Quantum coherence as a signature of chaos
We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos. We quantify this connection at two different levels: quantum states and quantum channels. At the level...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-06-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.023214 |
| _version_ | 1797211018003218432 |
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| author | Namit Anand Georgios Styliaris Meenu Kumari Paolo Zanardi |
| author_facet | Namit Anand Georgios Styliaris Meenu Kumari Paolo Zanardi |
| author_sort | Namit Anand |
| collection | DOAJ |
| description | We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos. We quantify this connection at two different levels: quantum states and quantum channels. At the level of states, we show how several well-studied quantifiers of chaos are, in fact, quantum coherence measures in disguise (or closely related to them). We further this connection for all quantum coherence measures by using tools from majorization theory. Then we numerically study the coherence of chaotic-versus-integrable eigenstates and find excellent agreement with random matrix theory in the bulk of the spectrum. At the level of channels, we show that the coherence-generating power (CGP)—a measure of how much coherence a dynamical process generates on average—emerges as a subpart of the out-of-time-ordered correlator (OTOC), a measure of information scrambling in many-body systems. Via numerical simulations of the (nonintegrable) transverse-field Ising model, we show that the OTOC and CGP capture quantum recurrences in quantitatively the same way. Moreover, using random matrix theory, we analytically characterize the OTOC-CGP connection for the Haar and Gaussian ensembles. In closing, we remark on how our coherence-based signatures of chaos relate to other diagnostics, namely, the Loschmidt echo, OTOC, and the Spectral Form Factor. |
| first_indexed | 2024-04-24T10:19:49Z |
| format | Article |
| id | doaj.art-c7a8f4228ee44361bbf5793d094280a3 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:19:49Z |
| publishDate | 2021-06-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-c7a8f4228ee44361bbf5793d094280a32024-04-12T17:10:49ZengAmerican Physical SocietyPhysical Review Research2643-15642021-06-013202321410.1103/PhysRevResearch.3.023214Quantum coherence as a signature of chaosNamit AnandGeorgios StyliarisMeenu KumariPaolo ZanardiWe establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos. We quantify this connection at two different levels: quantum states and quantum channels. At the level of states, we show how several well-studied quantifiers of chaos are, in fact, quantum coherence measures in disguise (or closely related to them). We further this connection for all quantum coherence measures by using tools from majorization theory. Then we numerically study the coherence of chaotic-versus-integrable eigenstates and find excellent agreement with random matrix theory in the bulk of the spectrum. At the level of channels, we show that the coherence-generating power (CGP)—a measure of how much coherence a dynamical process generates on average—emerges as a subpart of the out-of-time-ordered correlator (OTOC), a measure of information scrambling in many-body systems. Via numerical simulations of the (nonintegrable) transverse-field Ising model, we show that the OTOC and CGP capture quantum recurrences in quantitatively the same way. Moreover, using random matrix theory, we analytically characterize the OTOC-CGP connection for the Haar and Gaussian ensembles. In closing, we remark on how our coherence-based signatures of chaos relate to other diagnostics, namely, the Loschmidt echo, OTOC, and the Spectral Form Factor.http://doi.org/10.1103/PhysRevResearch.3.023214 |
| spellingShingle | Namit Anand Georgios Styliaris Meenu Kumari Paolo Zanardi Quantum coherence as a signature of chaos Physical Review Research |
| title | Quantum coherence as a signature of chaos |
| title_full | Quantum coherence as a signature of chaos |
| title_fullStr | Quantum coherence as a signature of chaos |
| title_full_unstemmed | Quantum coherence as a signature of chaos |
| title_short | Quantum coherence as a signature of chaos |
| title_sort | quantum coherence as a signature of chaos |
| url | http://doi.org/10.1103/PhysRevResearch.3.023214 |
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