximal compact subalgebra kr of r,0, together with their geometric global realizations. These representations occur, as in the ordinary setting, in the superspaces of sections of holomorphic super vector bundles on the associated Hermitian superspaces Gr/Kr
Quantum random access codes and incompatibility of measurements
Get PDFIt is one of the peculiar features of quantum physics that some sets of measurements are incompatible in the sense that they cannot be performed simultaneously. Incompatibility is an important quantum resource as it enables Bell nonlocality and steering. Here we show that incompatibility is crucial also in certain communication tasks; we prove that quantum random access code performs better than its classical counterpart only when incompatible quantum measurements are used in the decoding task. As a consequence, evaluating the average success probability for quantum random access code provides a semi-device-independent test for the detection of quantum incompatibility. We further demonstrate that any incompatible pair of projective measurements gives an advantage over all classical strategies. Finally, we establish a connection between the maximal average success probability for quantum random access code and earlier quantities introduced to assess incompatibility
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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