Detecting Entanglement with Partial State Information

TL;DR

This paper presents a sequence of numerical tests capable of detecting entanglement or separability in quantum states using only partial information, such as linear constraints, without requiring full state reconstruction.

Contribution

It introduces a novel method for entanglement detection from partial data, providing certificates for entanglement or separability and bounds on entanglement measures.

Findings

Effective detection of entanglement with incomplete information

Construction of entanglement witnesses from partial data

Provision of separable decompositions when applicable

Abstract

We introduce a sequence of numerical tests that can determine the entanglement or separability of a state even when there is not enough information to completely determine its density matrix. Given partial information about the state in the form of linear constraints on the density matrix, the sequence of tests can prove that either all states satisfying the constraints are entangled, or there is at least one separable state that satisfies them. The algorithm works even if the values of the constraints are only known to fall in a certain range. If the states are entangled, an entanglement witness is constructed and lower bounds on entanglement measures and related quantities are provided; if a separable state satisfies the constraints, a separable decomposition is provided to certify this fact.