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Broadcasting of Entanglement and Consequences on Quantum Information ProcessingAuthor: jaya j Date: 2017-12-08 Report no: IIIT/TH/2017/87 Advisor:Indranil Chakrabarty AbstractInformation theory plays a vital role in today’s computational world. According to the past research, the capabilities of the quantum information processing exceeds that of the classical methods in most of the cases. However, there are few phenomena where quantum mechanics puts limitations such as’cloning’ information. In classical computers, we can copy the information from one place to another without any alteration. But, we cannot achieve the similar results following the quantum rules. This limitations of the quantum mechanics comes from ’no cloning theorem’ which says that it is impossible to copy an arbitrary pure state (information) perfectly. But the possibility of an imperfect cloning is never denied. Broadly, two types of quantum cloning machines have been discussed in past: approximate cloning machine, which gives imperfect copies and probabilistic cloning machines, which gives a perfect copy but only with some non-unit probability. The quality of the state cloned is measured in terms of ’fidelity of cloning’. The approximate cloning machines, whose fidelity depends on the input state, are called state dependent cloning machines. However, the state independent cloning machine copies any state with the same fidelity. In this work, we talk about the state independent approximate cloning machines. We extend the already existing 1 to N local cloning machine and give the cloning transformations to apply it non-locally. Along with the cloning of a state, one more phenomena is of interest here, that is, cloning of entanglement. Quantum entanglement is one of the peculiarities of quantum mechanics, which makes the phenomena such as quantum teleportation and super-dense coding possible. When we refer broadcasting of an entangled state, we mean creating more pairs of less entangled state from a given entangled state. One way of doing this is by applying local cloning transformations on each qubit of the given entangled state. This can also be done by applying global cloning operations on the entangled state itself. It is known that the broadcasting of entanglement into more than two entangled pairs is not possible using only local operations. Also, Inseparability is optimally broadcast when symmetric cloners are applied. This is mostly required when we perform distributed information processing tasks. It is natural to expect in a bi-partite situation that these newly created entangled states are less suitable in tasks like teleportation and super-dense coding than the parent state. However, the dependence of the usability of such states in information processing tasks on our ability of broadcasting is not well known. In this work we obtain several complementary relations manifesting the interdependence of their information processing capabilities and fidelity of broadcasting. We extend our investigation in a situation where vi vii instead of using 1-2 cloning, we have used 1-N cloning transformations both locally and non-locally. Eventually we find out the fidelity of broadcasting and the change in the information processing capacities for different values of N(3,4,5) and investigate how these complementary relations behave with the increase in number of copies(N). Full thesis: pdf Centre for Computational Natural Sciences and Bioinformatics |
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