Local Unitary Equivalent Classes of Symmetric N-Qubit Mixed States

Majorana Representation (MR) of symmetric $N$-qubit pure states has been used successfully in entanglement classification. Generalization of this has been a long standing open problem due to the difficulties faced in the construction of a Majorana like geometric representation for symmetric mixed state. We have overcome this problem by developing a method of classifying local unitary (LU) equivalent classes of symmetric $N$-qubit mixed states based on the geometrical Multiaxial Representation (MAR) of the density matrix. In addition to the two parameters defined for the entanglement classification of the symmetric pure states based on MR, namely, diversity degree and degeneracy configuration, we show that another parameter called rank needs to be introduced for symmetric mixed state classification. Our scheme of classification is more general as it can be applied to both pure and mixed states. To bring out the similarities/ differences between the MR and MAR, $N$-qubit GHZ state is taken up for a detailed study. We conclude that pure state classification based on MR is not a special case of our classification scheme based on MAR. We also give a recipe to identify the most general symmetric $N$-qubit pure separable states. The power of our method is demonstrated using several well known examples of symmetric two qubit pure and mixed states as well as three qubit pure states. Classification of uniaxial, Biaxial and triaxial symmetric two qubit mixed states which can be produced in the laboratory is studied in detail

SU(2) Invariants of Symmetric Qubit States

Density matrix for N-qubit symmetric state or spin-j state (j = N/2) is expressed in terms of the well known Fano statistical tensor parameters. Employing the multiaxial representation [1], wherein a spin-j density matrix is shown to be characterized by j(2j+1) axes and 2j real scalars, we enumerate the number of invariants constructed out of these axes and scalars. These invariants are explicitly calculated in the particular case of pure as well as mixed spin-1 state.Comment: 7 pages, 1 fi

Entangling capabilities of Symmetric two qubit gates

Our work addresses the problem of generating maximally entangled two spin-1/2 (qubit) symmetric states using NMR, NQR, Lipkin-Meshkov-Glick Hamiltonians. Time evolution of such Hamiltonians provides various logic gates which can be used for quantum processing tasks. Pairs of spin-1/2's have modeled a wide range of problems in physics. Here we are interested in two spin-1/2 symmetric states which belong to a subspace spanned by the angular momentum basis {|j = 1, {\mu}>; {\mu} = +1, 0,-1}. Our technique relies on the decomposition of a Hamiltonian in terms of SU(3) generators. In this context, we define a set of linearly independent, traceless, Hermitian operators which provides an alternate set of SU(n) generators. These matrices are constructed out of angular momentum operators Jx,Jy,Jz. We construct and study the properties of perfect entanglers acting on a symmetric subspace i.e., spin-1 operators that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power.Comment: 12 page

Coexistence: a new perspective, a new field

With the entrance into force of Directive (EU) 2015/412 of the European Parliament and of the Council of 11 March 2015 amending Directive 2001/18/EC as regards the possibility for the Member States to restrict or prohibit the cultivation of genetically modified organisms (GMOs) in their territory the legislative framework and the perspective of agricultural land use related to the use of a given plant variety are drammatically changed.- The new Directive not only opens the way for different solutions within the European Union but also seems to have filed the decades-long debate on coexistence. However on consider the two aspect of coexistence: as principle and set of measures

Social Media and Revenue Management; Where Should the Two Meet?

The objective of this study is to explore how social media strategies can be integrated with the function of revenue management. A survey was used to evaluate the extent to which some travel firms use/perceive social media. This study explores possible synergy between the time spent developing social media channels and the opportunities these might generate for travel firms active in the application of revenue management tactics. This has lead to the recommendation of new practices that could potentially enhance future revenue and profit. The present study identifies that travel firms can build opportunities to capture additional revenues by focusing on building engaging and useful content for customers. The travel industry is just beginning to embrace the need to combine public relations (PR) activities with new marketing approaches that must engage, rather that use interruption and coercion to generate sales. As engagement of the public with social media grows, it is evident that this will have implications for revenue management approaches, in the same way that approaches to PR and marketing have needed to evolve with the growth in online interaction between consumers. A shift in strategic outlook may enhance the ability of travel companies to sell valued products, improve customer relationships and increase their bottom-line; hence it becomes even more important for such organizations to ensure they have a solid social media strategy

I mercati contadini tra teoria e prassi

Editoriale del fascicolo che affronta la diffusione di forme di commercializzazione dei prodotti agroalimentari alternative rispetto al modello dominante - caratterizzato dalla presenza di intermediari e dalla prevalenza della grande distribuzione organizzata – e le questioni giuridiche che in Italia stanno emergendo, in presenza di un quadro normativo generale e di una normativa specifica in progressiva formazione

In tema di etichettatura dei prodotti geneticamente modificati

Le regole sulla etichettatura dei prodotti ogm si devono leggere in un contesto profondamente inciso dalla pluralità delle fonti informative e tenendo conto dei movimenti che negli USA stanno spingendo per una revisione delle regole dell'informazione del consumator