We show a simple relation connecting entangling power and local invariants of two-qubit gates. From the relation, a general condition under which gates have same entangling power is derived. The relation also helps in finding the lower bound of entangling power for perfect entanglers, from which the classification of gates as perfect and non perfect entanglers is obtained in terms of local invariants.Entanglement, a nonlocal property of a quantum state, is regarded as a resource for realizing various fascinating features such as teleportation, quantum cryptography and quantum computation [1,2]. On one side, much work has been carried out to understand and exploit the entanglement for various information processing. On the other side, attention has been given to quantum operations (gates) as they are responsible for creating entanglement when acting on a state.Since two-qubit gates are capable of producing entanglement, it is of vital importance to understand their entangling characterization. One such useful tool is the entangling power of an operator which quantifies the average entanglement produced [3]. Another tool to characterize the nonlocal attributes of a two-qubit gate is local invariants, namely and (first introduced in Ref.[4]) such that gates differing only by local operations possess same invariants. Furthermore, nonlocal two-qubit gates form an irreducible geometry of tetrahedron known as Weyl chamber. Of all the gates, exactly half of them are perfect entanglers (operators capable of producing maximally entangled state from some input product state) and they form a polyhedron within the Weyl chamber [5].It is known that gates differing only by local operations possess the same entangling power.Similarly, gates which are inverse to each other possess the same entangling power. For instance, SWAP α and SWAP -α assume the same entangling power as they are inverse to each other. From our earlier study on the geometrical edges of two-qubit gates [6], it was found that gates which do not belong to the preceding category also possess same entangling power. For

The aim of the present study was to investigate the protective effect of Withaferin-A on red blood cell integrity during 7,12-dimethylbenz[a]anthracene (DMBA) induced oral carcinogenesis. The protective effect of Withaferin-A was assessed by measuring the status of glycoconjugates, membrane bound enzyme activity and red blood cell osmotic fragility. Oral squamous cell carcinoma was induced in the buccal pouch of Syrian golden hamsters by painting with 0.5% DMBA in liquid paraffin thrice a week for 14 weeks. The levels of glycoconjugates, membrane bound enzyme activity, osmotic fragility and thiobarbituric acid reactive substances (TBARS) were analyzed by using specific colorimetric methods. We observed 100% tumor formation in DMBA painted hamsters. Increase in plasma glycoconjugates at the expense of red blood cell membrane glycoconjugates levels were observed in DMBA painted hamsters as compared to control hamsters. Erythrocytes from DMBA painted hamsters were more fragile than those from control hamsters. The activity of membrane bound enzyme (Na + K + ATPase) decreased whereas TBARS level was increased in DMBA painted hamsters as compared to control hamsters. Oral administration of Withaferin-A at a dose of 20mg kg -1 bw significantly prevented the tumor formation as well as normalized the biochemical variables in DMBA painted hamsters. Our results thus demonstrate the protective effect of Withaferin-A on red blood cell integrity during DMBA induced oral carcinogenesis.

Nonlocal two-qubit gates are geometrically represented by tetrahedron known as Weyl chamber within which perfect entanglers form a polyhedron. We identify that all edges of the Weyl chamber and polyhedron are formed by single parametric gates. Nonlocal attributes of these edges are characterized using entangling power and local invariants. In particular, SWAP -α family of gates with 1 0 ≤ ≤ α constitutes one edge of the Weyl chamber with SWAP -1/2 being the only perfect entangler.Finally, optimal constructions of controlled-NOT using SWAP -1/2 gate and gates belong to three edges of the polyhedron are presented.

The objective of this study was to explore the functional anatomy of the globus pallidus internus (GPi) by studying the effects of unilateral pallidotomy on parkinsonian 'off' signs and levodopa-induced dyskinesias (LID). We found significant positive correlations between the preoperative levodopa responsiveness of motor signs and the levodopa responsiveness of scores in timed tests (Core Assessment Program for Intracerebral Transplantations) in the contralateral limbs and the improvement in these scores after surgery, whereas there was no correlation with the improvement in LID. We also found a highly significant correlation (P: < 0.0001, r = 0.8) between the volume of the ventral lesion in the GPi and the improvement in LID in the contralateral limbs, whereas there was no correlation between the ventral volume and the improvement in parkinsonian 'off' signs. The volumes of the total lesion cylinder and the dorsal lesion did not correlate with the outcome of either dyskinesias or parkinsonian 'off' signs. The differential predictive value of levodopa responsiveness for the outcome of parkinsonian 'off' signs and LID and the different correlations of ventral lesion volume with dyskinesias and parkinsonian 'off' signs indicate that different anatomical or pathophysiological substrates may be responsible for the generation of parkinsonian 'off' signs and dyskinesias. Whereas cells in a wider area of the GPi may be implicated in parkinsonism, the ventral GPi seems to be crucial for the manifestation of LID. We suggest that our observations are additional proof of the functional somatotopy of the systems within the GPi that mediate parkinsonism and dyskinesias, especially along the dorsoventral trajectory used in pallidotomy. The outcome of pallidotomy in which the lesion involves the ventral and dorsal GPi could be the net effect of alteration in the activity of pathways which mediate different symptoms, and hence could be variable.

We study the entangling power and perfect entangler nature of family. On the other hand, a subset of CU which is locally equivalent to CNOT is identified. It is shown that the subset, which is a perfect entangler, must necessarily possess the maximum entangling power.