Non-local measurements

F. de Felice, Donato Bini

Aharon Brodutch, Lev Vaidman A

Some recent attempts at measuring non local weak values via local measurements are discussed and shown to be less robust than standard weak measurements. A method for measuring some non local weak values via non local measurements (non local weak measurements) is introduced. The meaning of non local weak values is discussed.

Aharon Brodutch, Eliahu Cohen

We present a scheme to generate an effective interaction Hamiltonian for systems that cannot interact directly and show how it can be used in scenarios such as non-local measurements and photon-photon interactions.

Lev Vaidman A

Fedor Herbut, Milan Vujičić

Tommaso Brambilla, Alessandro Tosini, Paolo Perinotti

The formulation of quantum measurements compatible with relativistic causality is obstructed by the tension between the locality of observable algebras and the dynamical state transformations induced by measurement processes. We develop a local measurement theory for quantum cellular automata, lattices of finite-dimensional quantum systems with a causal reversible dynamics evolving in discrete time steps. Measurement processes are described by localized completely positive maps and organized into operational measurement protocols, finite non-adaptive sequences of local instruments distributed across the causal cone induced by the automaton local dynamics. Each protocol induces an effective measurement on the initial time slice, whose support is constrained by the causal structure generated by the automaton. Non-local measurement effects therefore arise through causal propagation and composition of local operations, rather than from primitive non-local interventions or instantaneous collapse prescriptions. We establish the corresponding spatial support bounds and characterize the resulting measurement architecture. As an explicit example, we construct a two-step protocol for a one-dimensional nearest-neighbour qubit automaton which, for suitable automaton parameters, realizes a Bell-basis projective measurement on two neighbouring sites after coarse-graining of the local outcomes. Away from this point, the same protocol generates a continuous family of deformed Bell measurements whose entanglement and stabilizer Rényi non-classicality can be quantified explicitly. The framework thus provides a causally consistent operator-algebraic mechanism for synthesizing spatially extended quantum measurements from strictly local operations.