A generalised framework for non-classicality of states

TL;DR

This paper introduces a unified, operational framework for characterizing and quantifying non-classicality in quantum states, applicable to coherence and entanglement in two-level systems.

Contribution

It develops a formalism that systematically constructs and quantifies non-classicality, unifying various existing approaches without ad-hoc definitions.

Findings

Provides a measure of coherence in two-level systems

Demonstrates quantification of pure state entanglement

Offers a systematic approach for non-classicality conditions

Abstract

Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions of non-classicality of states that have been proposed so far. This paper sets up such a formalism. It is based on elementary considerations, free of ad-hoc definitions, and is completely operational. It permits a systematic construction of non-classicality conditions on states and also to quantify the non-classicality, at the same time. This quantification, as shown for the example of two level systems, can serve as a measure of coherence and can be furthermore, harnessed to obtain a measure for pure state entanglement for coupled two level systems.