Quantum / CONCEPT

A state stabilized by binary operators that is not locally a stabilizer state

The six-qubit state v = sum over j of (|e_j> - |complement of e_j>) is, up to a factor, the only common +1 eigenvector of four tensor products of binary operators, yet no Pauli stabilizer state is locally equivalent to it. This refutes the conjecture of E. Descamps and B. Dakic (arXiv:2309.09815) that every state stabilized by binary operators and the identity is locally equivalent to a standard stabilizer state.