A Protocol For Cooling and Controlling Composite Systems by Local Interactions

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Given two systems A A and B B of dimenstion d d , characterized by canonical basis { | 1 ⟩ A , ⋯ , | d ⟩ A } \{|1\rangle_{A},\cdots,|d\rangle_{A}\} and { | 1 ⟩ B , ⋯ , | d ⟩ B } \{|1\rangle_{B},\cdots,|d\rangle_{B}\} , respectively, the swap operators introduced in Sec. II.1

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