The LU-LC Conjecture is False

摘要

The LU-LC conjecture is an important open problem concerning the structure of entanglement in the stabilizer formalism. It states that two stabilizer states equivalent under local unitaries are also equivalent under local Clifford operations. If true, local equivalence of stabilizer states would admit a simple characterization. Unfortunately, building on progress by Gross and Van den Nest, we show that the conjecture is false. A preliminary version appeared in The 11th Workshop on Quantum Information Processing (QIP 2007).