You can't test if quantum uses complex numbers
20 hours ago
- #entanglement
- #quantum mechanics
- #complex numbers
- Renou et al's 2021 paper in Nature claimed that quantum theory based on real numbers can be experimentally falsified.
- The paper's core idea was to distinguish between quantum mechanics using complex numbers (CHMT gateset) and a restricted version using only real numbers (CHM gateset).
- The author argues that the paper is wrong because it fails to account for the possibility of pre-shared entanglement, which can spoof the test.
- A spoofing method is proposed using phase gradient states and phase kickback to emulate complex-number behavior with real-only operations.
- The mistake in Renou et al's paper lies in assuming that the real-only quantum players start without any pre-shared entangled states.
- The author criticizes the paper for burying this critical caveat deep in the supplementary materials rather than highlighting it prominently.