Abstract
Abstract
It is well known that the majorization condition is the necessary and sufficient for the deterministic transformations of pure-coherent states under incoherent operation (IO). In this paper, we present the protocol 1 (product-form) which provides a method for the pure-coherent transformation under IO and overcomes the restriction of the number of Kraus operators of Protocol I (Torun and Yildiz 2018 Phys. Rev. A 97 052331). Then, we show that the corresponding uncorrelated-catalytic protocol (discarding the catalytic state) is not incoherent-preserving. We construct the protocol 2 such that the uncorrelated-catalytic transformation with four-dimensional catalyst state can be implemented probabilistically under dephasing-covariant IO. Especially, the protocol 2 provides the target state from the catalyst-assisted transformation and its equivalent states with respect to Pauli operators
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Subject
Industrial and Manufacturing Engineering,Condensed Matter Physics,Instrumentation,Atomic and Molecular Physics, and Optics
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