Canonical steering ellipsoids of pure symmetric multiqubit states with two distinct spinors and volume monogamy of steering

Quantum steering ellipsoid formalism provides a faithful representation of all two-qubit states and helps in obtaining correlation properties of the state through the steering ellipsoid. The steering ellipsoids corresponding to the two-qubit subsystems of permutation symmetric $N$-qubit states is analysed here. The steering ellipsoids of two-qubit states that have undergone local operations on both the qubits so as to bring the state to its canonical form are the so-called canonical steering ellipsoids. We construct and analyze the geometric features of the canonical steering ellipsoids corresponding to pure permutation symmetric $N$-qubit states with two distinct spinors. Depending on the degeneracy of the two spinors in the pure symmetric $N$-qubit state, there arise several families which cannot be converted into one another through Stochastic Local Operations and Classical Communications (SLOCC). The canonical steering ellipsoids of the two-qubit states drawn from the pure symmetric $N$-qubit states with two distinct spinors allow for a geometric visualization of the SLOCC-inequivalent class of states. We show that the states belonging to the W-class correspond to oblate spheroid centered at $(0,0,1/(N-1))$ with fixed semiaxes lengths $1/\sqrt{N-1}$ and $1/(N-1)$. The states belonging to all other SLOCC inequivalent families correspond to ellipsoids centered at the origin of the Bloch sphere. We also explore volume monogamy relations of states belonging to these families, mainly the W-class of states.Comment: 13 pages, 13 figures; Revised version; Comments welcom

ALKAPTONURIA SYNDROME-A REVIEW

Alkaptonuria, also called endogenous ochronosis, and also called as Black Urine Disease, is a rare metabolic autosomal recessive disorder. It occurs by complete inhibition of homogentisic acid oxidase enzyme having its deposition in various tissues. Alkaptonuria is caused due to deficiency of homogentisic acid oxidase involved in the metabolism of tyrosine. Dark discolouration of urine, ochronosis at cartilage and connective tissues, arthritis at the third of fourth decade of life, renal stone disease, spontaneous tendon rupture etc. May be seen in alkaptonuria. Disease severity varies among individual patients, even between siblings, and increase with age because of homogentisic acid accumulation. Usually, life span is not shortened in AKU, but the quality of life is severely effected. Several studies have suggested that Nitisinone may be effective in the treatment of alkaptonuria. Characteristically, the excess HGA means sufferers pass dark urine, which upon standing turns black. This is a feature present from birth. Over time patients develop other manifestations of AKU, due to the deposition of HGA in collagenous tissues, namely ochronosis and ochronotic osteoarthropathy. Although this condition does not reduce life expectancy, it significantly affects the quality of life. The natural history of this condition is becoming better understood, despite gaps in knowledge. Clinical assessment of the condition has also improved along with the development of potentially disease-modifying therapy. Furthermore, recent developments in AKU research have to lead to new understanding of the disease, and further study of the AKU arthropathy has the potential to influence therapy in the management of osteoarthritis

Quantum Dissension: Generalizing Quantum Discord for Three-Qubit States

We introduce the notion of quantum dissension for a three-qubit system as a measure of quantum correlations. We use three equivalent expressions of three-variable mutual information. Their differences can be zero classically but not so in quantum domain. It generalizes the notion of quantum discord to a multipartite system. There can be multiple definitions of the dissension depending on the nature of projective measurements done on the subsystems. As an illustration, we explore the consequences of these multiple definitions and compare them for three-qubit pure and mixed GHZ and W states. We find that unlike discord, dissension can be negative. This is because measurement on a subsystem may enhance the correlations in the rest of the system. This approach can pave a way to generalize the notion of quantum correlations in the multiparticle setting.Comment: 9 pages 6 figures typo fixed and some arguments adde

Squeezing of a coupled state of two spinors

The notion of spin squeezing involves reduction in the uncertainty of a component of the spin vector below a certain limit. This aspect has been studied earlier for pure and mixed states of definite spin. In this paper, this study has been extended to coupled spin states which do not possess sharp spin value. A general squeezing criterion has been obtained by requiring that a direct product state for two spinors is not squeezed. The squeezing aspect of entangled states is studied in relation to their spin- spin correlations.Comment: Typeset in LaTeX 2e using the style iopart, packages iopams,times,amssymb,graphicx; 17 pages, 5 eps figure file

Quantum discord evolution of three-qubit states under noisy channels

We investigated the dissipative dynamics of quantum discord for correlated qubits under Markovian environments. The basic idea in the present scheme is that quantum discord is more general, and possibly more robust and fundamental, than entanglement. We provide three initially correlated qubits in pure Greenberger-Horne-Zeilinger (GHZ) or W state and analyse the time evolution of the quantum discord under various dissipative channels such as: Pauli channels $\sigma_{x}$, $\sigma_{y}$, and $\sigma_{z}$, as well as depolarising channels. Surprisingly, we find that under the action of Pauli channel $\sigma_{x}$, the quantum discord of GHZ state is not affected by decoherence. For the remaining dissipative channels, the W state is more robust than the GHZ state against decoherence. Moreover, we compare the dynamics of entanglement with that of the quantum discord under the conditions in which disentanglement occurs and show that quantum discord is more robust than entanglement except for phase flip coupling of the three qubits system to the environment.Comment: 17 pages, 4 figures, accepted for publication in EPJ

Separability criteria and entanglement witnesses for symmetric quantum states

We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss entanglement conditions and entanglement witnesses for states with a positive partial transpose.Comment: 5 pages, no figures, LaTeX; v2: typos corrected, introduction extended; v3: small corrections, published version; for the proceedings of the DPG spring meeting, Hamburg, March 200