Exact Emergent Quantum State Designs from Quantum Chaotic Dynamics
We present exact results on a novel kind of emergent random matrix universality that quantum many-body systems at infinite temperature can exhibit. Specifically, we consider an ensemble of pure states supported on a small subsystem, generated from projective measurements of the remainder of the...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society (APS)
2022
|
| Online Access: | https://hdl.handle.net/1721.1/141460 |
| _version_ | 1811086663575666688 |
|---|---|
| author | Ho, Wen Wei Choi, Soonwon |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Ho, Wen Wei Choi, Soonwon |
| author_sort | Ho, Wen Wei |
| collection | MIT |
| description | We present exact results on a novel kind of emergent random matrix
universality that quantum many-body systems at infinite temperature can
exhibit. Specifically, we consider an ensemble of pure states supported on a
small subsystem, generated from projective measurements of the remainder of the
system in a local basis. We rigorously show that the ensemble, derived for a
class of quantum chaotic systems undergoing quench dynamics, approaches a
universal form completely independent of system details: it becomes uniformly
distributed in Hilbert space. This goes beyond the standard paradigm of quantum
thermalization, which dictates that the subsystem relaxes to an ensemble of
quantum states that reproduces the expectation values of local observables in a
thermal mixed state. Our results imply more generally that the distribution of
quantum states themselves becomes indistinguishable from those of uniformly
random ones, i.e. the ensemble forms a quantum state-design in the parlance of
quantum information theory. Our work establishes bridges between quantum
many-body physics, quantum information and random matrix theory, by showing
that pseudo-random states can arise from isolated quantum dynamics, opening up
new ways to design applications for quantum state tomography and benchmarking. |
| first_indexed | 2024-09-23T13:29:19Z |
| format | Article |
| id | mit-1721.1/141460 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:29:19Z |
| publishDate | 2022 |
| publisher | American Physical Society (APS) |
| record_format | dspace |
| spelling | mit-1721.1/1414602023-01-26T21:52:06Z Exact Emergent Quantum State Designs from Quantum Chaotic Dynamics Ho, Wen Wei Choi, Soonwon Massachusetts Institute of Technology. Center for Theoretical Physics We present exact results on a novel kind of emergent random matrix universality that quantum many-body systems at infinite temperature can exhibit. Specifically, we consider an ensemble of pure states supported on a small subsystem, generated from projective measurements of the remainder of the system in a local basis. We rigorously show that the ensemble, derived for a class of quantum chaotic systems undergoing quench dynamics, approaches a universal form completely independent of system details: it becomes uniformly distributed in Hilbert space. This goes beyond the standard paradigm of quantum thermalization, which dictates that the subsystem relaxes to an ensemble of quantum states that reproduces the expectation values of local observables in a thermal mixed state. Our results imply more generally that the distribution of quantum states themselves becomes indistinguishable from those of uniformly random ones, i.e. the ensemble forms a quantum state-design in the parlance of quantum information theory. Our work establishes bridges between quantum many-body physics, quantum information and random matrix theory, by showing that pseudo-random states can arise from isolated quantum dynamics, opening up new ways to design applications for quantum state tomography and benchmarking. 2022-04-01T15:33:21Z 2022-04-01T15:33:21Z 2022-02-11 2022-04-01T15:27:13Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/141460 Ho, Wen Wei and Choi, Soonwon. 2022. "Exact Emergent Quantum State Designs from Quantum Chaotic Dynamics." Physical Review Letters, 128 (6). en 10.1103/physrevlett.128.060601 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society (APS) APS |
| spellingShingle | Ho, Wen Wei Choi, Soonwon Exact Emergent Quantum State Designs from Quantum Chaotic Dynamics |
| title | Exact Emergent Quantum State Designs from Quantum Chaotic Dynamics |
| title_full | Exact Emergent Quantum State Designs from Quantum Chaotic Dynamics |
| title_fullStr | Exact Emergent Quantum State Designs from Quantum Chaotic Dynamics |
| title_full_unstemmed | Exact Emergent Quantum State Designs from Quantum Chaotic Dynamics |
| title_short | Exact Emergent Quantum State Designs from Quantum Chaotic Dynamics |
| title_sort | exact emergent quantum state designs from quantum chaotic dynamics |
| url | https://hdl.handle.net/1721.1/141460 |
| work_keys_str_mv | AT howenwei exactemergentquantumstatedesignsfromquantumchaoticdynamics AT choisoonwon exactemergentquantumstatedesignsfromquantumchaoticdynamics |