The modified trace distance of coherence is constant on most pure states

Abstract

Recently, the much-used trace distance of coherence was shown to not be a proper measure of coherence, so a modification of it was proposed. We derive an explicit formula for this modified trace distance of coherence on pure states. Our formula shows that, despite satisfying the axioms of proper coherence measures, it is likely not a good measure to use, since it is maximal (equal to 1) on all except for an exponentially-small (in the dimension of the space) fraction of pure states.

5 pages, 3 figures

References in corpus (5)

• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum coherence, time-translation symmetry and thermodynamics
• Witnessing Quantum Coherence: from solid-state to biological systems
• Quantifying Entanglement with Witness Operators
• Alternative framework for quantifying coherence

Cited by in corpus (3)

• Some notes on the robustness of k-coherence and k-entanglement
• Coherence measures induced by norm functions
• Completely positive completely positive maps (and a resource theory for non-negativity of quantum amplitudes)