Semidefinite Program for One‐Shot Dilution of Quantum Coherence

Abstract Quantum coherence is one of the fundamental properties of quantum mechanics and also acts as a valuable resource for a variety of practical applications, which includes quantum computing and quantum information processing. Evaluating the dilution of coherence is a basic problem in the framework of resource theory. The coherence dilution problem is considered in the one‐shot scenario. A semidefinite program of one‐shot coherence dilution of pure state under maximally incoherent operation is identified. A similar but not semidefinite program form is provided under dephasing‐covariant incoherent operation. Moreover, it is proved that the known lower bound of the one‐shot dilution is strict. This numerical experiment clearly demonstrates that the maximally incoherent operation and dephasing‐covariant incoherent operation have different power in the coherence dilution.