From 4899b0c70e2b0700007d54230515eba5db210945 Mon Sep 17 00:00:00 2001
From: "Victor V. Albert" <valbert4@gmail.com>
Date: Fri, 17 Nov 2023 11:38:55 -0500
Subject: [PATCH] ea mds, two mode binomial

---
 .../constant_excitation/two-mode_binomial.yml | 44 +++++++++++++++++++
 .../fock_state/rotation/binomial.yml          |  2 -
 codes/quantum/properties/block/ea_mds.yml     | 28 ++++++++++++
 .../quantum/properties/block/quantum_mds.yml  |  2 +-
 4 files changed, 73 insertions(+), 3 deletions(-)
 create mode 100644 codes/quantum/oscillators/fock_state/constant_excitation/two-mode_binomial.yml
 create mode 100644 codes/quantum/properties/block/ea_mds.yml

diff --git a/codes/quantum/oscillators/fock_state/constant_excitation/two-mode_binomial.yml b/codes/quantum/oscillators/fock_state/constant_excitation/two-mode_binomial.yml
new file mode 100644
index 000000000..e6f4c92ec
--- /dev/null
+++ b/codes/quantum/oscillators/fock_state/constant_excitation/two-mode_binomial.yml
@@ -0,0 +1,44 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: two-mode_binomial
+physical: oscillators
+logical: qudits
+
+name: 'Two-mode binomial code'
+introduced: '\cite{doi:doi:10.1103/PhysRevA.56.1114}'
+
+description: |
+  Two-mode constant-energy CLY code whose coefficients are square-roots of binomial coefficients.
+
+  The simplest two-mode \(S=1\) code is an analogue of the "0-2-4" single-mode binomial code, with codewords
+  \begin{align}
+  \begin{split}
+    |\overline{0}\rangle&=\frac{1}{\sqrt{2}}\left(|40\rangle+|04\rangle\right)\\
+    |\overline{1}\rangle&=|22\rangle~.
+  \end{split}
+  \end{align}
+
+  The general codewords are
+  \begin{align}
+    |\overline{\mu}\rangle=\frac{1}{2^{J}}\sum_{m=0}^{2J}\left(-1\right)^{\mu m}\sqrt{{2J \choose m}}\left|2J-(S+1)m,(S+1)m\right\rangle~,
+  \end{align}
+  with spacing \(S\) and dephasing error parameter \(N\) such that \(J = \frac{1}{2}(N+1)(S+1)\) \cite{arXiv:1602.00008}.
+  The \(S=0\) version can be obtained by applying a \(50:50\) beamsplitter to the highest-weight Fock state \(|2J,0\rangle\) \cite{arxiv:1512.07605}.
+
+
+relations:
+  parents:
+    - code_id: chuang-leung-yamamoto
+  cousins:
+    - code_id: binomial
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2023-11-17'
diff --git a/codes/quantum/oscillators/fock_state/rotation/binomial.yml b/codes/quantum/oscillators/fock_state/rotation/binomial.yml
index 3a6e1c3df..0e92c1fe6 100644
--- a/codes/quantum/oscillators/fock_state/rotation/binomial.yml
+++ b/codes/quantum/oscillators/fock_state/rotation/binomial.yml
@@ -59,8 +59,6 @@ relations:
       detail: 'For a fixed \(S\), binomial codes with \(N \to \infty\) coincide with cat codes as \(\alpha \to \infty\) \cite{arXiv:1602.00008}.'
     - code_id: number_phase
       detail: 'In the limit as \(N,S \to \infty\), phase measurement in the binomial code has vanishing variance, just like in a number-phase code \cite{arxiv:1901.08071}.'
-    - code_id: chuang-leung-yamamoto
-      detail: 'Two-mode version of binomial codes correspond to two-mode "0-2-4" CLY codes (see Sec. IV.A of Ref. \cite{arXiv:1602.00008}).'
 
 
 # Begin Entry Meta Information
diff --git a/codes/quantum/properties/block/ea_mds.yml b/codes/quantum/properties/block/ea_mds.yml
new file mode 100644
index 000000000..81a28d0b7
--- /dev/null
+++ b/codes/quantum/properties/block/ea_mds.yml
@@ -0,0 +1,28 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: ea_mds
+
+
+name: 'EQ MDS code'
+introduced: '\cite{arxiv:quant-ph/9610043}'
+
+description: |
+  EQ code that satisfies the generalization of the quantum Singleton bound to EQ codes \cite[Thm. 6]{arxiv:2010.07902}.
+
+
+relations:
+  parents:
+    - code_id: eaqecc
+  cousins:
+    - code_id: quantum_mds
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2023-11-17'
diff --git a/codes/quantum/properties/block/quantum_mds.yml b/codes/quantum/properties/block/quantum_mds.yml
index f0fba1998..91e014be5 100644
--- a/codes/quantum/properties/block/quantum_mds.yml
+++ b/codes/quantum/properties/block/quantum_mds.yml
@@ -17,7 +17,7 @@ description: |
   2(d-1) \leq n-k
   \end{align}
   becomes an equality.
-
+  Such codes are pure \cite{arxiv:1907.07733}.
 
 protection: 'Given \(n\) and \(k\), MDS codes have the highest distance possible of all codes and so have the best possible error correction properties.'