Applied Quantum Foundations

Although entangled state vectors do not have a representation in terms of localized variables, any given entanglement experiment can be built up from basic quantum circuit components with well-defined locations.  By analyzing the local (post-selected) weak values for any given run of any circuit, one can find evidence for a localized account of the circuit's actual behavior.  Specifically, the local weak values only change at their local circuit elements, even if the state is massively entangled.  More surprisingly, when two qubits are brought together in an exchange interaction, their local weak values evolve according to a simple classical equation.  For each gate in a set of universal quantum gates, a globally-constrained [1] model inspired by this analysis can generate local weak values without using state vectors as an intermediate step.  This evidence all supports the claim that any quantum circuit can plausibly be underpinned by localized variables, a result that would be of crucial importance to quantum foundations.

 

[1] See K. Wharton and N. Argaman, Rev. Mod. Phys. v92 021002 (2020) for a detailed account of how Bell/CHSH-inequality violations occur in models where the future settings act as constraints on the entire history, which must then be solved globally, or "all at once", as in action principles.