An introductory review on resource theories of generalized nonclassical light

Quantum resource theory is perhaps the most revolutionary framework that quantum physics has ever experienced. It plays vigorous roles in unifying the quantification methods of a requisite quantum effect as wells as in identifying protocols that optimize its usefulness in a given application in areas ranging from quantum information to computation. Moreover, the resource theories have transmuted radical quantum phenomena like coherence, nonclassicality and entanglement from being just intriguing to being helpful in executing realistic thoughts. A general quantum resource theoretical framework relies on the method of categorization of all possible quantum states into two sets, namely, the free set and the resource set. Associated with the set of free states there is a number of free quantum operations emerging from the natural constraints attributed to the corresponding physical system. Then, the task of quantum resource theory is to discover possible aspects arising from the restricted set of operations as resources. Along with the rapid growth of various resource theories corresponding to standard harmonic oscillator quantum optical states, significant advancement has been expedited along the same direction for generalized quantum optical states. Generalized quantum optical framework strives to bring in several prosperous contemporary ideas including nonlinearity, PT -symmetric non-Hermitian theories, q-deformed bosonic systems, etc., to accomplish similar but elevated objectives of the standard quantum optics and information theories. In this article, we review the developments of nonclassical resource theories of different generalized quantum optical states and their usefulness in the context of quantum information theories.

Expansions of abelian square-free groups

We investigate finitary functions from [Formula: see text] to [Formula: see text] for a square-free number [Formula: see text]. We show that the lattice of all clones on the square-free set [Formula: see text] which contain the addition of [Formula: see text] is finite. We provide an upper bound for the cardinality of this lattice through an injective function to the direct product of the lattices of all [Formula: see text]-linearly closed clonoids, [Formula: see text], to the [Formula: see text] power, where [Formula: see text]. These lattices are studied in [S. Fioravanti, Closed sets of finitary functions between products of finite fields of pair-wise coprime order, preprint (2020), arXiv:2009.02237 ] and there we can find an upper bound for their cardinality. Furthermore, we prove that these clones can be generated by a set of functions of arity at most [Formula: see text].

An Intelligent Control Approach for Defect-Free Friction Stir Welding

An intelligent control approach is proposed as an alternative for the friction stir welding of an aluminum alloy. A validated empirical model is re-written from transfer functions to a set of ordinary differential equations, allowing to observe the force dynamics as a function of inputs of interest. A defect-free set-point is proposed for exploiting available labeled experimental data which defines operational boundaries and a region in which the probability of achieving defect-free welds with good mechanical properties is the highest. An intelligent controller in the fashion of a Recurrent Neural Network is constructed. Computational experiments were carried out to verify the adequacy in disturbance rejection as well as to visualize the capabilities in achieving the proposed defect-free set-point by the controller. The intelligent approach is compared with a set of decoupled proportional-integral controllers and a linear model predictive control strategy. From this study it is concluded that the intelligent controller shows superiority and good applicability for the studied problem.

Probing new U(1) gauge symmetries via exotic Z → Z′γ decays

New U(1) gauge theories involving Standard Model (SM) fermions typically require additional electroweak fermions for anomaly cancellation. We study the non-decoupling properties of these new fermions, called anomalons, in the Z − Z′ − γ vertex function, reviewing the connection between the full model and the effective Wess-Zumino operator. We calculate the exotic Z → Z′γ decay width in U(1)B−L and U(1)B models, where B and L denote the SM baryon and lepton number symmetries. For U(1)B−L gauge symmetry, each generation of SM fermions is anomaly free and the exotic Z →$$ {Z}_{BL}^{\prime}\gamma $$ Z BL ′ γ decay width is entirely induced by intragenerational mass splittings. In contrast, for U(1)B gauge symmetry, the existence of two distinct sources of chiral symmetry breaking enables a heavy, anomaly-free set of fermions to have an irreducible contribution to the Z →$$ {Z}_B^{\prime}\gamma $$ Z B ′ γ decay width. We show that the current LEP limits on the exotic Z →$$ {Z}_B^{\prime}\gamma $$ Z B ′ γ decay are weaker than previously estimated, and low-mass $$ {Z}_B^{\prime } $$ Z B ′ dijet resonance searches are currently more constraining. We present a summary of the current collider bounds on U(1)B and a projection for a TeraZ factory on the Z →$$ {Z}_B^{\prime}\gamma $$ Z B ′ γ exotic decay, and emphasize how the Z → Z′γ decay is emblematic of new anomalous U(1) gauge symmetries.

Groups containing locally maximal product-free sets of size 4

Every locally maximal product-free set S in a finite group G satisfies G=S∪SS∪S−1S∪SS−1∪S−−√, where SS={xy∣x,y∈S}, S−1S={x−1y∣x,y∈S}, SS−1={xy−1∣x,y∈S} and S−−√={x∈G∣x2∈S}. To better understand locally maximal product-free sets, Bertram asked whether every locally maximal product-free set S in a finite abelian group satisfy |S−−√|≤2|S|. This question was recently answered in the negation by the current author. Here, we improve some results on the structures and sizes of finite groups in terms of their locally maximal product-free sets. A consequence of our results is the classification of abelian groups that contain locally maximal product-free sets of size 4, continuing the work of Street, Whitehead, Giudici and Hart on the classification of groups containing locally maximal product-free sets of small sizes. We also obtain partial results on arbitrary groups containing locally maximal product-free sets of size 4, and conclude with a conjecture on the size 4 problem as well as an open problem on the general case.

Spatiotemporal Fusion in Remote Sensing

Remote sensing images and techniques are powerful tools to investigate earth’s surface. Data quality is the key to enhance remote sensing applications and obtaining clear and noise-free set of data is very difficult in most situations due to the varying acquisition (e.g., atmosphere and season), sensor and platform (e.g., satellite angles and sensor characteristics) conditions. With the increasing development of satellites, nowadays Terabytes of remote sensing images can be acquired every day. Therefore, information and data fusion can be particularly important in the remote sensing community. The fusion integrates data from various sources acquired asynchronously for information extraction, analysis, and quality improvement. In this chapter, we aim to discuss the theory of spatiotemporal fusion by investigating previous works, in addition to describing the basic concepts and some of its applications by summarizing our prior and ongoing works.