Concentratable Entanglement: Determining the entanglement of multipartite states with parallelized operations

Abstract

Entanglement is a vital resource in quantum computation and information. In general, the amount of entanglement in a state determines its usefulness. The standard methods for detecting and characterising quantum entanglement are either resource intensive or require prior knowledge of the state in question. We extend the two-qubit pure state entanglement measure concurrence to the multipartite entanglement measure Concentratable Entanglement (CE) and provide two efficient
methods of experimentally estimating it, the Bell-basis test and the controlled SWAP test, the output probabilities of which are related to the CE and purity of the input ensemble state. We show these results are robust to small variations in the input states and are therefore suitable for experimental estimation. The Bell-basis test can be achieved experimentally on multipartite states with current hardware with number of trials at maximum according to Hoeffding’s inequality, and is particularly suited to larger (n > 3) multipartite states. Unlike many other multipartite measures, Concentratable Entanglement (CE) has a simple form, can be directly estimated from experiment, and can be used for mixed states; therefore, we present CE as a standard entanglement measure for multipartite states.