Does the remote measurement disturbance of the quantum state of a system $B$ by a measurement on system $A$ entangled with $B$ constitute a real disturbance, i.e., an objective alteration, of $B$ in an operational sense? Employing information-theoretic criteria motivated by operational considerations alone, we argue that the disturbance in question is real for a subset of steerable correlations. This result highlights the distinction between quantum no-signaling and the relativistic signal locality. It furthermore suggests a natural reason why a convex operational theory should be nonsignaling, namely, to ensure consistency between the properties of reduced systems and those of single systems.
Does the remote measurement disturbance of the quantum state of a system B by a measurement on system A entangled with B constitute a real disturbance, i.e., an objective alteration, of B in an operational sense? Employing information-theoretic criteria motivated by operational considerations alone, we argue that the disturbance in question is real for a subset of steerable correlations. This result highlights the distinction between quantum no-signaling and the relativistic signal locality. It furthermore suggests a natural reason why a convex operational theory should be nonsignaling, namely, to ensure consistency between the properties of reduced systems and those of single systems.
Is the quantum state real? Does the reduction of the state of a quantum system by a measurement on another system, entangled with it and distant, constitute a real disturbance? As is well acknowledged, there is a lack of consensus among physicists over such ontological questions concerning quantum mechanics (QM). Here we argue that it is possible, surprisingly, to address such questions on the basis of only operational considerations. More generally, we show that the operational perspective itself provides an intrinsic interpretation of QM. The theory's syntax supplies its semantics, as it were. This interpretational framework, which we call ``signaling ontology'', builds on the simple insight that unconditional quantum state reduction, namely the state change of a measured quantum system due to a nonselective measurement, can be used for signaling locally, and that this signal provides a natural, operational criterion for the reality of the state reduction. This argument is formalized in the framework of generalized probability theories and extended to multipartite systems. Among other consequences of this approach, the two questions posed above at the beginning are testably answered in the affirmative. In particular, a steering inequality is proposed whose violation, together with a local signaling condition, provides an experimental test for the reality of the remote disturbance referenced in the second question. Accordingly, quantum correlations that meet this criterion are nonlocal in an operationally real sense. A further ramification of our work is an elucidation of the contrast between quantum no-signaling and relativistic signal locality.
An operational concept of locality whose quantum violation is indicated independently of any other assumption(s) seems to be lacking in the quantum foundations literature so far. Bell's theorem only shows that quantum correlations violate the conjunction of the ontological assumptions of localism and determinism. Taking a cue from computational complexity theory, here we define such a concept of locality in terms of a class of operational decision problems, and propose that Einstein-Podolsky-Rosen (EPR) steering in its basic asymmetric formulation gives a specific realization of this class. Various nonclassical (convex) operational theories, including quantum mechanics, are shown to be nonlocal according to this operational criterion. We discuss several ramifications arising from this result. It indicates a basic difference between quantum no-signaling and relativistic no-signaling, and suggests an information theoretic derivation of the former from other basic principles in the convex framework. It elucidates the connection between two different bounds on nonlocality, due to Oppenheim and Wehner (2010) and Banik et al. (2015), thereby highlighting the interplay and contrast between uncertainty and measurement incompatibility. Our result provides an argument supporting the realist interpretation of the quantum state, and helps clarify why Spekkens' toy model (2007) features steering but not Bell nonlocality.
A local measurement on one member of an entangled composite system is said to change the distant member's state instantaneously. Taken without qualification, this is misleading. A selective measurement changes the conditional state assigned to the remote subsystem once a local outcome is specified; a non-selective measurement, where that outcome is ignored, leaves the remote reduced density operator unchanged. This distinction reconciles quantum state update with operational no-signalling and provides the setting for Einstein–Podolsky–Rosen steering. This review develops measurement using density operators, completely positive instruments, Kraus representations, partial traces, conditional states, and steering assemblages. It derives the invariance of remote marginal statistics under local trace-preserving operations and contrasts this with Bell-local factorization. It examines the hierarchy among entanglement, steering, and Bell nonlocality, joint measurability, remote state preparation, and one-sided device-independent protocols. The article considers spacelike-separated measurements, microcausality in relativistic quantum theory, and ontological readings of selective state update offered by Everettian, Bohmian, collapse, and relational approaches. Decoherence is treated as the process through which local outcomes become records, while quantum Darwinism accounts for their redundant local accessibility. It highlights gaps in literature, and concludes that entanglement permits nonclassical conditional correlations, but local measurement supplies no controllable superluminal signal.
In several recent communications (Khrennikov 2019a, b, c, 2020a, b), A. Khrennikov argued for "eliminating the issue of quantum nonlocality" from the analysis of quantum entanglement and quantum phenomena in general. He proposed to differentiate quantum and classical phenomena and entanglement not by their respective nonlocality and locality, as is common, but by the discreteness of quantum phenomena vs. the continuity of classical phenomena, supplemented by Bohr's complementarity in the case of quantum phenomena. As I argue here, however, the question may not be that of "eliminating the issue of quantum nonlocality" but instead of illuminating this issue, a task that can, I also argue, be pursued by relating quantum nonlocality to other key features of quantum phenomena. I suggest that the following features of quantum phenomena and quantum mechanics, distinguishing them from classical phenomena and classical physics--(1) the irreducible role of measuring instruments in defining quantum phenomena; (2) discreteness; (3) complementarity; (4) entanglement; (5) quantum nonlocality; and (6) the irreducibly probabilistic nature of quantum predictions--are all interconnected in defining quantum phenomena and distinguishing them from classical ones, so that it is difficult to give an unconditional priority to any one of them. To argue this case, I consider quantum phenomena and quantum mechanics from a nonrealist or, in terms adopted here, "reality-without-realism" (RWR) perspective. This perspective extends and gives new dimensions to Bohr's view, grounded in his analysis of the irreducible tole of measuring instruments in the constitution of quantum phenomena, with quantum measurement defined by the entanglements between the quantum object under investigation and the instrument used.
What guarantees the "peaceful coexistence" of quantum nonlocality and special relativity? The tension arises because entanglement leads to locally inexplicable correlations between distant events that have no absolute temporal order in relativistic spacetime. This paper identifies a relativistic consistency condition that is weaker than Bell locality but stronger than the no-signaling condition meant to exclude superluminal communication. While justifications for the no-signaling condition often rely on anthropocentric arguments, relativistic consistency is simply the requirement that joint outcome distributions for spacelike separated measurements (or measurement-like processes) must be independent of their temporal order. This is necessary to obtain consistent statistical predictions across different Lorentz frames. We first consider ideal quantum measurements, derive the relevant consistency condition on the level of probability distributions, and show that it implies no-signaling (but not vice versa). We then extend the results to general quantum operations and derive corresponding operator conditions. This will allow us to clarify the relationships between relativistic consistency, no-signaling, and local commutativity. We argue that relativistic consistency is the basic physical principle that ensures the compatibility of quantum statistics and relativistic spacetime structure, while no-signaling and local commutativity can be justified on this basis.
According to the no-signaling theorem, the nonlocal collapse of the wavefunction of an entangled particle by the measurement on its twin particle at a remote location cannot be used to send useful information. Given that experiments on nonlocal correlations continue to have loopholes, we propose a stronger principle that the nonlocality of quantum mechanics itself is veiled. In practical terms, decoherence and noise compels us to view the wavefunction as representing knowledge of potential outcomes rather than the reality. Experimental evidence in favor of naked nonlocality would support the view of the wavefunction as an objective description of physical reality.