Measuring Quantum Coherence with Entanglement

Abstract

Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of coherence as an operational resource are still very limited. Here we show that any degree of coherence with respect to some reference basis can be converted to entanglement via incoherent operations. This finding allows us to define a novel general class of measures of coherence for a quantum system of arbitrary dimension, in terms of the maximum bipartite entanglement that can be generated via incoherent operations applied to the system and an incoherent ancilla. The resulting measures are proven to be valid coherence monotones satisfying all the requirements dictated by the resource theory of quantum coherence. We demonstrate the usefulness of our approach by proving that the fidelity-based geometric measure of coherence is a full convex coherence monotone, and deriving a closed formula for it on arbitrary single-qubit states. Our work provides a clear quantitative and operational connection between coherence and entanglement, two landmark manifestations of quantum theory and both key enablers for quantum technologies.

5+3 pages, 1 figure. To appear in PRL

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Cited by in corpus (11)

• Detecting macroscopic quantum coherence with a cavity optomechanical system
• Uncertainty Relations for Quantum Coherence
• Coherence breaking channels and coherence sudden death
• Experimental Quantum Randomness Processing
• The complementarity relations of quantum coherence in quantum information processing
• Average coherence and its typicality for random mixed quantum states
• Remote Creation of Quantum Coherence
• Trace distance measure of coherence for a class of qudit states
• Coherence convertibility for mixed states
• Relating quantum coherence and correlations with entropy-based measures
• Protecting coherence in the non-Hermitian two-level system