A quantum mechanical theory of local observables and local operations

Dennis Dieks

In relativistic quantum field theory the notion of a local operation is regarded as basic: each open space-time region is associated with an algebra of observables representing possible measurements performed within this region. It is much more difficult to accommodate the notions of events taking place in such regions or of localized objects. But how can the notion of a local operation be basic in the theory if this same theory would not be able to represent localized measuring devices and localized events? After briefly reviewing these difficulties we discuss a strategy for eliminating the tension, namely by interpreting quantum theory in a realist way. To implement this strategy we use the ideas of the modal interpretation of quantum mechanics. We then consider the question of whether the resulting scheme can be made Lorentz invariant.

K.Kong Wang, Tony Jackson

Xiongfeng Ma

Quantum measurement resolves a superposition into a definite outcome by correlating it with an observer's memory -- a reality register. While the global quantum state remains coherent, the observer's local reality becomes singular and definite. This work introduces reality steering, a protocol that allows an observer to probabilistically access a different reality already supported by the initial quantum state, without reversing decoherence on the environment. The mechanism relies on locally erasing the 'which-outcome' information stored in the observer's brain. Here, 'local' means operations confined to the observer's memory, excluding the environment, which may be cosmically large. Reality steering nevertheless faces intrinsic constraints: successful navigation requires coherent participation from the observer's counterparts across the relevant branches, and any transition is operationally indistinguishable from non-transition. After arriving in a new reality, all memory records are perfectly consistent with that reality, leaving no internal evidence that a switch occurred. This makes conscious confirmation impossible within standard quantum mechanics. We show that nonlinear operations beyond the standard theory could, in principle, enable verifiable and deliberate navigation. Our results shift multi-reality exploration from philosophical speculation toward a concrete -- though fundamentally constrained -- quantum-informational framework.

Carlos Lopez

Lea Krämer, Lídia del Rio

Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here, we propose exploring the opposite direction: to take agents as the basic building blocks through which we test a physical theory, and recover operational notions of locality from signalling conditions. First, we introduce an operational model for the effective state spaces of individual agents, as well as the range of their actions. We then formulate natural secrecy conditions between agents and identify the aspects of locality relevant for signalling. We discuss the possibility of taking commutation of transformations as a primitive of physical theories, as well as applications to quantum theory and generalized probability frameworks. This 'it from bit' approach establishes an operational connection between local actions and local observations, and gives a global interpretation to concepts like discarding a subsystem or composing local functions.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

Lawrence J. Landau