{"schema":"pith.reference-change-event.v1","doi":"10.1103/physrevd.109.l081701","canonical_url":"https://pith.science/event/10.1103/physrevd.109.l081701","json_url":"https://pith.science/event/10.1103/physrevd.109.l081701.json","not_a_judgment":"This page records that a citing paper's bibliography includes a work with a published notice. It is not a judgment on the citing paper.","primary":{"event_id":213810,"doi":"10.1103/physrevd.109.l081701","event_type":"correction","event_type_label":"Correction","source":"crossref","source_label":"Crossref","event_date":"2024-04-22","title":"Krylov complexity is not a measure of distance between states or operators","work_title":null,"work_doi":"10.1103/physrevd.109.l081701","work_arxiv_id":null,"notice_doi":"10.1103/physrevd.109.l081701","flag_count":0,"flags_open":0,"flags_disputed":0,"latest_flag_at":null,"human_href":"/event/10.1103/physrevd.109.l081701","json_href":"/event/10.1103/physrevd.109.l081701.json"},"events":[{"event_id":213810,"doi":"10.1103/physrevd.109.l081701","event_type":"correction","event_type_label":"Correction","source":"crossref","source_label":"Crossref","event_date":"2024-04-22","title":"Krylov complexity is not a measure of distance between states or operators","work_title":null,"work_doi":"10.1103/physrevd.109.l081701","work_arxiv_id":null,"notice_doi":"10.1103/physrevd.109.l081701","flag_count":0,"flags_open":0,"flags_disputed":0,"latest_flag_at":null,"human_href":"/event/10.1103/physrevd.109.l081701","json_href":"/event/10.1103/physrevd.109.l081701.json"}],"flags":[{"id":2314,"status":"open","status_label":"Open","citing_arxiv_id":"2405.09628","citing_title":"Quantum Dynamics in Krylov Space: Methods and Applications","ref_index":196,"evidence_raw":"a complementary measure of the dynamics focused on the spread of the operator in the Krylov lattice. The Krylov variance is defined as [187] ∆K(t)2 := DK −1X n=0 n2|φn(t)|2 − \u0010 DK −1X n=0 n|φn(t)|2\u00112 = DK −1X n=0 |φn(t)|2(n − K(t))2 . (27) An alternative definition was considered in [195, 196], which in our notation stands for∆K(t)2/K(t)2. The higher moments of the distribution can be similarly defined [196]. For this, it is interesting to consider the Krylov operator K such that [197] K |On) = n|On) , ⇔ K := DK −1X n=0 n|On)(On| . (28) In other words, the Krylov operator acts as a number operator on the Krylov basis,K = diag(0, 1, 2 · · · , DK− 1). In terms of the definition (28), the Krylov complexity is associated with the expectation value of the Krylov operator K in the time-evolved operator |O(t)), i.","evidence_cleaned":"a complementary measure of the dynamics focused on the spread of the operator in the Krylov lattice. The Krylov variance is defined as [187] ∆K(t)2 := DK −1X n=0 n2|φn(t)|2 − \u0010 DK −1X n=0 n|φn(t)|2\u00112 = DK −1X n=0 |φn(t)|2(n − K(t))2 . (27) An alternative definition was considered in [195, 196], which in our notation stands for∆K(t)2/K(t)2. The higher moments of the distribution can be similarly defined [196]. For this, it is interesting to consider the Krylov operator K such that [197] K |On) = n|On), ⇔ K := DK −1X n=0 n|On)(On| . (28) In other words, the Krylov operator acts as a number operator on the Krylov basis,K = diag(0, 1, 2 · · ·, DK− 1). In terms of the definition (28), the Krylov complexity is associated with the expectation value of the Krylov operator K in the time-evolved operator |O(t)), i","evidence_source_label":"citation context","event_type":"correction","event_type_label":"Correction","source_label":"Crossref","event_date":"2024-04-22","work_title":null,"work_doi":"10.1103/physrevd.109.l081701","event_doi":"10.1103/physrevd.109.l081701","flag_href":"/flags/2314","event_href":"/event/10.1103/physrevd.109.l081701","paper_href":"/paper/2405.09628","created_at":"2026-07-11T03:18:58.832664Z","dispute_note":null,"disputed_at":null,"disputed_by":null},{"id":2313,"status":"open","status_label":"Open","citing_arxiv_id":"2506.07257","citing_title":"A Quantum Computational Perspective on Spread Complexity","ref_index":1,"evidence_raw":"Krylov complexity is not a mea- sure of distance between states or operators. Phys. Rev. D 109, L081701. doi:10.1103/PhysRevD.109.L081701, arXiv:2311.04093. Avdoshkin, A., Dymarsky, A., Smolkin, M.,","evidence_cleaned":"Krylov complexity is not a mea- sure of distance between states or operators. Phys. Rev. D 109, L081701. doi:10.1103/PhysRevD.109.L081701, arXiv:2311.04093. Avdoshkin, A., Dymarsky, A., Smolkin, M","evidence_source_label":"bibliography line","event_type":"correction","event_type_label":"Correction","source_label":"Crossref","event_date":"2024-04-22","work_title":null,"work_doi":"10.1103/physrevd.109.l081701","event_doi":"10.1103/physrevd.109.l081701","flag_href":"/flags/2313","event_href":"/event/10.1103/physrevd.109.l081701","paper_href":"/paper/2506.07257","created_at":"2026-07-11T03:18:58.832664Z","dispute_note":null,"disputed_at":null,"disputed_by":null}],"flag_count":2,"flags_open":2,"flags_disputed":0,"desk_url":"https://pith.science/flags"}