Minimal tomography with entanglement witnesses

TL;DR

This paper presents a method for minimal quantum state tomography using entanglement witnesses, enabling efficient detection of entanglement with fewer measurements in high-dimensional systems.

Contribution

It introduces a systematic construction of informationally complete measurements based on entanglement witnesses, optimizing the measurement process for entanglement detection.

Findings

Witness-based measurements can exponentially improve efficiency in high dimensions

The method reduces the number of measurements needed for entanglement detection

Illustrated with a two-qubit example

Abstract

We introduce informationally complete measurements whose outcomes are entanglement witnesses and so answer the question of how many witnesses need to be measured to decide whether an arbitrary state is entangled or not: as many as the dimension of the state space. The optimized witness-based measurement can provide exponential improvement with respect to witness efficiency in high-dimensional Hilbert spaces, at the price of a reduction in the tomographic efficiency. We describe a systematic construction, and illustrate the matter at the example of two qubits.