Colloquium: Quantum coherence as a resource

The coherent superposition of states, in combination with the quantization of observables, represents one of the most fundamental features that mark the departure of quantum mechanics from the classical realm. Quantum coherence in many-body systems embodies the essence of entanglement and is an essential ingredient for a plethora of physical phenomena in quantum optics, quantum information, solid state physics, and nanoscale thermodynamics. In recent years, research on the presence and functional role of quantum coherence in biological systems has also attracted considerable interest. Despite the fundamental importance of quantum coherence, the development of a rigorous theory of quantum coherence as a physical resource has been initiated only recently. This Colloquium discusses and reviews the development of this rapidly growing research field that encompasses the characterization, quantification, manipulation, dynamical evolution, and operational application of quantum coherence.

Figure 1

Plan of the Colloquium. (Top) Sec. 2: Resource theories of quantum coherence; the inset depicts a comparison between some classes of incoherent operations. Adapted from [53]. (Right) Sec. 3: Quantifying quantum coherence; the inset depicts the construction of coherence monotones from entanglement. Adapted from [252]. (Bottom) Sec. 4: Dynamics of quantum coherence; the inset depicts an illustration of coherence freezing under local incoherent channels. Adapted from [33]. (Left) Sec. 5: Applications of quantum coherence; the insets depicts a schematic of a quantum phase discrimination protocol. Adapted from [176]. The Introduction (Sec. 1) and Conclusions (Sec. 6) complete the Colloquium.