Superdensity operators for spacetime quantum mechanics
Abstract
We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space techniques and Dirac’s transformation theory as traditionally applied to standard density operators. Superdensity operators can be measured experimentally, but accessing their full content requires novel procedures. We demonstrate these statements on several examples. The superdensity formalism suggests useful definitions of spacetime entropies and spacetime quantum channels. For example, we show that the von Neumann entropy of a super-density operator is related to a quantum generalization of the Kolmogorov-Sinai entropy, and compute this for a many-body system. Here, we also suggest experimental protocols for measuring spacetime entropies.
- Authors:
-
- Stanford Univ., Stanford, CA (United States). Stanford Inst. for Theoretical Physics
- Microsoft Research, Santa Barbara, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. of Theoretical Physics
- Stanford Univ., Stanford, CA (United States). Stanford Inst. for Theoretical Physics; Inst. for Advanced Study, Princeton, NJ (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics; Stockholm Univ., Stockholm (Sweden). The Oskar Klein Centre for Cosmoparticle Physics; Shanghai Jiao Tong Univ., Shanghai (China). T. D. Lee Inst. and Wilczek Quantum Center; Arizona State Univ., Tempe, AZ (United States). Dept. of Physics and Origins Project
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1499044
- Grant/Contract Number:
- SC0012567
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 9; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Space-Time Symmetries; Lattice Quantum Field Theory
Citation Formats
Cotler, Jordan, Jian, Chao -Ming, Qi, Xiao -Liang, and Wilczek, Frank. Superdensity operators for spacetime quantum mechanics. United States: N. p., 2018.
Web. doi:10.1007/jhep09(2018)093.
Cotler, Jordan, Jian, Chao -Ming, Qi, Xiao -Liang, & Wilczek, Frank. Superdensity operators for spacetime quantum mechanics. United States. https://doi.org/10.1007/jhep09(2018)093
Cotler, Jordan, Jian, Chao -Ming, Qi, Xiao -Liang, and Wilczek, Frank. Mon .
"Superdensity operators for spacetime quantum mechanics". United States. https://doi.org/10.1007/jhep09(2018)093. https://www.osti.gov/servlets/purl/1499044.
@article{osti_1499044,
title = {Superdensity operators for spacetime quantum mechanics},
author = {Cotler, Jordan and Jian, Chao -Ming and Qi, Xiao -Liang and Wilczek, Frank},
abstractNote = {We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space techniques and Dirac’s transformation theory as traditionally applied to standard density operators. Superdensity operators can be measured experimentally, but accessing their full content requires novel procedures. We demonstrate these statements on several examples. The superdensity formalism suggests useful definitions of spacetime entropies and spacetime quantum channels. For example, we show that the von Neumann entropy of a super-density operator is related to a quantum generalization of the Kolmogorov-Sinai entropy, and compute this for a many-body system. Here, we also suggest experimental protocols for measuring spacetime entropies.},
doi = {10.1007/jhep09(2018)093},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2018,
place = {United States},
year = {Mon Sep 17 00:00:00 EDT 2018},
month = {Mon Sep 17 00:00:00 EDT 2018}
}
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Works referenced in this record:
Building up spacetime with quantum entanglement
journal, June 2010
- Van Raamsdonk, Mark
- General Relativity and Gravitation, Vol. 42, Issue 10
A cold-atom Fermi–Hubbard antiferromagnet
journal, May 2017
- Mazurenko, Anton; Chiu, Christie S.; Ji, Geoffrey
- Nature, Vol. 545, Issue 7655
Building up Space–Time with Quantum Entanglement
journal, December 2010
- Van Raamsdonk, Mark
- International Journal of Modern Physics D, Vol. 19, Issue 14
Robustness of dynamical entropy
journal, February 2005
- Fannes, M.; Haegeman, B.; Vanpeteghem, D.
- Journal of Physics A: Mathematical and General, Vol. 38, Issue 10
Mathematical Methods of Classical Mechanics
book, January 1989
- Arnold, V. I.
- Graduate Texts in Mathematics
Measuring Entanglement Entropy of a Generic Many-Body System with a Quantum Switch
journal, July 2012
- Abanin, Dmitry A.; Demler, Eugene
- Physical Review Letters, Vol. 109, Issue 2
Entangled histories: Unravelling the impact of colonial connections of both Javanese and Dutch women’s work and household labour relations, c. 1830-1940
journal, March 2017
- van Nederveen Meerkerk, Elise
- Tijdschrift voor Genderstudies, Vol. 20, Issue 1
Measuring Entanglement Growth in Quench Dynamics of Bosons in an Optical Lattice
journal, July 2012
- Daley, A. J.; Pichler, H.; Schachenmayer, J.
