(a) Input states that are fully incoherent (S and A) cannot be converted to entanglement via incoherent operations. (b) But when the input state S has coherence, the coherence can be converted to entanglement. Credit: Streltsov, et al.
In order to be able to do science, we need a way to quantify things. For example, finding a way to quantify "temperature" and "heat" led to the development of thermodynamics.
But how do we quantify "quantumness"? A popular way to measure quantumness is by measuring entanglement. We can say that a bi-partite system is more quantum if it is more entangled. This is justifiable since entanglement can be used as a resource to perform tasks such as dense-coding and device-independent quantum key distribution which would otherwise not be possible.
Lately, several new measures of quantumness have been proposed. They include: discord, negativity of wigner-function, interferometric power and coherence to list a few. A state has "coherence" if it is in a superposition of some classical states. Each of these measures measures a different aspect of quantumness. But they can be interrelated. For example, coherence can be converted to entanglement via incoherent operations.
The aim of this project is to find a relation between some of these measures. We also aim to explore new distance based measures of quantumness and investigate their properties. Specifically, we aim to establish a link between coherence and quantum metrology. A state with high coherence will provide better precision when used for metrology.