From 7bcc5d48d81e55462feb801ec911e6f2ccca5466 Mon Sep 17 00:00:00 2001 From: "Victor V. Albert" Date: Tue, 10 Dec 2024 18:49:43 -0500 Subject: [PATCH] ~ --- codes/classical/bits/reed_muller/biorthogonal.yml | 2 ++ codes/classical/spherical/polytope/polychoron/120cell.yml | 3 +++ codes/classical/spherical/polytope/polyhedron/dodecahedron.yml | 2 +- codes/classical/spherical/polytope/polytope.yml | 2 +- .../oscillators/coherent_state/psk/quantum_bpsk.yml | 1 + 5 files changed, 8 insertions(+), 2 deletions(-) diff --git a/codes/classical/bits/reed_muller/biorthogonal.yml b/codes/classical/bits/reed_muller/biorthogonal.yml index a5b1a046d..b1ce4cf36 100644 --- a/codes/classical/bits/reed_muller/biorthogonal.yml +++ b/codes/classical/bits/reed_muller/biorthogonal.yml @@ -42,6 +42,8 @@ relations: - code_id: biorthogonal_spherical detail: 'Each first-order RM code maps to a \((2^m,2^{m+1})\) biorthogonal spherical code under the \hyperref[topic:antipodal-mapping]{antipodal mapping} \cite{doi:10.1109/18.720542}\cite[Sec. 6.4]{manual:{Forney, G. D. (2003). 6.451 Principles of Digital Communication II, Spring 2003.}}\cite[pg. 19]{preset:EricZin}. In other words, first-order RM (biorthogonal spherical) codes form orthoplexes in Hamming (Euclidean) space.' + - code_id: dual_polytope + detail: 'Orthoplexes and hypercubes are dual to each other.' # Begin Entry Meta Information diff --git a/codes/classical/spherical/polytope/polychoron/120cell.yml b/codes/classical/spherical/polytope/polychoron/120cell.yml index db6cb140a..62c5dfcc7 100644 --- a/codes/classical/spherical/polytope/polychoron/120cell.yml +++ b/codes/classical/spherical/polytope/polychoron/120cell.yml @@ -22,6 +22,9 @@ relations: - code_id: polytope - code_id: spherical_design detail: 'The code forms a spherical 11-design because its vertices can be divided into five 600-cells, each of which forms said design.' + cousins: + - code_id: dual_polytope + detail: 'The 600-cell and 120-cell are dual to each other.' # Begin Entry Meta Information diff --git a/codes/classical/spherical/polytope/polyhedron/dodecahedron.yml b/codes/classical/spherical/polytope/polyhedron/dodecahedron.yml index 04e73b48b..4a1646766 100644 --- a/codes/classical/spherical/polytope/polyhedron/dodecahedron.yml +++ b/codes/classical/spherical/polytope/polyhedron/dodecahedron.yml @@ -10,7 +10,7 @@ logical: reals name: 'Dodecahedron code' description: | - Spherical \((3,20,2-2\sqrt{5}/2)\) code whose codewords are the vertices of the dodecahedron (alternatively, the centers of the faces of a icosahedron, the dodecahedron's dual polytope). + Spherical \((3,20,2-2\sqrt{5}/3)\) code whose codewords are the vertices of the dodecahedron (alternatively, the centers of the faces of a icosahedron, the dodecahedron's dual polytope). relations: diff --git a/codes/classical/spherical/polytope/polytope.yml b/codes/classical/spherical/polytope/polytope.yml index a0049e03d..6a727635d 100644 --- a/codes/classical/spherical/polytope/polytope.yml +++ b/codes/classical/spherical/polytope/polytope.yml @@ -11,7 +11,7 @@ name: 'Polytope code' description: | Spherical code whose codewords are the vertices of a polytope, i.e., a geometrical figure bounded by lines, planes, and hyperplanes \cite{preset:coxeter}. - Polytopes in two (three) real or complex dimensions are called polygons (polyhedra). + Polytopes in two (three, four) real or complex dimensions are called polygons (polyhedra, polychora). relations: diff --git a/codes/classical_into_quantum/oscillators/coherent_state/psk/quantum_bpsk.yml b/codes/classical_into_quantum/oscillators/coherent_state/psk/quantum_bpsk.yml index e8d4e5fc0..bedca65ac 100644 --- a/codes/classical_into_quantum/oscillators/coherent_state/psk/quantum_bpsk.yml +++ b/codes/classical_into_quantum/oscillators/coherent_state/psk/quantum_bpsk.yml @@ -23,6 +23,7 @@ features: - 'Photon-number resolving detector \cite{arxiv:1807.05199}.' - 'Non-Gaussian near-optimal receiver \cite{arxiv:0706.1038}.' - 'Multi-stage quantum receiver \cite{arxiv:1404.5033}.' + - 'Quantum receiver attaining the Helstrom bound in the low-photon regime \cite{arxiv:2410.21800}.' realizations: - 'Linear-optical quantum receiver \cite{arxiv:1103.5592}.'