SDP for One-shot Dilution of Quantum Coherence

TL;DR

This paper develops semidefinite programming methods to analyze one-shot quantum coherence dilution under different operations, revealing differences in their effectiveness and providing new bounds in resource theory.

Contribution

It introduces a semidefinite program for one-shot coherence dilution under maximally incoherent operations and compares it with dephasing-covariant operations, highlighting their differences.

Findings

Semidefinite program for one-shot coherence dilution under maximally incoherent operations.

Comparison shows different power of maximally incoherent and dephasing-covariant operations.

Lower bound of one-shot dilution is proven to be strict.

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.