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W-States have achieved the status of the standard fully symmetric entangledstates, for many entanglement application purposes. Z-States are ageneralization of W-States that display an elegant algebra, enabling shortpaths to desired results. This paper describes Z-States algebra starting fromneat definitions and laying down explicitly some fundamental theorems oncomposition and distillation, needed for applications. These theorems aresynthesized into a generic tunable Entanglement-Distillation Protocol.Applications are readily developed based upon the tunable protocol. A fewexamples are provided to illustrate the approach generality. A concomitantgraphical representation allows fast comprehension of the protocol inputs,operations and outcomes.

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