- Physical Review Letters, Vol. 109, Issue 2
An Algebraic Approach to the Kolmogorov-Sinai Entropy
journal, February 1996
- Alicki, R.; Andries, J.; Fannes, M.
- Reviews in Mathematical Physics, Vol. 08, Issue 02
Topos theory and consistent histories: The internal logic of the set of all consistent sets
journal, April 1997
- Isham, C. J.
- International Journal of Theoretical Physics, Vol. 36, Issue 4
Gravitational dynamics from entanglement “thermodynamics”
journal, April 2014
- Lashkari, Nima; McDermott, Michael B.; Van Raamsdonk, Mark
- Journal of High Energy Physics, Vol. 2014, Issue 4
Quantum Computation and Quantum Information
book, January 2011
- Nielsen, Michael A.; Chuang, Isaac L.
- Cambridge University Press
Theoretical framework for quantum networks
journal, August 2009
- Chiribella, Giulio; D’Ariano, Giacomo Mauro; Perinotti, Paolo
- Physical Review A, Vol. 80, Issue 2
Gauge theory correlators from non-critical string theory
journal, May 1998
- Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M.
- Physics Letters B, Vol. 428, Issue 1-2
Measurement Protocol for the Entanglement Spectrum of Cold Atoms
journal, November 2016
- Pichler, Hannes; Zhu, Guanyu; Seif, Alireza
- Physical Review X, Vol. 6, Issue 4
The spectrum in the Sachdev-Ye-Kitaev model
journal, April 2016
- Polchinski, Joseph; Rosenhaus, Vladimir
- Journal of High Energy Physics, Vol. 2016, Issue 4
Optimal Quantum Tomography
journal, January 2009
- Bisio, A.; Chiribella, G.; D'Ariano, G. M.
- IEEE Journal of Selected Topics in Quantum Electronics, Vol. 15, Issue 6
Consistent interpretation of quantum mechanics using quantum trajectories
journal, April 1993
- Griffiths, Robert B.
- Physical Review Letters, Vol. 70, Issue 15
Consistent histories and the interpretation of quantum mechanics
journal, July 1984
- Griffiths, Robert B.
- Journal of Statistical Physics, Vol. 36, Issue 1-2
Continuous histories and the history group in generalized quantum theory
journal, October 1995
- Isham, C. J.; Linden, N.
- Journal of Mathematical Physics, Vol. 36, Issue 10
Quantum dynamical entropy and decoherence rate
journal, April 2004
- Alicki, Robert; ozi ski, Artur; Pako ski, Prot
- Journal of Physics A: Mathematical and General, Vol. 37, Issue 19
Anti de Sitter space and holography
journal, January 1998
- Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2
Experimental test of entangled histories
journal, December 2017
- Cotler, Jordan; Duan, Lu-Ming; Hou, Pan-Yu
- Annals of Physics, Vol. 387
Time Symmetry in the Quantum Process of Measurement
journal, June 1964
- Aharonov, Yakir; Bergmann, Peter G.; Lebowitz, Joel L.
- Physical Review, Vol. 134, Issue 6B
Emergence and Frustration of Magnetism with Variable-Range Interactions in a Quantum Simulator
journal, May 2013
- Islam, R.; Senko, C.; Campbell, W. C.
- Science, Vol. 340, Issue 6132
Quantum causal modelling
journal, June 2016
- Costa, Fabio; Shrapnel, Sally
- New Journal of Physics, Vol. 18, Issue 6
Mathematical methods of classical mechanics
journal, March 1990
- Rota, Gian-Carlo
- Advances in Mathematics, Vol. 80, Issue 1
Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet
journal, May 2017
- Gärttner, Martin; Bohnet, Justin G.; Safavi-Naini, Arghavan
- Nature Physics, Vol. 13, Issue 8
Multiple-time states and multiple-time measurements in quantum mechanics
journal, May 2009
- Aharonov, Yakir; Popescu, Sandu; Tollaksen, Jeff
- Physical Review A, Vol. 79, Issue 5
Extending the lifetime of a quantum bit with error correction in superconducting circuits
journal, July 2016
- Ofek, Nissim; Petrenko, Andrei; Heeres, Reinier
- Nature, Vol. 536, Issue 7617
Measuring multipartite entanglement through dynamic susceptibilities
journal, March 2016
- Hauke, Philipp; Heyl, Markus; Tagliacozzo, Luca
- Nature Physics, Vol. 12, Issue 8
Probing many-body dynamics on a 51-atom quantum simulator
journal, November 2017
- Bernien, Hannes; Schwartz, Sylvain; Keesling, Alexander
- Nature, Vol. 551, Issue 7682
Relative entropy equals bulk relative entropy
journal, June 2016
- Jafferis, Daniel L.; Lewkowycz, Aitor; Maldacena, Juan
- Journal of High Energy Physics, Vol. 2016, Issue 6
The gravity dual of a density matrix
journal, July 2012
- Czech, Bartłomiej; Karczmarek, Joanna L.; Nogueira, Fernando
- Classical and Quantum Gravity, Vol. 29, Issue 15
The operator tensor formulation of quantum theory
journal, July 2012
- Hardy, Lucien
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 370, Issue 1971
Area Laws in Quantum Systems: Mutual Information and Correlations
journal, February 2008
- Wolf, Michael M.; Verstraete, Frank; Hastings, Matthew B.
