http://dspace.dtu.ac.in:8080/jspui/handle/123456789/25 2026-04-28T04:03:38Z http://dspace.dtu.ac.in:8080/jspui/handle/repository/17479 Title: MUTUAL UNCERTAINTY, CONDITIONAL UNCERTAINTY, AND STRONG SUBADDITIVITY Authors: SAZIM, SK; SATYABRATA, ADHIKARI; ARUN K., PATI; PANKAJ, AGRAWAL Abstract: We introduce a concept, called the mutual uncertainty between two observables in a given quantum state, which enjoys features similar to those of the mutual information for two random variables. Further, we define conditional uncertainty as well as conditional variance and show that conditioning on more observables reduces the uncertainty. Given three observables, we prove a “strong subadditivity” relation for the conditional uncertainty under certain conditions. As an application, we show that by using the conditional variance one can detect bipartite higher dimensional entangled states. The efficacy of our detection method lies in the fact that it gives better detection criteria than most of the existing criteria based on geometry of the states. Interestingly, we find that for N qubit product states, the mutual uncertainty is exactly equal to N-sqrt(N), and if it is other than this value, the state is entangled. We also show that using the mutual uncertainty between two observables, one can detect non-Gaussian steering where Reid's criterion fails to detect it. Our results may open a direction of exploration in quantum theory and quantum information using mutual uncertainty, conditional uncertainty, and the strong subadditivity for multiple observables. 2018-09-01T00:00:00Z http://dspace.dtu.ac.in:8080/jspui/handle/repository/17404 Title: Mutual uncertainty, conditional uncertainty, and strong subadditivity Authors: Sazim, Sk; Adhikari, Satyabrata; Pati, Arun; Agrawal, Pankaj 2018-09-28T00:00:00Z http://dspace.dtu.ac.in:8080/jspui/handle/repository/16799 Title: A NOTE ON IMPROVED ESTIMATIONS FOR INTEGRATED SZASZ-MIRAKYAN OPERATORS Authors: DEO, NAOKANT; GUPTA, VIJAY Abstract: In the present paper, we propose a modification of the integrated Sz´asz-Mirakyan operators having the weight function of general Beta basis function. We study some direct results on the modified operators. It is also observed that our modified operators have better estimates over the original operators. 2011-01-01T00:00:00Z http://dspace.dtu.ac.in:8080/jspui/handle/repository/16798 Title: FASTER RATE OF CONVERGENCE ON SRIVASTAVA-GUPTA OPERATORS Authors: DEO, NAOKANT Abstract: In this paper, we consider a modification of Srivastava–Gupta operators, which is a general sequence of summation-integral operators. We are able to achieve faster convergence for our modified operators over the well known Srivastava–Gupta operators. Our results include some approximation properties, which include rate of convergence and Voronovskaya kind results. In the last section of this paper we give Stancu variant of these operators. 2012-01-01T00:00:00Z