SDP for One-shot Dilution of Quantum Coherence

• URL: http://arxiv.org/abs/2409.08876v1
• Date: Fri, 13 Sep 2024 14:39:04 GMT
• Title: SDP for One-shot Dilution of Quantum Coherence
• Authors: Yikang Zhu, Zhaofeng Su,
• Abstract summary: We find a semidefinite program of one-shot coherence dilution of pure state under maximally incoherent operation. We further give a similar but not semidefinite program form under dephasing-covariant incoherent operation. Our numerical experiment clearly demonstrates that the maximally incoherent operation and dephasing-covariant incoherent operation have different power in the coherence dilution.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. We consider the coherence dilution problem in the one-shot scenario. We find a semidefinite program of one-shot coherence dilution of pure state under maximally incoherent operation. We further give a similar but not semidefinite program form under dephasing-covariant incoherent operation. Moreover, we prove that the known lower bound of the one-shot dilution is strict. Our numerical experiment clearly demonstrates that the maximally incoherent operation and dephasing-covariant incoherent operation have different power in the coherence dilution.

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