- Physical Review Letters, Vol. 100, Issue 7
Quantum correlations which imply causation
journal, December 2015
- Fitzsimons, Joseph F.; Jones, Jonathan A.; Vedral, Vlatko
- Scientific Reports, Vol. 5, Issue 1
Defining quantum dynamical entropy
journal, September 1994
- Alicki, R.; Fannes, M.
- Letters in Mathematical Physics, Vol. 32, Issue 1
Efficient quantum tomography
conference, January 2016
- O'Donnell, Ryan; Wright, John
- Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2016
A bound on chaos
journal, August 2016
- Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
- Journal of High Energy Physics, Vol. 2016, Issue 8
The Interpretation of Quantum Mechanics
conference, January 2009
- Stenholm, Stig; Accardi, Luigi; Adenier, Guillaume
- FOUNDATIONS OF PROBABILITY AND PHYSICS—5, AIP Conference Proceedings
Cool horizons for entangled black holes
journal, August 2013
- Maldacena, J.; Susskind, L.
- Fortschritte der Physik, Vol. 61, Issue 9
Quantum temporal logic and decoherence functionals in the histories approach to generalized quantum theory
journal, October 1994
- Isham, C. J.; Linden, N.
- Journal of Mathematical Physics, Vol. 35, Issue 10
The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999
- Maldacena, Juan
- International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133
Operational formulation of time reversal in quantum theory
journal, July 2015
- Oreshkov, Ognyan; Cerf, Nicolas J.
- Nature Physics, Vol. 11, Issue 10
Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006
- Ryu, Shinsei; Takayanagi, Tadashi
- Physical Review Letters, Vol. 96, Issue 18
The Quantum Mechanics of Cosmology
conference, January 2014
- Hartle, James B.
- Proceedings of the 7th Jerusalem Winter School for Theoretical Physics, Quantum Cosmology and Baby Universes
Quantum networks: General theory and applications
journal, June 2011
- Bisio, A.; Chiribella, G.; D'Ariano, G.
- Acta Physica Slovaca. Reviews and Tutorials, Vol. 61, Issue 3
14-Qubit Entanglement: Creation and Coherence
journal, March 2011
- Monz, Thomas; Schindler, Philipp; Barreiro, Julio T.
- Physical Review Letters, Vol. 106, Issue 13
An Introduction to Operational Quantum Dynamics
journal, December 2017
- Milz, Simon; Pollock, Felix A.; Modi, Kavan
- Open Systems & Information Dynamics, Vol. 24, Issue 04
Non-Markovian quantum stochastic processes and their entropy
journal, October 1979
- Lindblad, G�ran
- Communications in Mathematical Physics, Vol. 65, Issue 3
Many-body chaos at weak coupling
journal, October 2016
- Stanford, Douglas
- Journal of High Energy Physics, Vol. 2016, Issue 10
Interpretation of quantum mechanics
journal, November 1987
- Omnès, Roland
- Physics Letters A, Vol. 125, Issue 4
Generalized gravitational entropy
journal, August 2013
- Lewkowycz, Aitor; Maldacena, Juan
- Journal of High Energy Physics, Vol. 2013, Issue 8
Mathematical methods of classical mechanics
journal, July 1983
- Rota, Gian-Carlo
- Advances in Mathematics, Vol. 49, Issue 1
The Interpretation of Quantum Mechanics
journal, July 1995
- Omnes, Roland; Scalettar, Richard
- Physics Today, Vol. 48, Issue 7
Characteristic Lyapunov Exponents and Smooth Ergodic Theory
journal, August 1977
- Pesin, Ya B.
- Russian Mathematical Surveys, Vol. 32, Issue 4
Robust procedures for converting among Lindblad, Kraus and matrix representations of quantum dynamical semigroups
journal, January 2003
- Havel, Timothy F.
