Remarks on Legal Entanglement: No-Signaling, Local Operations, and Legal Updates
Mikołaj Sienicki, Krzysztof Sienicki
TL;DR
The note addresses whether a quantum no-signaling constraint constrains formulative entanglement in a legal-entanglement framework. It shows that no-signaling holds for all local CPTP maps on $A$, not just unitaries, and that the standard Kraus formalism yields $\rho_B' = \rho_B$ when $\rho_{AB}' = (\mathcal{E}_A \otimes \mathrm{Id}_B)(\rho_{AB})$. The critique identifies that the target paper's mapping stems from treating legislation as a local operation on $A$ that changes $\rho_B$ pre-measurement, and proposes two QM-consistent reframings: (i) a global rule/constraint update to the model, and (ii) LOCC-style conditioning with public dissemination. These updates separate physical locality from institutional constraint propagation, and connect to algorithmic-state jurisprudence, clarifying that no-signaling is preserved while preserving the intended legal intuitions. The work thus reframes reformulating entanglement as an informational, non-signaling update in law.
Abstract
Godfrey and Sichelman propose a quantum-inspired framework, legal entanglement, to model coupled legal relations and interpretations, with quantitative proxies for modularity and information cost. We identify a specific technical issue in their account of formulative entanglement: legislation is modeled as a local operation on subsystem A that changes the reduced state of a distant entangled subsystem B (rho_B' != rho_B) prior to any measurement at B, presented as a departure from quantum no-signaling. In standard quantum mechanics, however, no-signaling holds for all local, trace-preserving operations, not only unitaries. This note states the correct no-signaling result, locates where the mapping becomes inconsistent, and proposes a repair that preserves the legal intuition: treat legislation as (i) a global update of the rule or constraint structure (altering the admissible state space or observables), and or (ii) an LOCC-style process (local operations plus public dissemination of authoritative classical information). We also connect this to an updating-first perspective that helps separate (a) physical locality or no-signaling from (b) institutional or semantic constraint propagation in legal systems.