Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-16T20:13:33.129465Z
Paper Citation Record · LEDGER
As of 2 August 2026, this Paper Citation Record lists 64 of 64 outbound references and 1 inbound Pith citation observation for arXiv:2512.20787.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-16T20:13:33.129465Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-02T06:30:47.504484+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-01T15:40:18.614186Z
A source-named dated measurement, never combined with another source.
Source: cited_works
64 of 64 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 5954f712-5b29-437a-8c5b-5c5dd90e8aa6 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 16e48798-5782-4793-8d49-55b1e7d9a43e · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Clif- ford group
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation c9bdd034-21b5-4ac1-a752-5e91c297fe29 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Underχ, adding 1 modulod corresponds to adding (1,1) in the product ring
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation f611e70c-c212-4064-b34a-410f779a5c9e · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 44b014a0-ce08-4add-9824-5d237849b6ed · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Cliffordness
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 889c834f-fcc3-4225-8e23-1626635f962b · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources We will show that Cp is a maximal finite subgroup of SU(p)/U(1)
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 6eaa0974-d055-4e1f-813f-211b8c85ca65 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources We distinguish two cases based on the prime factorization ofd
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation c9d489c5-bda0-4422-878d-ea3df1b6f0ec · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Forp≥3, this order is strictly smaller than that of the sym- metric group|S p2 |= (p 2)!
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation aa06e412-b7e9-468c-a281-4a5a880901b3 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources However, maxi- mality fails in the kernel of Φ (the subgroup fixing the blocks)
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 8e3c51c0-e5ae-4906-8f44-575594035d79 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 8b106c02-7554-4a16-bceb-fc4e44c1eb96 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation da72c1f5-135e-4ded-a3de-772e8bb0a73a · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation f218e3ca-c375-46b5-9cb9-d42690cd6c68 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources To prove infinite- ness, we apply Theorem 17
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 6c7bd05b-a4db-47a3-9fea-6c4793bdbe44 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Explicitly, the adjoint action yields the diagonal operatorD π given by: PπZP † π =D π,where (D π)yy =ω π−1(y)
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 36352a40-40f4-4e41-9487-22b74c3ca1b2 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Proposition 35.Letτ= (j k)be the transposition swapping indicesjandkwithj < k
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 97c48479-ab40-4af0-b11c-2209c5033cf1 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Letd=p m withm≥2, and letτ= (0 1)
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation e93b68e2-4829-4edf-96b2-f070b76dad32 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources d=%o: Infinite=%o\n
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation bf922d3a-e2ac-49e7-a9b8-8ac759bfb1de · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources •The group generated byHand the SWAP operator S, ifk=l, whereS(u⊗v) =v⊗u
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 4aebfc5e-cf47-4626-b89e-b229ac935f52 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources As a particular case we obtain: Corollary 44.Letk, l≥2
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation fcabf854-efd4-4045-9924-4c9c116ac46b · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 345eb8da-f41c-4a22-9bb5-fbf9474aae67 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation a781d086-e26c-439e-9827-f1a605e8ed67 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Consider a subsystemkof dimensiond k
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 429f88a0-b5e0-49ea-ae0e-91caa3b6df46 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Since global irreducibility is guaranteed, it suffices to demon- strate that the group contains a dense subgroup onat least onelocal subsystem
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 055c7160-6e35-440b-b1fa-ecd63f32d022 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources The Heisenberg Representation of Quantum Computers
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation ed5ca486-221b-4f00-83a7-cb7d4e442f6e · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Aaronson and D
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation a28c2f04-cc51-491f-b402-2fdb2988ba2e · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Gheorghiu, Physics Letters A378, 505 (2014)
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 65b4ee6b-e45e-4984-9054-09bdd201a01a · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources de Beaudrap, Quantum Information and Computation 13, 73 (2013)
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation b42c7a24-77fb-4f7e-9c12-c956470f96de · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 356b18b2-3553-4d4e-8df5-e37a0771bc14 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Gottesman and I
