Logarithmic coherence: Operational interpretation of ${\ell }_1$-norm coherence

Abstract

We show that the distillable coherence---which is equal to the relative entropy of coherence---is, up to a constant factor, always bounded by the ${\ell }_1$-norm measure of coherence (defined as the sum of absolute values of off diagonals). Thus the latter plays a similar role as logarithmic negativity plays in entanglement theory and this is the best operational interpretation from a resource-theoretic viewpoint. Consequently the two measures are intimately connected to another operational measure, the robustness of coherence. We find also relationships between these measures, which are tight for general states, and the tightest possible for pure and qubit states. For a given robustness, we construct a state having minimum distillable coherence.

V3: 6+5 pages, 2 figures. Published version

References in corpus (15)

• Measuring Quantum Coherence with Entanglement
• Dephasing assisted transport: Quantum networks and biomolecules
• Distillation of secret key and entanglement from quantum states
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum coherence, time-translation symmetry and thermodynamics
• Frozen Quantum Coherence
• Role of quantum coherence in chromophoric energy transport
• Individual quantum probes for optimal thermometry
• Witnessing Quantum Coherence: from solid-state to biological systems
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Quantum coherence and uncertainty in the anisotropic XY chain
• Entanglement Theory and the Second Law of Thermodynamics
• Coherence number as a discrete quantum resource
• Operations and single particle interferometry
• Fidelity and Coherence Measures from Interference

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