Invariant-based entanglement monotones as expectation values and their experimental detection

Abstract

Characterization and quantification of multipartite entanglement is one of the challenges in state-of-the-art experiments in quantum-information processing. According to theory, this is achieved via entanglement monotones, that is, functions that do not increase under stochastic local operations and classical communication (SLOCC). Typically such monotones include the wave function and its time reversal (antilinear-operator formalism) or they are based on not completely positive maps (e.g., partial transpose). Therefore, they are not directly accessible to experimental observations. We show how entanglement monotones derived from polynomial local SL$(2,\phantom{\rule{2.40005pt}{0ex}}\mathrm{width}.04\mathrm{em}\mathrm{height}1.46\mathrm{ex}\mathrm{depth}\ensuremath{-}.07\mathrm{ex}\mathrm{C})$ invariants can be re-written in terms of expectation values of observables. Consequently, the amount of entanglement---of specific SLOCC classes---in a given state can be extracted from the measurement of correlation functions of local operators.