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 934cabe3-0a2d-484b-9159-22992b3abdbb · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Gottesman, Chaos, Solitons & Fractals10, 1749 (1999)
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 1f25b55b-089a-4ee6-af1b-169f0451ee23 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 0b71430e-9a15-4e07-9c2c-cd5bc3422349 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Bravyi and A
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 9e8745df-9e40-45a2-929e-851d479cc764 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Fault-Tolerant Postselected Quantum Computation: Schemes
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 9568889c-12b1-4203-aba9-8f55a6b3882e · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Howard and J
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 8b493478-4f7f-415a-9bb8-0dd73d0f9879 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 5885058b-fbad-45d4-b482-566d0b298b04 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Ringbauer, M
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 0dba7ac5-776d-423e-b6ba-9ec53056bd27 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation cb9f7e96-7509-4d61-9172-84e68ac76fdf · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Chicco, G
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 73ad9a9d-ce64-49d6-8d1b-d169a0f32517 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Luo and X.-J
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 3b4b5583-38e9-4d6a-8545-2d91e28850a2 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 176fdb42-af2a-4d66-81ab-e5e9c3f91c1b · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 88d16f53-336d-4859-af40-7f440232e17c · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Brylinski and R
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 13782ec9-09fc-47fa-8b62-e564e281b2e1 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Tolar, Journal of Physics: Conference Series1071, 012022 (2018)
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 9473f3c0-99ba-41ba-8ad3-71c1f677e162 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 15f65f2b-2069-4fe6-b714-f019a6ed4449 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 54006be0-3d21-4f19-8191-51d8b3e2d67e · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation abcbb7bd-f89c-4ad2-873a-0cb6edd2c0f3 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation aaaa5e37-8b8b-4801-a13f-c0c17f1a905f · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Serre,Linear Representations of Finite Groups, Graduate Texts in Mathematics, Vol
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation edc29996-8e02-4732-9e08-efe7fd1c3edb · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Clifford groups are not always 2-designs
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 2a8f5e00-ef81-4a9d-9cb5-d49baca29b17 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 383138f5-77a9-4b3b-9eb2-e80aa7b7c68c · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation cb820104-0629-491b-a227-9c3e1727d9ec · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Brauer, Mathematische Annalen169, 73 (1967)
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation be1d73b9-da4e-44d4-bf3e-c9f61db653f5 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Bosma, J
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 9bca2e67-5dde-4fb2-bfaa-cf6ec1dacea8 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Beverland, E
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation aa65d667-05f2-476e-86f4-6e49b8692a59 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Veitch, S
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 778ff5b9-49fb-404b-ba35-077718eb8a79 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Howard and E
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation be58ed04-3d67-4d20-9abf-204a317318a5 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Bravyi, D
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 740b3705-0ffa-4170-8274-95f054c9274d · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 16dc9121-9b41-4776-8e07-c12807b910c1 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Morvan, V
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 0172649c-e5de-4f09-a1a7-61afba489929 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Unresolved cited work
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 8f391e1a-41d2-4a4e-90bb-69e1db2c0a02 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Heralded High-Dimensional Photon-Photon Quantum Gate
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation ce415fd1-f52c-4d46-bdd9-8e8581a79e35 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Litinski, Quantum3, 205 (2019)
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 8a70e6c6-1ef4-413c-ac70-c81751964f9d · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Gidney and M
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation 7a34d32e-389f-4d29-bf4c-5473393b9295 · outbound
Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources Magic state cultivation: growing T states as cheap as CNOT gates
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-02T06:30:47.504484+00:00.
Observation c8ef2980-6f10-4f27-b967-b73990f25c74 · inbound
Magic-protected entanglement and Clifford-irreducible structure in magic state space Quantum Universality in Composite Systems: A Trichotomy of Clifford Resources
Reference 36
Source-reported events for the cited work
Unavailable: canonical work link unavailable.