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Superposition of Orthogonal States and No-go Theorems in Quantum Mechanics

Doosti, Mina | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50397 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Karimipour, Vahid
  7. Abstract:
  8. Quantum mechanics, because of its special structure, on one hand offers us possibilities for doing un-classical tasks and on the other hand imposes limitations on performing some quantum tasks. We know these limitations as no-go theorems in Quantum mechanics. Studying these no-go theorems and properties which can be used as Quantum resources, has a wide variety of applications in Quantum information and Quantum computation, also they can lead us to a deeper understanding of the Quantum mechanics theory.One of these non-classical properties is Superposition. Quantum superposition is both a source for other Quantum properties like entanglement, and a Quantum resource for Quantum tasks. But recently has been shown that Quantum mechanics will not allow to produce superposition of arbitrary unknown states. Like many other no-go theorems such as no-cloning, one can surpass these limitations with rather approximate or probabilistic protocols. A probabilistic protocol has been suggested recently for creating superposition of arbitrary states. But this superposition machine can generate the superposition only by having a partial prior knowledge about input states. In this thesis, by limiting our inputs to a class of arbitrary orthogonal states,we presented a superposition machine which can produce a desired form of the superposition for this class. This machine has a higher probability of success than the previous machine and more important, has no need of any information about initial states. Also by introducing a well-defined form for the superposition of two states, we could find a machine with mixed output and a total probability of success equal to unity. One of the advantages of our machine is that it can be used as a resource for producing states with quantum coherence. And at the end, having our construction in hand, we could investigate the relation between the no-superposition theorem and nocloning theorem and we showed that existence of one ideal cloning machine will lead to the existence of the ideal superposition machine for all input states
  9. Keywords:
  10. Superposition Principle ; No-Cloning ; Quantum Mechanics ; No-Go Theorems in Quantum Mechanics ; Quantum Resource Theories

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