Z-States Algebra for a Tunable Multi-Party Entanglement-Distillation Protocol

Abstract: W-States have achieved the status of the standard fully symmetric entangled states, for many entanglement application purposes. Z-States are a generalization of W-States that display an elegant algebra, enabling short paths to desired results. This paper describes Z-States algebra starting from neat definitions and laying down explicitly some fundamental theorems on composition and distillation, needed for applications. These theorems are synthesized into a generic tunable Entanglement-Distillation Protocol. Applications are readily developed based upon the tunable protocol. A few examples are provided to illustrate the approach generality. A concomitant graphical representation allows fast comprehension of the protocol inputs, operations and outcomes.