Multipartite subspaces containing no locally inaccessible information

Abstract

One notion of non-locality in quantum theory is the fact that information may be encoded in a composite system in such a way that it is not accessible through local measurements, even with the assistance of classical communication. Thus, contrary to the classical case, there exists information in quantum many body systems which cannot be accessed locally. We show however that, remarkably, two-dimensional subspaces do not have this property: any physically allowed measurement on information encoded in any two-dimensional subspace, regardless of entanglement or multi-partite structure, may be performed locally. Further, this requires only local measurement and feed-forward of classical information, readily achievable in many experimental platforms. As an application to quantum secret sharing we suggest a twist on a well known quantum information splitting protocol, which ensures that no receiving party ever has access to the full state sent, but parties must work together to perform measurements on the state. These results may have practical applications to the measurement of encoded qubits in e.g. quantum secret sharing, quantum error correction, and reveal a fundamental property unique to two-dimensional subspaces.

Taxonomy for physics beyond quantum mechanics

“…Even in quantum foundations, non-locality may refer to different properties. For example, entanglement itself is sometimes considered non-local despite being locally created [35]. The latter in particular has created a lot of confusion, because while it has been experimentally shown that entanglement is a non-local correlation and does in fact exist, this does not imply that nature is non-local in the sense that the term has been used in Bell’s theorem, which has of course not been shown [36].…”