Coherence estimation of quantum superposition states

Abstract Quantum coherence is a fundamental resource in quantum information science and one of the most distinctive features of quantum mechanics. In this paper, we derive a tight upper bound for the coherence of the superposition composed of two orthogonal states using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> -norm coherence measure, demonstrating that our upper bound is tighter than the one presented by Yue et al (2017 Sci. Rep. 7 4006). Furthermore, we extend the result to the superposition of n orthogonal states and establish the optimal upper bound for its coherence. Our results provide a more accurate estimate of the coherence of the superposition state.