On Locality of Quantum Information in the Heisenberg Picture for Arbitrary States

Abstract: The locality issue of quantum mechanics is a key issue to a proper understanding of quantum physics and beyond. What has been commonly emphasized as quantum nonlocality has received an inspiring examination through the notion of Heisenberg picture of quantum information. Deutsch and Hayden established a local description of quantum information in a setting of quantum information flow in a system of qubits. With the introduction of a slightly modified version of what we call the Deutsch-Hayden matrix values of observables, together with our recently introduced parallel notion of the noncommutative values from a more fundamental perspective, we clarify all the locality issues based on such values as quantum information carried by local observables in any given arbitrary state of a generic composite system. Quantum information as the {\em `quantum' values} of observables gives a transparent conceptual picture of all the. Spatial locality for a projective measurement is also discussed. The pressing question is if and how such information for an entangled system can be retrieved through local processes which can only be addressed with new experimental thinking.