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Ignorance is strength: Quantum measurements in a non-local world

In quantum theory we often use the term 'observable' interchangeably with 'Hermitian operator'. However, not all Hermitian operators correspond to quantities that can be `observed' in the usual quantum mechanical sense, i.e a projective measurement.  Causality, the finite speed of light, and measurement-disturbance relations, impose constraint on the types of non-local observables that can be measured without additional resources such as communication (i.e time) and/or entanglement.  Unfortunately, there are no generic methods to identify and quantify the types of resources necessary to measure a specific non-local observable while maintaining ignorance about the local properties.  I will present a number of cases where the resource requirements are surprising, and present one probabilistic protocol for an instantaneous measurement of an important class of observables.