{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"50ce19641359096b78f3b13246282a4449388f0e47be3afbf81eda621fedda21","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","f6d64e6549d380a918e0f747875789012bc4c786b6b351aa03701b680a56a3e8"],"salt":"7aa089c6524d62246de0735c485d53fe3111d84533c40e7ea3789aba10d2a2a1","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":"2","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":"f6d64e6549d380a918e0f747875789012bc4c786b6b351aa03701b680a56a3e8","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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9c83e13da0672bf6ae1d5c4fda6c93e20ddd2c7ca15a23339053945cd3d09de4","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"41b21e159051a9d6877dee2bf945c79a0b48c281edf75720fc19b727f3fe7712","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"_gA-cwx_z8it2h6Euddvzas3RzZWXkBz6Vl9hiQQIzEVMG_MYD_YAXMCHriFMKLWB3zkQBp-rP2XDCeeeXaPBQ"},"schema":"pubphys.envelope/1"},"record_hash":"9c83e13da0672bf6ae1d5c4fda6c93e20ddd2c7ca15a23339053945cd3d09de4","leaf_index":3762}