Quantum mereology: Factorizing Hilbert space into subsystems with quasiclassical dynamics

Carroll, Sean M.; Singh, Ashmeet

doi:10.1103/physreva.103.022213

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

Abstract

We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any preexisting 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 quasiclassical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their entanglement with the environment does not continually and dramatically increase) and remain localized around approximately classical trajectories. We present an in-principle algorithm for finding such a decomposition by minimizing a combination of entanglement growth and internal spreading of the system. Both of these properties are related to locality in different ways. Furthermore, this formalism is relevant to questions in the foundations of quantum mechanics and the emergence of spacetime from quantum entanglement.

Authors:

Carroll, Sean M. ^[1];

^[1]

California Institute of Technology (CalTech), Pasadena, CA (United States)

Publication Date:: Tue Feb 16 00:00:00 EST 2021

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1833823

Grant/Contract Number:: SC0011632

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review A

Additional Journal Information:: Journal Volume: 103; Journal Issue: 2; Journal ID: ISSN 2469-9926

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Open quantum systems & decoherence; Quantum entanglement; Quantum formalism; Quantum foundations; Quantum theory; Quantum-to-classical transition

Citation Formats


                    Carroll, Sean M., and Singh, Ashmeet. Quantum mereology: Factorizing Hilbert space into subsystems with quasiclassical dynamics.  United States: N. p., 2021. 
Web.  doi:10.1103/physreva.103.022213.

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                    Carroll, Sean M., & Singh, Ashmeet. Quantum mereology: Factorizing Hilbert space into subsystems with quasiclassical dynamics.  United States.  https://doi.org/10.1103/physreva.103.022213

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                    Carroll, Sean M., and Singh, Ashmeet. Tue .  
"Quantum mereology: Factorizing Hilbert space into subsystems with quasiclassical dynamics".  United States.  https://doi.org/10.1103/physreva.103.022213.  https://www.osti.gov/servlets/purl/1833823.

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@article{osti_1833823,

  title        = {Quantum mereology: Factorizing Hilbert space into subsystems with quasiclassical dynamics},

  author       = {Carroll, Sean M. and Singh, Ashmeet},

  abstractNote = {We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any preexisting 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 quasiclassical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their entanglement with the environment does not continually and dramatically increase) and remain localized around approximately classical trajectories. We present an in-principle algorithm for finding such a decomposition by minimizing a combination of entanglement growth and internal spreading of the system. Both of these properties are related to locality in different ways. Furthermore, this formalism is relevant to questions in the foundations of quantum mechanics and the emergence of spacetime from quantum entanglement.},

  doi          = {10.1103/physreva.103.022213},

  journal      = {Physical Review A},

  number       = 2,

  volume       = 103,

  place        = {United States},

  year         = {Tue Feb 16 00:00:00 EST 2021},

  month        = {Tue Feb 16 00:00:00 EST 2021}

}

Copy to clipboard

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

Abstract

Citation Formats

The emergence of classical properties through interaction with the environment journal, June 1985

Uncertainty relation and non-dispersive states in finite quantum mechanics journal, October 1997

Virtual Quantum Subsystems journal, July 2001

Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse? journal, September 1981

Quantum Tensor Product Structures are Observable Induced journal, February 2004

Glimmers of a Pre-geometric Perspective journal, December 2009

Hilbert space structure in quantum gravity: an algebraic perspective journal, December 2015

Quantum state reduction: Generalized bipartitions from algebras of observables journal, March 2020

The stretched horizon and black hole complementarity journal, October 1993

The rise and fall of redundancy in decoherence and quantum Darwinism journal, August 2012

The world as a hologram journal, November 1995

Atom lasers, coherent states, and coherence. I. Physically realizable ensembles of pure states journal, March 2002

Finite-dimensional quantum mechanics of a particle. II journal, May 1982

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

The Ryu–Takayanagi Formula from Quantum Error Correction journal, May 2017

Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance journal, July 2005

Classical World Arising out of Quantum Physics under the Restriction of Coarse-Grained Measurements journal, November 2007

Consistent histories and the interpretation of quantum mechanics journal, July 1984

A general theoretical framework for decoherence in open and closed systems journal, July 2008

