Notes on quantum coherence with l_1-norm and convex-roof l_-norm
Jiayao Zhu, Jian Ma, Tinggui Zhang
TL;DR
This paper investigates quantum coherence measures using l_1-norm and convex-roof l_1-norm, introducing new inequalities, calculation methods for specific states, and improved upper bounds.
Contribution
It presents novel triangle-like inequalities, a calculation method for convex-roof l_1-norm in certain states, and tighter upper bounds for coherence measures.
Findings
New triangle-like inequalities for quantum coherence
Method for calculating convex-roof l_1-norm in 3D states
Improved upper bounds for l_1-norm coherence
Abstract
In this work, we evaluate quantum coherence using the l_1-norm and convex-roof l_1-norm and obtain several new results. First, we provide some new general triangle-like inequalities of quantum coherence, with results better than existing ones. Second, for some special three-dimensional quantum states, a method for calculating the convex-roof l_1-norm is presented. Lastly, we offer distinct upper bounds in the l_1-norm measure of coherence based on the quantum state itself.
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Taxonomy
TopicsQuantum Information and Cryptography · Quantum Computing Algorithms and Architecture · Quantum Mechanics and Applications