2026.03.16_Entropy-Induced_Collapse_III_False-Collapse_Statistics_in_Quantum_Error_Correction_Regimes

Entropy-Induced Collapse (EIC) is a theoretical framework that approaches the quantum measurement problem from the perspective of information recoverability. In the first paper of this series, a structural entropy threshold was introduced to separate regimes in which quantum coherence remains recoverable from those in which the information required to reconstruct coherence becomes effectively inaccessible. The second paper examined the dynamical processes leading toward this threshold, describing how system–environment interactions progressively disperse phase information across environmental degrees of freedom. This third paper investigates how the recoverability structure proposed by the EIC framework manifests in quantum information systems operating under quantum error correction (QEC). In such systems, environmental noise gradually reduces the recoverability of encoded quantum information, while QEC recovery operations attempt to restore coherence. Within this regime, transient events may occur in which quantum coherence appears to collapse locally but remains, in principle, recoverable through appropriate recovery operations. These transient phenomena are referred to as false-collapse events. The paper develops a statistical framework describing how environmental entropy growth, noise processes, and periodic QEC recovery cycles interact to produce such events. By introducing a recoverability function and analyzing entropy-driven information dispersal in open quantum systems, the work derives statistical conditions under which apparent collapse-like behavior may emerge without violating the underlying unitary evolution of the global quantum state. The analysis establishes a conceptual bridge between the foundations of the quantum measurement problem and experimentally accessible quantum information platforms. In particular, the statistical signatures of false-collapse events may be observable in modern quantum processors implementing QEC, such as superconducting qubits, trapped-ion systems, and neutral-atom processors. This paper is Part III of the four-paper Entropy-Induced Collapse series: 1. Structural entropy threshold for collapse 2. Pre-threshold information recoverability dynamics 3. False-collapse statistics in quantum error correction regimes (this paper) 4. Experimental architectures and engineering tests of entropy-based collapse diagnostics