Preferred States, Predictability, Classicality and the Environment-Induced Decoherence journal, February 1993

Consciousness as a state of matter journal, July 2015

Decoherence: A Closed-System Approach journal, August 2013

"Relative State" Formulation of Quantum Mechanics journal, July 1957

Quantum Histories journal, January 1998

Environment-induced decoherence, classicality, and consistency of quantum histories journal, September 1993

Locality from the Spectrum journal, February 2019

Unitary Operator Bases journal, April 1960

The Hilbert space of quantum gravity is locally finite-dimensional journal, October 2017

Self-induced decoherence: a new approach journal, March 2004

Quantum-optical Phase and Canonical Conjugation journal, November 1990

Classical dynamics of the quantum harmonic chain journal, November 1999

On the consistent histories approach to quantum mechanics journal, March 1996

Quantum mechanics in finite dimensions journal, October 1976

Bulk entanglement gravity without a boundary: Towards finding Einstein’s equation in Hilbert space journal, April 2018

Space from Hilbert space: Recovering geometry from bulk entanglement journal, January 2017

“A Little Flip Goes a Long Way”—The Impact of a Flipped Classroom Design on Student Performance and Engagement in a First-Year Undergraduate Economics Classroom journal, November 2020

Consciousness as a State of Matter text, January 2014

Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance text, January 2005

Classical Dynamics of the Quantum Harmonic Chain text, January 1999

The emergence of classical properties through interaction with the environment
journal, June 1985

Uncertainty relation and non-dispersive states in finite quantum mechanics
journal, October 1997

Virtual Quantum Subsystems
journal, July 2001

Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?
journal, September 1981

Quantum Tensor Product Structures are Observable Induced
journal, February 2004

Glimmers of a Pre-geometric Perspective
journal, December 2009

Hilbert space structure in quantum gravity: an algebraic perspective
journal, December 2015

Quantum state reduction: Generalized bipartitions from algebras of observables
journal, March 2020

The stretched horizon and black hole complementarity
journal, October 1993

The rise and fall of redundancy in decoherence and quantum Darwinism
journal, August 2012

The world as a hologram
journal, November 1995

Atom lasers, coherent states, and coherence. I. Physically realizable ensembles of pure states
journal, March 2002

Finite-dimensional quantum mechanics of a particle. II
journal, May 1982

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

The Ryu–Takayanagi Formula from Quantum Error Correction
journal, May 2017

Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance
journal, July 2005

Classical World Arising out of Quantum Physics under the Restriction of Coarse-Grained Measurements
journal, November 2007

Consistent histories and the interpretation of quantum mechanics
journal, July 1984

A general theoretical framework for decoherence in open and closed systems
journal, July 2008

Preferred States, Predictability, Classicality and the Environment-Induced Decoherence
journal, February 1993

Consciousness as a state of matter
journal, July 2015

Decoherence: A Closed-System Approach
journal, August 2013

"Relative State" Formulation of Quantum Mechanics
journal, July 1957

Quantum Histories
journal, January 1998

Environment-induced decoherence, classicality, and consistency of quantum histories
journal, September 1993

Locality from the Spectrum
journal, February 2019

Unitary Operator Bases
journal, April 1960

The Hilbert space of quantum gravity is locally finite-dimensional
journal, October 2017

Self-induced decoherence: a new approach
journal, March 2004

Quantum-optical Phase and Canonical Conjugation
journal, November 1990

Classical dynamics of the quantum harmonic chain
journal, November 1999

On the consistent histories approach to quantum mechanics
journal, March 1996

Quantum mechanics in finite dimensions
journal, October 1976

Bulk entanglement gravity without a boundary: Towards finding Einstein’s equation in Hilbert space
journal, April 2018

Space from Hilbert space: Recovering geometry from bulk entanglement
journal, January 2017

“A Little Flip Goes a Long Way”—The Impact of a Flipped Classroom Design on Student Performance and Engagement in a First-Year Undergraduate Economics Classroom
journal, November 2020

Consciousness as a State of Matter
text, January 2014

Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance
text, January 2005

Classical Dynamics of the Quantum Harmonic Chain
text, January 1999