- Journal of Mathematical Physics, Vol. 44, Issue 2
Quantum-gas microscopes: a new tool for cold-atom quantum simulators
journal, April 2016
- Kuhr, Stefan
- National Science Review, Vol. 3, Issue 2
Quantum thermalization through entanglement in an isolated many-body system
journal, August 2016
- Kaufman, A. M.; Tai, M. E.; Lukin, A.
- Science, Vol. 353, Issue 6301
Quantum correlations with no causal order
journal, January 2012
- Oreshkov, Ognyan; Costa, Fabio; Brukner, Časlav
- Nature Communications, Vol. 3, Issue 1
Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas
journal, February 2012
- Trotzky, S.; Chen, Y-A.; Flesch, A.
- Nature Physics, Vol. 8, Issue 4
Gravitation from entanglement in holographic CFTs
journal, March 2014
- Faulkner, Thomas; Guica, Monica; Hartman, Thomas
- Journal of High Energy Physics, Vol. 2014, Issue 3
Ergodic theory of chaos and strange attractors
journal, July 1985
- Eckmann, J. -P.; Ruelle, D.
- Reviews of Modern Physics, Vol. 57, Issue 3
10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit
journal, November 2017
- Song, Chao; Xu, Kai; Liu, Wuxin
- Physical Review Letters, Vol. 119, Issue 18
Quantum logic and the histories approach to quantum theory
journal, May 1994
- Isham, C. J.
- Journal of Mathematical Physics, Vol. 35, Issue 5
The large N limit of superconformal field theories and supergravity
conference, January 1999
- Maldacena, Juan
- The second meeting on trends in theoretical physics, AIP Conference Proceedings
Mathematical Methods of Classical Mechanics
book, January 1978
- Arnold, V. I.
- Graduate Texts in Mathematics
Quantum computation and quantum information†
journal, February 2006
- Nagy, Marius; Akl, Selim G.
- International Journal of Parallel, Emergent and Distributed Systems, Vol. 21, Issue 1
Multiple-time states and multiple-time measurements in quantum mechanics
text, January 2007
- Aharonov, Y.; Popescu, S.; Tollaksen, J.
- arXiv
Theoretical framework for quantum networks
text, January 2009
- Chiribella, Giulio; D'Ariano, Giacomo M.; Perinotti, Paolo
- arXiv
Measuring entanglement entropy of a generic many-body system with a quantum switch
text, January 2012
- Abanin, Dmitry A.; Demler, Eugene
- arXiv
Quantum correlations which imply causation
preprint, January 2013
- Fitzsimons, Joseph; Jones, Jonathan; Vedral, Vlatko
- arXiv
Operational formulation of time reversal in quantum theory
text, January 2015
- Oreshkov, Ognyan; Cerf, Nicolas J.
- arXiv
Quantum Networks: general theory and applications
text, January 2016
- Bisio, Alessandro; Chiribella, Giulio; D'Ariano, Giacomo Mauro
- arXiv
The Spectrum in the Sachdev-Ye-Kitaev Model
text, January 2016
- Polchinski, Joseph; Rosenhaus, Vladimir
- arXiv
Quantum thermalization through entanglement in an isolated many-body system
text, January 2016
- Kaufman, Adam M.; Tai, M. Eric; Lukin, Alexander
- arXiv
Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
text, January 2016
- Gärttner, Martin; Bohnet, Justin G.; Safavi-Naini, Arghavan
- arXiv
Optimal quantum tomography
text, January 2017
- Bisio, Alessandro; Chiribella, Giulio; D'Ariano, Giacomo Mauro
- arXiv
Quantum temporal logic and decoherence functionals in the histories approach to generalised quantum theory
text, January 1994
- Isham, Chris; Linden, Noah
- arXiv
Gauge Theory Correlators from Non-Critical String Theory
text, January 1998
- Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M.
- arXiv
Procedures for Converting among Lindblad, Kraus and Matrix Representations of Quantum Dynamical Semigroups
text, January 2002
- Havel, Timothy F.
- arXiv
Quantum dynamical entropy and decoherence rate
text, January 2003
- Alicki, Robert; Lozinski, Artur; Pakonski, Prot
- arXiv
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- Cotler, Jordan; Han, Xizhi; Qi, Xiao-Liang
- Journal of High Energy Physics, Vol. 2019, Issue 7
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journal, January 2020
- Taranto, Philip
- International Journal of Quantum Information, Vol. 18, Issue 02
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- Kull, Ilya; Allard Guèrin, Philippe; Brukner, Caslav
- Zenodo
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- Zenodo
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- arXiv
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- Berk, Graeme D.; Garner, Andrew J. P.; Yadin, Benjamin
- arXiv
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- Dias, Eduardo O.
- arXiv
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- Dong, Xi; Qi, Xiao-Liang; Shangnan, Zhou
- arXiv
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- Zhang, Tian
- arXiv