Operational Quantum Mereology and Minimal Scrambling

Abstract

In this paper we will attempt to answer the following question: what are the natural quantum subsystems which emerge out of a system's dynamical laws? To answer this question we first define generalized tensor product structures (gTPS) in terms of observables, as dual pairs of an operator subalgebra $\mathcal{A}$ and its commutant. Second, we propose an operational criterion of minimal information scrambling at short time scales to dynamically select gTPS. In this way the emergent subsystems are those which maintain the longest informational identity. This strategy is made quantitative by defining a Gaussian scrambling rate in terms of the short-time expansion of an algebraic version of the Out of Time Order Correlation (OTOC) function i.e., the $\mathcal{A}$-OTOC. The Gaussian scrambling rate is computed analytically for physically important cases of general division into subsystems, and is shown to have an intuitive and compelling physical interpretation in terms of minimizing the interaction strength between subsystems.

10+2 pages, 3 figures. Version to appear in Quantum

References in corpus (27)

• Reference frames, superselection rules, and quantum information
• Notes on Some Entanglement Properties of Quantum Field Theory
• Quantum Entanglement in Fermionic Lattices
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Quantum tensor product structures are observable-induced
• A subsystem-independent generalization of entanglement
• Virtual Quantum Subsystems
• Entanglement of Quantum Evolutions
• A Unified and Generalized Approach to Quantum Error Correction
• Stabilizing Quantum Information
• Information Scrambling and Loschmidt Echo
• Three Qubit Randomized Benchmarking
• Holographic Renyi Entropy from Quantum Error Correction
• Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality
• Topological Protection and Quantum Noiseless Subsystems
• Coherence generating power of quantum unitary maps and beyond
• Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics
• Measures of coherence generating power for quantum unital operations
• Quantum coherence as a signature of chaos
• Scrambling of Algebras in Open Quantum Systems
• Quantum coherence and the localization transition
• Suppressing ZZ Crosstalk of Quantum Computers through Pulse and Scheduling Co-Optimization
• Locality from the Spectrum
• Quantum State Reduction: Generalized Bipartitions from Algebras of Observables
• Quantum scrambling of observable algebras
• Quantum Coarse-Graining, Symmetries and Reducibility of Dynamics
• Quantum coherence generating power, maximally abelian subalgebras, and Grassmannian Geometry

Cited by in corpus (6)

• Operator Space Entangling Power of Quantum Dynamics and Local Operator Entanglement Growth in Dual-Unitary Circuits
• Quantum mereology and subsystems from the spectrum
• Quantum speed limit for the OTOC from an open systems perspective
• Holographic phenomenology via overlapping degrees of freedom
• Tensor Product Structure Geometry under Unitary Channels
• A Search for Classical Subsystems in Quantum Worlds