Entanglement Detection with Fewer Measurements based on the Geometric Criterion

TL;DR

This paper introduces a geometric criterion-based method for entanglement detection that reduces the number of measurements needed, using local Pauli measurements and a heuristic reinterpretation of existing algorithms, effective for small to medium qubit systems.

Contribution

It presents a new entanglement detection technique that minimizes measurements, is easy to implement, and works without prior system knowledge for any number of qubits.

Findings

Fewer measurements required for 3-6 qubits compared to existing algorithms.

Method is simple to construct and does not need prior system information.

Effective for any number of qubits, demonstrated via numerical simulations.

Abstract

We present a new technique to reduce the expected number of measurements to declare an unknown quantum state as entangled. Our method is based on the geometric criterion and so requires only local Pauli measurements. Using concentration of measure, we provide a heuristic which allows us to reinterpret a previous decision tree algorithm due to Laskowski et al and that forms the basis for our new algorithm. Numerical simulations show that for three to six qubits we use fewer measurements than either the trivial algorithm or the decision tree algorithm. In addition, our method is easy to construct, assumes no prior knowledge of the system and works for any number of qubits.