Secret Broadcasting of W-type state.pdfVIP

a r X i v : 0 8 0 3 .3 3 9 3 v 2 [ q u a n t - p h ] 2 5 M a r 2 0 0 8 Secret Broadcasting of W-type state I.Chakrabarty 1,2?,B.S.Choudhury 2 1 Heritage Institute of Technology,Kolkata-107,West Bengal,India 2 Bengal Engineering and Science University, Howrah, West Bengal, India Abstract In this work we investigate the problem of secretly broadcasting W type states between three different partners. The problem is interesting in the sense that here we have showed that one can broadcast two W-states between three distant part- ners from a W-type state initially shared by them, with the help of local cloning operations. 1 Introduction: Linearity of quantum theory forbids us from amplifying and deleting an unknown quantum state. The consequence of which is the no-cloning theorem [1] and no-deletion theorem [6]. Although nature prevents us from amplifying an unknown quantum state but nevertheless one can construct a quantum cloning machine that duplicates an unknown quantum state with a fidelity less than unity [1,2,3,4,5]. Beyond the no-cloning theorem, one can clone an arbitrary quantum state probabilistically [7]. In the past years,much progress has been made in designing quantum cloning machine. Buzek-Hillery took the first step towards the construction of approximate quantum cloning machine [2]. They showed that the quality of the copies produced by their machine remain same for all input state.This machine is known as universal quantum cloning ?Corresponding author: E-Mail-indranilc@ 1 machine (UQCM). Later Gissin -Massar showed the machine to be optimal [3]. After that the different sets of quantum cloning machines like the set of universal quantum cloning machines, the set of state dependent quantum cloning machines (i.e. the quality of the copies depend on the input state) and the probabilistic quantum cloning machines were proposed. Entanglement[8], the heart of quantum information theory,play a crucial role in computational and communicational purposes.