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It is well known that the majorization condition is the necessary andsufficient condition for the deterministic transformations of both purebipartite entangled states by local operations and coherent states underincoherent operations. In this paper, we present two explicit protocols forthese transformations. We first present a permutation-based protocol whichprovides a method for the single-step transformation of $d$-dimensionalcoherent states. We also obtain generalized solutions of this protocol for somespecial cases of $d$-level systems. Then, we present an alternative protocolwhere we use $d'$-level ($d'$ $<$ $d$) subspace solutions of thepermutation-based protocol to achieve the complete transformation as a sequenceof coherent-state transformations. We show that these two protocols alsoprovide solutions for deterministic transformations of pure bipartite entangledstates.

Deterministic transformations of coherent states under incoherent operations