Ordering states with various coherence measures

Abstract

Quantum coherence is one of the most significant theories in quantum physics. Ordering states with various coherence measures is an intriguing task in quantification theory of coherence. In this paper, we study this problem by use of four important coherence measures -- the $l_1$ norm of coherence, the relative entropy of coherence, the geometric measure of coherence and the modified trace distance measure of coherence. We show that each pair of these measures give a different ordering of qudit states when $d\ge 3$. However, for single-qubit states, the $l_1$ norm of coherence and the geometric coherence provide the same ordering. We also show that the relative entropy of coherence and the geometric coherence give a different ordering for single-qubit states. Then we partially answer the open question proposed in [Quantum Inf. Process. 15, 4189 (2016)] whether all the coherence measures give a different ordering of states.

12 pages

References in corpus (11)

• Measuring Quantum Coherence with Entanglement
• Dephasing assisted transport: Quantum networks and biomolecules
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum coherence, time-translation symmetry and thermodynamics
• Role of quantum coherence in chromophoric energy transport
• Witnessing Quantum Coherence: from solid-state to biological systems
• Maximally coherent mixed states: Complementarity between maximal coherence and mixedness
• Estimation on geometric measure of quantum coherence
• Notes on modified trace distance measure of coherence
• Hilbert-Schmidt quantum coherence in multi-qudit systems
• Coherent-induced state ordering with fixed mixedness

Cited by in corpus (1)

• Dynamics of coherence-induced state ordering under Markovian channels