A Search for Classical Subsystems in Quantum Worlds

Abstract: Decoherence and einselection have been effective in explaining several features of an emergent classical world from an underlying quantum theory. However, the theory assumes a particular factorization of the global Hilbert space into constituent system and environment subsystems, as well as specially constructed Hamiltonians. In this work, we take a systematic approach to discover, given a fixed Hamiltonian, (potentially) several factorizations (or tensor product structures) of a global Hilbert space that admit a quasi-classical description of subsystems in the sense that certain states (the "pointer states") are robust to entanglement. We show that every Hamiltonian admits a pointer basis in the factorization where the energy eigenvectors are separable. Furthermore, we implement an algorithm that allows us to discover a multitude of factorizations that admit pointer states and use it to explore these quasi-classical "realms" for both random and structured Hamiltonians. We also derive several analytical forms that the Hamiltonian may take in such factorizations, each with its unique set of features. Our approach has several implications: it enables us to derive the division into quasi-classical subsystems, demonstrates that decohering subsystems do not necessarily align with our classical notion of locality, and challenges ideas expressed by some authors that the propensity of a system to exhibit classical dynamics relies on minimizing the interaction between subsystems. From a quantum foundations perspective, these results lead to interesting ramifications for relative-state interpretations. From a quantum engineering perspective, these results may be useful in characterizing decoherence free subspaces and other passive error avoidance protocols.

• The paper demonstrates that every Hamiltonian admits a pointer basis where energy eigenvectors are separable.
• The paper employs a variational algorithm and numerical simulations to uncover multiple tensor product structures with quasi-classical properties.
• The paper challenges conventional views by showing that complex system-environment interactions can facilitate the emergence of classicality.

Analyzing Subsystem Identification in Quantum Theory

The paper "A Search for Classical Subsystems in Quantum Worlds" by Arsalan Adil et al. presents a systematic investigation into the identification of quasi-classical subsystems from quantum systems described by a given Hamiltonian. The study hinges on the phenomenon of decoherence and einselection, which have been pivotal in explaining how classical behavior emerges from quantum theory. This work extends these concepts by seeking multiple possible factorizations of a global Hilbert space that can accommodate quasi-classical descriptions. This inquiry is particularly concerned with the derivation of tensor product structures that yield robust pointer states, those resilient to entanglement, thus establishing a notion of classicality.

The paper demonstrates that for any Hamiltonian, a pointer basis can be determined in which the energy eigenvectors are separable. This claim is substantiated through the authors' development and implementation of an algorithm capable of discovering numerous tensor product structures. This algorithm reveals distinct characteristics within the factorization allowing pointer states to emerge, effectively dividing quantum systems into quasi-classical subsystems.

Methodology and Numerical Findings

The methodological approach involves both analytical derivations and numerical simulations using a variational algorithm. The focus is on identifying product states that maintain robustness against entanglement during their evolution under a given Hamiltonian. The study finds that each Hamiltonian inherently supports a pointer basis, indicating separable energy eigenvectors.

The numerical component involves implementing the algorithm across various Hamiltonian classes and initial conditions. Three levels of initial condition complexity are tested: no optimization, system state optimization, and optimization that includes both system and environment states. The numerical search confirms the existence of diverse tensor product structures that accommodate classicality across different Hamiltonians, including central spin models and those characterized by random Hermitian matrices.

Significant Results and Implications

A prominent result is the derivation of a block-diagonal form for Hamiltonians, demonstrating that pointer states are indeed viable across different factorization choices, each with its distinct system-environment interaction features. The inquiry challenges the notion that minimizing subsystem interactions is a necessary criterion for classical behavior emergence, establishing that rich interactions might instead enable this emergence.

The implications of these findings are profound, both theoretically and practically. Theoretically, the work redefines the understanding of subsystems in quantum mechanics, suggesting that classical realities represent just one of many factorizations. Practically, this expanded framework is poised to impact quantum technologies, particularly in optimizing quantum systems by leveraging multiple subsystems and decoherence-free subspaces.

Theoretical and Future Directions

The theoretical impact includes potential challenges to existing quantum mechanics interpretations, specifically those about the preferred basis and the notion of objectivity in the quantum-to-classical transition. The observation of multiple realms coexisting within quantum descriptions offers new insights for interpretations like many-worlds and may influence future discussions on quantum ontological commitments.

Future directions may involve extending this framework to larger systems and multipartite factorization scenarios, enhancing the understanding of quasi-classical realms. Also, the development of measures to quantify or prioritize certain factorizations could advance the practical application of these frameworks in quantum engineering, effectively steering quantum system optimization strategies.

Overall, this paper enriches the discourse on quantum subsystems and their realizations, inviting further exploration into the complex transitions between quantum mechanics and emergent classicality.