{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"68998b77568511cbc2feec060b7d1b2268854b2c8802691d22c06dcae9d7a499","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"0b239f4b54be0ac84fe98b65768e8ca269691e37a7d474558cf001bfd6f72862","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qi.sic-mub.sic-existence","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"A SIC is a set of $d^2$ quantum states in dimension $d$ that are all equally far from one another. They have been found in many dimensions, but nobody has proven they exist in all.","posed_since":"1999","precise":"For every integer $d \\ge 2$, do there exist $d^{2}$ unit vectors $\\psi_j$ in $C^d$ with $\\mid\\langle\\psi_j\\mid\\psi_k\\rangle\\mid^{2} = 1/(d+1)$ for all $j != k$? Zauner's conjecture further asserts a Weyl-Heisenberg covariant solution whose fiducial vector is fixed by an order-3 Clifford unitary. Exact solutions are known in all $d$ up to about 50 and in some much larger $d$, numerical ones in all d up to about 150 (figures approximate).","problem_ref":null,"references":"","settled_by":"A proof of existence for all d, or a dimension with no SIC.","status_note":"A route via the Stark conjectures of algebraic number theory makes existence conditional for some infinite families (Appleby, Flammia, McConnell and Yard 2017 onward); no unconditional proof as of 2026.","title":"Do SIC-POVMs exist in every finite dimension","topic_ref":"1bdfc0d09903d73034d6e6510c6d21f380d002328cb4a356dee914b540fb53cc"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"f6d64e6549d380a918e0f747875789012bc4c786b6b351aa03701b680a56a3e8","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"d7ee4e98dfb2cac4f494811122955c58f990ceec7b298426070f7bf78e2129c0","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"Fpdg1Gi16jjBi5ctSEjqtUpUGoX81Pb0RCy7mnaWapmTYCIwHGExf5O2ZDPp2hK2_goq6GnE4UkCSbYwnaqSAQ"},"schema":"pubphys.envelope/1"},"record_hash":"f6d64e6549d380a918e0f747875789012bc4c786b6b351aa03701b680a56a3e8","leaf_index":2055}