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C. Carmeli

Publications and source records attributed to C. Carmeli.

18 recordsLinked to original sources
arXiv2025

Postponing the choice: advantage of deferred measurements in quantum information processing

Simultaneously implementing two arbitrary quantum measurements on the same system is impossible. The consequence of this limitation is that selecting one measurement actively excludes other possibilities. Two incompatible choices can then be forced together only at the cost of adding enough noise to the measurements. An intriguing alternative is to postpone the choice, or part of it, until a later stage. We explore the advantages of this deferred decision-making and discover that the benefits critically depends on the assumptions about the forthcoming choice. In certain scenarios postponing the choice introduces no additional cost, while in others partial postponement can be effectively the same as full postponement.

quant-ph↗
arXiv2020

Highest weight Harish-Chandra supermodules and their geometric realizations

In this paper we discuss the highest weight $\frak k_r$-finite representations of the pair $(\frak g_r,\frak k_r)$ consisting of $\frak g_r$, a real form of a complex basic Lie superalgebra of classical type $\frak g$ (${\frak g}\neq A(n,n)$), and the maximal compact subalgebra $\frak k_r$ of $\frak g_{r,0}$, 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 $G_r/K_r$.

math.RT↗
arXiv2019

Super Bundles

In this paper we give a brief account of the main aspects of the theory of associated and principal super bundles. As an application, we review the Borel-Weil-Bott Theorem in the super setting, and some results on projective embeddings of homogeneous spaces.

math.RT↗
arXiv2018

Highest weight Harish-Chandra supermodules and their geometric realizations. I. The infinitesimal theory

In this series of papers we want to discuss the highest weight ${\frak k}_r$-finite representations of the pair $({\frak g}_r,{\frak k}_r)$ consisting of ${\frak g}_r$, a real form of a complex basic Lie superalgebra of classical type ${\frak g}$ (${\frak g}\neq A(n,n)$), and the maximal compact subalgebra ${\frak k}_r$ of ${\frak} g_{r,0}$. These representations will be concretely realized through spaces of sections of holomorphic vector bundles on the associated Hermitian superspaces. In this part we shall discuss only the infinitesimal theory of the pair $({\frak g}_r, {\frak k}_r)$. We treat the global theory in subsequent papers of the series.

math.RT↗
arXiv2016

A Comparison of the functors of points of Supermanifolds

We study the functor of points and the local functor of points (here called the Weil--Berezin functor) 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.

math.RA↗
arXiv2015

The Peter-Weyl Theorem for SU(1|1)

We study a generalization of the results \in \cite{cfk} to the case of $SU(1|1)$ interpreted as the supercircle $S^{1|2}$. We describe all of its finite dimensional complex irreducible representations, we give a reducibility result for representations not containing the trivial character, and we compute explicitly the corresponding matrix elements. In the end we give the Peter-Weyl theorem for $S^{1|2}$.

math.RT↗
arXiv2014

SUSY structures, representations and Peter-Weyl theorem for $S^{1|1}$

The real compact supergroup $S^{1|1}$ is analized from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of $({\mathbf C}^{1|1})^\times$ with reduced Lie group $S^1$, and a link with SUSY structures on ${\mathbf C}^{1|1}$ is established. We describe a large family of complex semisimple representations of $S^{1|1}$ and we show that any $S^{1|1}$-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we give a proof of the Peter-Weyl theorem for $S^{1|1}$.

math.RT↗
arXiv2012

Super Distributions, Analytic and Algebraic Super Harish-Chandra pairs

The purpose of this paper is to extend the theory of Super Harish-Chandra pairs, originally developed by Koszul for Lie supergroups, to analytic and algebraic supergroups, in order to obtain information also about their representations. We also define the distribution superalgebra for algebraic and analytic supergroups and study its relation with the universal enveloping superalgebra

math.RA↗
arXiv2009

The local functors of points of Supermanifolds

We study the local functor of points (which we call the Weil-Berezin functor) for smooth supermanifolds, providing a characterization, representability theorems and applications to differential calculus.

math.RA↗
arXiv2009

Covalently Binding the Photosystem I to Carbon Nanotubes

We present a chemical route to covalently couple the photosystem I (PS I) to carbon nanotubes (CNTs). Small linker molecules are used to connect the PS I to the CNTs. Hybrid systems, consisting of CNTs and the PS I, promise new photo-induced transport phenomena due to the outstanding optoelectronic properties of the robust cyanobacteria membrane protein PS I.

cond-mat.mtrl-sci↗
arXiv2008

Vector valued reproducing kernel Hilbert spaces and universality

This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular we characterize the structure of translation invariant kernels on abelian groups and we relate it to the universality problem.

math.FA↗
arXiv2008

Quotients in supergeometry

The 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.

math.RA↗
arXiv2006

Intrinsic unsharpness and approximate repeatability of quantum measurements

The intrinsic unsharpness of a quantum observable is studied by introducing the notion of resolution width. This quantification of accuracy is shown to be closely connected with the possibility of making approximately repeatable measurements. As a case study, the intrinsic unsharpness and approximate repeatability of position and momentum measurements are examined in detail.

quant-ph↗
arXiv2005

Unitary representations of super Lie groups and applications to the classification and multiplet structure of super particles

It is well known that the category of super Lie groups (SLG) is equivalent to the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we define the category of unitary representations (UR's) of a super Lie group. We give an extension of the classical inducing construction and Mackey imprimitivity theorem to this setting. We use our results to classify the irreducible unitary representations of semidirect products of super translation groups by classical Lie groups, in particular of the super Poincaré groups in arbitrary dimension. Finally we compare our results with those in the physical literature on the structure and classification of super multiplets.

hep-th↗