EPR Revisited: Context-Indexed Elements of Reality and Operational Completeness
Mikołaj Sienicki, Krzysztof Sienicki
TL;DR
The paper addresses the EPR paradox by replacing context-free elements of reality with context-indexed conditional states within a GPT-like operational framework. It introduces the Revised Reality Criterion (RRC) and operational completeness, and proves that perfect predictability does not entail context-free, simultaneous predetermined values for incompatible tests. Through a qubit singlet example with CJWR steering, a continuous-variable finite-squeezing Reid criterion, and a PR-box–style one-sided assemblage, it shows that quantum theory sits strictly inside the no-signalling boundary and that PV-like assumptions are not warranted by predictability alone. The work offers practical experimental diagnostics and clarifies the interplay between measurement incompatibility and steering, deepening our understanding of context, locality, and realism in quantum foundations.
Abstract
We reframe the EPR argument through an operational lens, replacing the notion of fixed "elements of reality" with context-indexed conditional states - what's often referred to as a measurement assemblage. This move deliberately sidesteps the assumption of context-independent values for incompatible observables. Our updated version of the Reality Criterion works like this: if Alice measures observable x and obtains outcome a, then Bob's system must adopt a conditional state that ensures the corresponding outcome for that specific context. Crucially, we also assume operational completeness - a condition that quantum mechanics satisfies when we're dealing with quantum-reachable assemblages. Now, in any theory where one party cannot signal to the other (so-called one-sided no-signaling theories), perfect predictions do support drawing context-indexed inferences. But - and this is key - they don't legitimize assigning fixed values across all contexts. We rigorously demonstrate this distinction. To ground the argument, we offer examples: the qubit singlet scenario using Pauli settings and CJWR thresholds, a continuous-variable case based on the Reid criteria, and a counterexample in the spirit of the PR box, which highlights the boundaries of what quantum theory can actually reach.