Partition rank of tensor products of GHZ states across different partitions

Determine the partition rank, with respect to specified alternative sets of partitions, of a tensor product of GHZ states that is separable along one given partition.

Background

The paper concludes by translating an open problem from the mathematical literature into quantum-information-theoretic language. The proposed setting begins with a state formed as a tensor product of GHZ states along one partition and asks how its partition rank behaves when evaluated with respect to other partition sets.

This problem generalizes the preceding four-party example involving two maximally entangled pairs and is presented as a direction for future work. Unlike a generic research aspiration, the passage states a concrete unresolved question.