Quantum steampunk: Quantum information, thermodynamics, their intersection, and applications thereof across physics Thesis by Nicole Yunger Halpern In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Physics CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2018 Defended May 25, 2018 ii c 2018 Nicole Yunger Halpern ORCID: 0000-0001-8670-6212 All rights reserved except where otherwise noted iii ACKNOWLEDGEMENTS I am grateful to need to acknowledge many contributors. I thank my parents for the unconditional support and love, and for the sacrifices, that enabled me to arrive here. Thank you for communicating values that include diligence, discipline, love of education, and security in one’s identity. For a role model who embodies these virtues, I thank my brother. I thank my advisor, John Preskill, for your time, for mentorship, for the communi- cation of scientific values and scientific playfulness, and for investing in me. I have deeply appreciated the time and opportunity that you’ve provided to learn and cre- ate. Advice about “thinking big”; taking risks; prioritizing; embracing breadth and exhibiting nimbleness in research; and asking, “Are you having fun?” will remain etched in me. Thank you for bringing me to Caltech. Thank you to my southern-California family for welcoming me into your homes and for sharing holidays and lunches with me. You’ve warmed the past five years. The past five years have seen the passing of both my grandmothers: Dr. Rosa Halpern during year one and Mrs. Miriam Yunger during year four. Rosa Halpern worked as a pediatrician until in her 80s. Miriam Yunger yearned to attend college but lacked the opportunity. She educated herself, to the point of erudition on Rus- sian and American history, and amassed a library. I’m grateful for these role models who shared their industriousness, curiosity, and love. I’m grateful to my research collaborators for sharing time, consideration, and ex- pertise: Ning Bao, Daniel Braun, Lincoln Carr, Mahn-Soo Choi, Elizabeth Crosson, Oscar Dahlsten, Justin Dressel, Philippe Faist, Andrew Garner, José Raúl Gonzalez Alonso, Sarang Gopalakrishnan, Logan Hillberry, Andrew Keller, Chris Jarzynski, Jonathan Oppenheim, Patrick Rall, Gil Refael, Joe Renes, Brian Swingle, Vlatko Vedral, Mordecai Waegell, Sara Walker, Christopher White, and Andreas Winter. I’m grateful to informal advisors for sharing experiences and guidance: Michael Beverland, Sean Carroll, Ian Durham, Alexey Gorshkov, Daniel Harlow, Dave Kaiser, Shaun Maguire, Spiros Michalakis, Jenia Mozgunov, Renato Renner, Barry Sanders, many of my research collaborators, and many other colleagues and peers. Learning and laughing with my quantum-information/-thermodynamics colleagues has been a pleasure and a privilege: Álvaro Martín Alhambra, Lídia del Río, John Goold, David Jennings, Matteo Lostaglio, Nelly Ng, Mischa Woods, aforemen- iv tioned collaborators, and many others. I’m grateful to Caltech’s Institute for Quantum Information and Matter (IQIM) for conversations, collaborations, financial support, an academic and personal home, and more. I thank especially Fernando Brandão, Xie Chen, Manuel Endres, David Gosset, Stacey Jeffery, Alexei Kitaev, Alex Kubica, Roger Mong, Oskar Painter, Fernando Pastawski, Kristan Temme, and the aforementioned IQIM members. Thanks to my administrators for logistical assistance, for further logistical assistance, for hallway conversations that counterbalanced the rigors of academic life, for your be- lief in me, and for more logistical assistance: Marcia Brown, Loly Ekmekjian, Ann Harvey, Bonnie Leung, Jackie O’Sullivan, and Lisa Stewart. For more such conversations, and for weekend lunches in the sun on Beckman Lawn, I’m grateful to too many friends to name. Thank you for your camaraderie, candidness, and sincerity. Also too many to name are the mentors and teachers I encountered before arriving at Caltech. I recall your guidance and encouragement more often than you realize. Time ranks amongst the most valuable resources a theorist can hope for. I deeply ap- preciate the financial support that has offered freedom to focus on research. Thanks to Caltech’s Graduate Office; the IQIM; the Walter Burke Institute; the Kavli In- stitute for Theoretical Physics (KITP); and Caltech’s Division of Physics, Math- ematics, and Astronomy for a Virginia Gilloon Fellowship, an IQIM Fellowship, a Walter Burke Graduate Fellowship, a KITP Graduate Fellowship, and a Barbara Groce Fellowship. Thanks to John Preskill and Gil Refael for help with securing funding. Thanks to many others (especially the Foundational Questions Institute’s Large Grant for "Time and the Structure of Quantum Theory", Jon Barrett, and Os- car Dahlsten) for financial support for research visits. NSF grants PHY-0803371, PHY-1125565, and PHY-1125915 have supported this research. The IQIM is an NSF Physics Frontiers Center with support from the Gordon and Betty Moore Foun- dation (GBMF-2644). v ABSTRACT Combining quantum information theory (QIT) with thermodynamics unites 21st- century technology with 