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Towards Optimal Convergence Rates For the Quantum Central Limit Theorem

Mehrabi, Hami | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57241 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Beigi, Salman; Safdari, Mohammad
  7. Abstract:
  8. The Quantum Central Limit Theorem states that when you convolve a centered quantum state, the resulting sequence of states converges to a Gaussian quantum state with the same first and second moments as the original quantum state. Similar to the classical setting, there are various metrics to measure convergence in the Quantum Central Limit Theorem. In this thesis, we aim to examine this theorem under different metrics such as Quantum Relative Entropy and Trace distance, and to prove tight convergence rates for the Quantum Central Limit Theorem
  9. Keywords:
  10. Quantum Fisher Information ; Central Limit Theorem ; Quantum Relative Entropy Distance ; Quantum Central Limit Theorem ; Optimal Convergence Rate

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