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Alberti Uhlmann Conditions On Transfering Quantum States

Taheri, Mostafa | 2022

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 55117 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Karimipour, Vahid; Memarzadeh, Laleh
  7. Abstract:
  8. One of the main aspects of resource theory is finding conditions that one state can map to another state with “allowed” operations. In quantum, allowed operations are a subset of quantum channels. In quantum thermodynamics, for example, one usually asks whether a state σ can be generated from an initial state ρ via a Gibbs-preserving channel which is a special case of [2]. In 1980 Alberti and Uhlmann [2]found a condition for the existence of a quantum channel that simultaneously transforms an input-pair of states into an output-pair. This problem is addressed in resource theory[1, 3], statistical comparison[4] and etc. Since then, this problem and its generalizations[8, 23, 22, 31, 7, 6] have been extensively investigated from different points of view. In this thesis, we address an extension on the Alberti-Uhlmann theorem by relaxing the number of times that a channel can act. We try to find situations in which a quantum channel exists that can map(deterministic or approximate) the input-pair {ρ1, ρ2} to an output-pair {σ1, σ2} if we allow it to act at different times (Eni ρi = σi). Also, we are looking for the condition which in it there exist a Lindblad generator L such that by acting at different times on the input-pair can map it to the output-paire.
  9. Keywords:
  10. Quantum Channel ; Markovian Quantum Process ; Quantum Resource Theories ; Quantum Majorization ; Alberti-Uhlmann Conditions ; State Transfer

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