19th-century principles. The union elucidates the spread of information, the flow of time, and the leveraging of energy. This thesis con- tributes to the theory of quantum thermodynamics, particularly to QIT thermody- namics. The thesis also contains applications of the theory, wielded as a toolkit, across physics. Fields touched on include atomic, molecular, and optical physics; nonequilibrium statistical mechanics; condensed matter; high-energy physics; and chemistry. I propose the name quantum steampunk for this program. The term derives from the steampunk genre of literature, art, and cinema that juxtaposes fu- turistic technologies with 19th-century settings. vi PUBLISHED CONTENT The following publications form the basis for this thesis. The multi-author papers resulted from collaborations to which all parties contributed equally. [1] N. Yunger Halpern, A. J. P. Garner, O. C. O. Dahlsten, and V. Vedral, New Journal of Physics 17, 095003 (2015), 10.1088/1367-2630/17/9/095003. [2] N. Yunger Halpern and J. M. Renes, Phys. Rev. E 93, 022126 (2016), 10.1103/PhysRevE.93.022126. [3] N. Yunger Halpern, Journal of Physics A: Mathematical and Theoretical 51, 094001 (2018), 10.1088/1751-8121/aaa62f. [4] N. Bao and N. Yunger Halpern, Phys. Rev. A 95, 062306 (2017), 10.1103/PhysRevA.95.062306. [5] O. C. O. Dahlsten et al., New Journal of Physics 19, 043013 (2017), 10.1088/1367-2630/aa62ba. [6] N. Yunger Halpern, A. J. P. Garner, O. C. O. Dahlsten, and V. Vedral, Phys. Rev. E 97, 052135 (2018). [7] N. Yunger Halpern, Toward physical realizations of thermodynamic resource theories, in Information and Interaction: Eddington, Wheeler, and the Limits of Knowledge, edited by I. T. Durham and D. Rickles, Frontiers Collection, Springer, 2017, 10.1007/978-3-319-43760-6. [8] N. Yunger Halpern and C. Jarzynski, Phys. Rev. E 93, 052144 (2016), 10.1103/PhysRevE.93.052144. [9] N. Yunger Halpern, P. Faist, J. Oppenheim, and A. Winter, Nature Communi- cations 7, 12051 (2016), 10.1038/ncomms12051. [10] N. Yunger Halpern, Phys. Rev. A 95, 012120 (2017), 10.1103/Phys- RevA.95.012120. [11] N. Yunger Halpern, B. Swingle, and J. Dressel, Phys. Rev. A 97, 042105 (2018), 10.1103/PhysRevA.97.042105. [12] N. Yunger Halpern, C. D. White, S. Gopalakrishnan, and G. Refael, ArXiv e-prints (2017), 1707.07008. [13] N. Yunger Halpern and E. Crosson, ArXiv e-prints (2017), 1711.04801. [14] B. Swingle and N. Yunger Halpern, ArXiv e-prints (in press), 1802.01587, accepted by Phys. Rev. E. vii [15] J. Dressel, J. Raúl González Alonso, M. Waegell, and N. Yunger Halpern, ArXiv e-prints (2018), 1805.00667. viii TABLE OF CONTENTS Acknowledgements . iii Abstract . v Published Content . vi Bibliography . vi Table of Contents . viii Chapter I: Introduction . 1 Bibliography . 8 Chapter II: Jarzynski-like equality for the out-of-time-ordered correlator . 11 2.1 Set-up . 13 2.2 Definitions . 13 2.3 Result . 20 2.4 Conclusions . 23 Bibliography . 25 Chapter III: The quasiprobability behind the out-of-time-ordered correlator . 28 3.1 Technical introduction . 31 3.2 Experimentally measuring A˜ ρ and the coarse-grained A˜ρ . 53 3.3 Numerical simulations . 64 3.4 Calculation of A˜ρ averaged over Brownian circuits . 74 3.5 Theoretical study of A˜ ρ ........................ 81 3.6 Outlook . 107 Bibliography . 112 Chapter IV: MBL-Mobile: Many-body-localized engine . 119 4.1 Thermodynamic background . 121 4.2 The MBL Otto cycle . 122 4.3 Numerical simulations . 138 4.4 Order-of-magnitude estimates . 141 4.5 Formal comparisons with competitor engines . 143 4.6 Outlook . 146 Bibliography . 147 Chapter V: Non-Abelian thermal state: The thermal state of a quantum sys- tem with noncommuting charges . 153 5.1 Results . 155 5.2 Discussion . 166 Bibliography . 166 Appendix A: Appendices for “Jarzynski-like equality for the out-of-time- ordered correlator” . 169 A.1 Weak measurement of the combined quantum amplitude A˜ ρ . 169 A.2 Interference-based measurement of the combined quantum ampli- tude A˜ ρ .................................172 ix Bibliography . 174 Appendix B: Appendices for “The quasiprobability behind the out-of-time- ordered correlator” . 175 B.1 Mathematical properties of P(W;W0) . 175 B.2 Retrodiction about the symmetrized composite observable Γ˜ := i(K ::: A− A ::: K ) ................................177 Bibliography . 179 Appendix C: Appendices for “MBL-Mobile: Many-body-localized engine” . 180 C.1 Quantitative assessment of the mesoscopic MBL Otto engine . 180 C.2 Phenomenological model for the macroscopic MBL Otto engine . 200 C.3 Constraint 2 on cold thermalization: Suppression of high-order-in- the-coupling energy exchanges . 205 C.4 Optimization of the MBL Otto engine . 206 C.5 Numerical simulations of the MBL Otto engine . 214 C.6 Comparison with competitor Otto engines: Details and extensions . 220 Bibliography . 222 Appendix D: Appendices for “Microcanonical and resource-theoretic deriva- tions of the thermal state of a quantum system with noncommuting charges”224 D.1 Microcanonical derivation of the NATS’s form . 224 D.2 Dynamical considerations .