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Non-local observables play an important role in quantum theory, from Bell inequalities and various post-selection paradoxes to quantum error correction codes. Instantaneous measurement of these observables is known to be a difficult…

Relativity theory severely restricts the ability to perform nonlocal measurements in quantum mechanics. Studying such nonlocal schemes may thus reveal insights regarding the relations between these two fundamental theories. Therefore, for…

This article reviews six historically important papers in the development of the theory of measurement for nonlocal variables in quantum mechanics, with special emphasis the non violation of relativistic causality. Spanning more than…

We report the first implementation of the von Neumann instantaneous measurements of nonlocal variables which becomes possible due to technological achievements in creating hyperentangled photons. Tests of reliability and of the…

In this paper we reconsider the constraints which are imposed by relativistic requirements to any model of dynamical reduction. We review the debate on the subject and we call attention on the fundamental contributions by Aharonov and…

Naive attempts to put together relativity and quantum measurements lead to signaling between space-like separated regions. In QFT, these are known as impossible measurements. We show that the same problem arises in non-relativistic quantum…

Measuring a nonlocal observable on a space-like separated quantum system is a resource-hungry and experimentally challenging task. Several theoretical measurement schemes have already been proposed to increase its feasibility, using a…

In quantum mechanical bipartite systems, naive extensions of von Neumann's projective measurement to nonlocal variables can produce superluminal signals and thus violate causality. We analyze the projective quantum nondemolition…

We report results of an investigation of relativistic causality constraints on the measurability of nonlocal variables. We show that measurability of certain nondegenerate variables with entangled eigenstates contradicts the principle of…

Relativistic causality has dramatic consequences on the measurability of nonlocal variables and poses the fundamental question of whether it is physically meaningful to speak about the value of nonlocal variables at a particular time.…

The fact that not all quantum observables are jointly measurable is one of the major differences between quantum and classical theory. In the former, non-commuting observables can only be simultaneously measured with limited precision. We…

A well-recognised open conceptual problem in relativistic quantum field theory concerns the relation between measurement and causality. Naive generalisations of quantum measurement rules can allow for superluminal signalling ('impossible…

Although nondemolition, reliable, and instantaneous quantum measurements of some nonlocal variables are impossible, demolition reliable instantaneous measurements are possible for all variables. It is shown that this is correct also in the…

Instantaneous measurements of non-local observables between space-like separated regions can be performed without violating causality. This feat relies on the use of entanglement. Here we propose novel protocols for this task and the…

It is shown, under the assumption of possibility to perform an arbitrary local operation, that all nonlocal variables related to two or more separate sites can be measured instantaneously, except for a finite time required for bringing to…

We provide a framework and explicit construction for the regularized measurement of a large class of spacetime-localized observables in bosonic quantum field theory. The measurements fully satisfy relativistic causality and causal…

Consequences of relativistic causality for measurements of nonlocal characteristics of composite quantum systems are investigated. It is proved that verification measurements of entangled states necessarily erase local information. A…

The direct measurement of nonlocal properties of entangled quantum systems has been the subject of several recent experimental investigations. Of particular interest is the implementation of nonlocal measurements via indirect measurement…

The conflict between relativistic causality and localizability is analyzed in the light of the existence of unsharp localization observables. A theorem due to S. Schlieder is generalized, showing that the assumption of local commutativity…

Consistency with relativistic causality narrows down dramatically the class of measurable observables. We argue that by weakening the preparation role of ideal measurements, many of these observables become measurable. Particularly, we show…