The tensor rank of tensor product of two three-qubit W states is eight

TL;DR

This paper determines the exact tensor rank of the tensor product of two three-qubit W states as eight, providing a precise measure of their complexity in quantum information theory.

Contribution

It establishes the exact tensor rank of the tensor product of two three-qubit W states as eight, resolving a key open problem.

Findings

Tensor rank of the tensor product of two three-qubit W states is exactly eight.

Constructs an upper bound for the tensor rank of multiple three-qubit W states.

Confirms the tensor rank matches the previously known upper bound.

Abstract

We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.