Trace distance measure of coherence for a class of qudit states

Abstract

Recently, trace distance measure of coherence has been proposed for characterizing the coherence of a given quantum state. However, it seems difficult to estimate the optimal incoherent state for high dimensional states. An explicit expression for the trace distance measure of coherence for a class of qudit states is provided. We show that the closest incoherent state to the class of qudit states is just the diagonal matrix obtained from it by deleting all off-diagonal elements. It is also shown that the measure of coherence induced by trace distance can act as a measure of coherence for this class of qudit states with some restrictions on the strictly incoherent operations.

8 pages

References in corpus (7)

• Measuring Quantum Coherence with Entanglement
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Observable measure of quantum coherence in finite dimensional systems
• Quantum coherence, time-translation symmetry and thermodynamics
• The Fidelity and Trace Norm Distances for Quantifying Coherence
• Quantifying Superposition
• Geometric lower bound for a quantum coherence measure