Priyanka Mukhopadhyay

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In 1962 Hough earned the patent for a method [1], popularly called Hough Transform (HT) that efficiently identifies lines in images. It is an important tool even after the golden jubilee year of existence, as evidenced by more than 2500 research papers dealing with its variants, generalizations, properties and applications in diverse fields. The current(More)
In this paper we present a new operational interpretation of relative-entropy between quantum states in the form of the following protocol. P: Alice gets to know the eigen-decomposition of a quantum state ρ. Bob gets to know the eigen-decomposition of a quantum state σ. Both Alice and Bob know S (ρσ) def = Trρ log ρ − ρ log σ, the relative entropy between ρ(More)
We show that for any (partial) query function f : {0, 1} n → {0, 1}, the randomized communication complexity of f composed with Index n m (with m = poly(n)) is at least the random-ized query complexity of f times log n. Here Index m : [m] × {0, 1} m → {0, 1} is defined as Index m (x, y) = y x (the xth bit of y). Our proof follows on the lines of Raz and(More)
In this paper, we present the following quantum compression protocol `P': Let &#x03C1;,&#x03C3; be quantum states, such that S (&#x03C1;&#x2225;&#x03C3;) <sup>def</sup>= Tr(&#x03C1; log &#x03C1; - &#x03C1; log &#x03C3;), the relative entropy between &#x03C1; and &#x03C3;, is finite. Alice gets to know the eigendecomposition of &#x03C1;. Bob gets to know the(More)
Schubert polynomials were discovered by A. Lascoux and M. Schützenberger in the study of cohomology rings of flag manifolds in 1980s. These polynomials generalize Schur polynomials and form a linear basis of multivariate polynomials. In 2003, Lenart and Sottile introduced skew Schubert polynomials, which generalize skew Schur polynomials and expand in the(More)
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