Approximate Decoherence, Recoherence and Records in Isolated Quantum Systems

TL;DR

This paper investigates how approximate decoherence affects the detectability of records in isolated quantum systems, revealing a structure of decoherence, recoherence phenomena, and implications for the Many Worlds Interpretation.

Contribution

It introduces a framework analyzing approximate decoherence's impact on records, and uncovers decoherence structures and recoherence effects through a random matrix model.

Findings

Number of reliable records can be much smaller than possible events depending on decoherence.

Recoherence occurs between histories with small Hamming distance and high purity states.

Decoherence structure explains emergence of Born's rule and the self-location problem.

Abstract

Using the framework of decoherent histories, we study which past events leave detectable records in isolated quantum systems under the realistic assumption that decoherence is approximate and not perfect. In the first part we establish -- asymptotically for a large class of (pseudo-)random histories -- that the number of reliable records can be much smaller than the number of possible events, depending on the degree of decoherence. In the second part we reveal a clear decoherence structure for long histories based on a numerically exact solution of a random matrix model that, as we argue, captures generic aspects of decoherence. We observe recoherence between histories with a small Hamming distance, for localized histories admitting a high purity Petz recovery state, and for maverick histories that are statistical outliers with respect to Born's rule. From the perspective of the Many Worlds Interpretation, the first part -- which views the self-location problem as a coherent version of quantum state discrimination -- reveals a "branch selection problem", and the second part sheds light on the emergence of Born's rule and the theory confirmation problem.