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Quantum Estimation: Properties and Calculation of the Quantum Fisher Information and Adaptive Scheme

Hassani, Majid | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51872 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rezakhani, Ali
  7. Abstract:
  8. In this thesis , we study quantum estimation , its primary tools and different approaches . To this end , along with reviewing the main concepts of classical and quantum estimation , the Cramer-Rao inequlity which establishes a lower bound on the precision of estimation has been used . This lower bound can be calculated using the quantum Fisher information . In order to explore properties of the quantum Fisher information , we study the continuity relation of this quantity in the most general case and we calculate it for different quantum states . To underline the importance of the continuity relation , one can demonstrate an estimate of the value of the quantum Fisher information by establishing an upper bound on the quantum Fisher information using the continuity relation . Moreover, this continuity relation enables one to investigate relative robustness of estimation strategies against various sources of error. The aim of all these studies is to enhance the precision in quantum estimation (strategies) . Hence, we proceed with adaptive strategy. In the adaptive strategy, one performs a measurement on the probe (after a first sampling of the dynamics with unknown parameter), and use the result to determine what sort of preparation to make on a probe on a second sampling of the dynamics and so on. We use the quantum phase estimation algorithm as a simple example of this strategy . To this end , we have shown that quantum estimation can be investigated using an information-theoretic approach
  9. Keywords:
  10. Quantum Estimation ; Cramer-Rao Bound ; Quantum Fisher Information ; Bond ; Adaptive Strategy ; Mutual Information ; Fisher Information Matrix

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