# Quantum mereology: Factorizing Hilbert space into subsystems with quasiclassical dynamics

@article{Carroll2021QuantumMF, title={Quantum mereology: Factorizing Hilbert space into subsystems with quasiclassical dynamics}, author={S. Carroll and Ashmeet Singh}, journal={Physical Review A}, year={2021}, volume={103}, pages={022213} }

We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system" and "environment." Such a decomposition can be defined by looking for subsystems that exhibit quasi-classical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their… Expand

#### 9 Citations

Quantum decimation in Hilbert space: Coarse graining without structure

- Mathematics, Physics
- 2018

We present a technique to coarse grain quantum states in a finite-dimensional Hilbert space. Our method is distinguished from other approaches by not relying on structures such as a preferred… Expand

Reality as a Vector in Hilbert Space

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- 2021

I defend the extremist position that the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schrödinger equation. The laws of physics are determined… Expand

Towards space from Hilbert space: finding lattice structure in finite-dimensional quantum systems

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- 2018

Field theories place one or more degrees of freedom at every point in space. Hilbert spaces describing quantum field theories, or their finite-dimensional discretizations on lattices, therefore have… Expand

Decomposition of a Quantum System Into Subsystems in Finite Quantum Mechanics

- Computer Science, Physics
- ArXiv
- 2021

A simple tractable model for a constructive study of decompositions of quantum systems is proposed and it is shown that any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. Expand

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- Mathematics
- 2020

We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories,… Expand

Quantum state reduction: Generalized bipartitions from algebras of observables

- Physics, Mathematics
- 2019

Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward… Expand

3D-Space and the preferred basis cannot uniquely emerge from the quantum structure

- Physics, Mathematics
- 2021

Is it possible that only the state vector exists, and the 3D-space, a preferred basis, a preferred factorization of the Hilbert space, and everything else, emerge uniquely from the Hamiltonian and… Expand

Quantum scrambling of observable algebras

- Physics
- 2021

In this paper we describe an algebraic/geometrical approach to quantum scrambling. Generalized quantum subsystems are described by a ∗-closed unital subalgebra A of operators evolving through a… Expand

Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method

- Physics, Mathematics
- 2020

We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories,… Expand

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