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Entanglement Witness with no Shared Reference Frame

Jannesary, Vahid | 2023

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 57094 (04)
  4. University: Sharif University of Technology
  5. Department: Physics Science
  6. Advisor(s): Karimipour, Vahid; Raeisi, Sadegh
  7. Abstract:
  8. Many quantum protocols that utilize entanglement are implemented between two distant bases. For various reasons, these two bases may not have a shared reference frame. In such cases, the mentioned protocols need to operate independently of the coordinate system. Therefore, identifying the entanglement of shared states between these two bases is not feasible with conventional methods, and alternative approaches must be found. The main focus of this thesis is to develop methods for identifying entangled states between two bases without the existence of a shared reference frame. In this thesis, we begin with a comprehensive review of the history of entanglement witnesses. Next, we investigate some methods for constructing entanglement witnesses and optimizing them. At the end, we first provide a thorough review of methods for establishing a shared reference frame between two bases using quantum methods and introduce a new approach for this purpose. Then, we present a novel, comprehensive, and practical method for constructing entanglement witnesses using positive maps. Finally, a method for identifying entanglement using entanglement witnesses between two distant bases without a shared reference frame is also presented
  9. Keywords:
  10. Entangled State ; Bell Inequality ; Shared Reference Frame ; Entanglement Witness ; Positive Maps ; Einstein-Podolsky-Rosen Paradox ; Peres-Horodecki Criterion ; Separable State

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