Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2601.01806 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911353847939072 |
|---|---|
| author | Cheng, Caisheng Bao, Ruicheng |
| author_facet | Cheng, Caisheng Bao, Ruicheng |
| contents | In open quantum systems, a basic question at the interface of quantum information, statistical physics, and many-body dynamics is how well can one infer the structure of noise and dissipation generators from finite-time measurement statistics alone. Motivated by this question, we study the learnability and cryptographic applications of random open-system dynamics generated by Lindblad-Gorini-Kossakowski-Sudarshan (GKSL) master equations. Working in the affine hull of the GKSL cone, we introduce physically motivated ensembles of random local Lindbladians via a linear parametrisation around a reference generator. On top of this geometric structure, we extend statistical query (SQ) and quantum-process statistical query (QPStat) frameworks to the open-system setting and prove exponential (in the parameter dimension $M$) lower bounds on the number of queries required to learn random Lindbladian dynamics. In particular, we establish average-case SQ-hardness for learning output distributions in total variation distance and average-case QPStat-hardness for learning Lindbladian channels in diamond norm. To support these results physically, we derive a linear-response expression for the ensemble-averaged total variation distance and verify the required nonvanishing scaling in a random local amplitude-damping chain. Finally, we design two Lindbladian physically unclonable function (Lindbladian-PUF) protocols based on random Lindbladian ensembles with distribution-level and tomography-based verification, thereby providing open-system examples where learning hardness can be translated into cryptographic security guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01806 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Physically natural metric-measure Lindbladian ensembles and their learning hardness Cheng, Caisheng Bao, Ruicheng Quantum Physics In open quantum systems, a basic question at the interface of quantum information, statistical physics, and many-body dynamics is how well can one infer the structure of noise and dissipation generators from finite-time measurement statistics alone. Motivated by this question, we study the learnability and cryptographic applications of random open-system dynamics generated by Lindblad-Gorini-Kossakowski-Sudarshan (GKSL) master equations. Working in the affine hull of the GKSL cone, we introduce physically motivated ensembles of random local Lindbladians via a linear parametrisation around a reference generator. On top of this geometric structure, we extend statistical query (SQ) and quantum-process statistical query (QPStat) frameworks to the open-system setting and prove exponential (in the parameter dimension $M$) lower bounds on the number of queries required to learn random Lindbladian dynamics. In particular, we establish average-case SQ-hardness for learning output distributions in total variation distance and average-case QPStat-hardness for learning Lindbladian channels in diamond norm. To support these results physically, we derive a linear-response expression for the ensemble-averaged total variation distance and verify the required nonvanishing scaling in a random local amplitude-damping chain. Finally, we design two Lindbladian physically unclonable function (Lindbladian-PUF) protocols based on random Lindbladian ensembles with distribution-level and tomography-based verification, thereby providing open-system examples where learning hardness can be translated into cryptographic security guarantees. |
| title | Physically natural metric-measure Lindbladian ensembles and their learning hardness |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.01806 |