The reduction of the number of incoherent Kraus operations for qutrit systems
Lingyun Sun, Jing Wang, Ming Li, Shu-Qian Shen, Lei Li, Shao-Ming Fei, and Jianhuan Qiao
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Submission date: 08. May. 2020
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Quantum coherence is a fundamental property that can emerge within any quantum system. Incoherent operations, defined in terms of the Kraus decomposition, take an important role in state transformation. The maximum number of incoherent Kraus operators has been present in [A. Streltsov, S. Rana, P. Boes, J. Eisert, Phys. Rev. Lett. 119. 140402 (2017)]. In this work, we show that the number of incoherent Kraus operators for a single qubit can be reduce from 5 to 4 by constructing a proper unitary matrix. For qutrit systems we further obtain 32 incoherent Kraus operators, while the upper bound in the research of Sterltsov gives 39 Kraus operators. Besides, we reduce the number of strictly incoherent Kraus operators from more than 15 to 13. And we consider the state transformation via single qutrit strictly incoherent operation and incoherent operation.