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codes/classical/ecc.yml

@@ -24,7 +24,8 @@ relations:
   cousins:
     - code_id: classical_into_quantum
       detail: 'Any ECC can be embedded into a quantum Hilbert space, and thus passed through a quantum channel, by associating elements of the alphabet with basis vectors in a Hilbert space over the complex numbers.
-      In other words, classical codewords are elements of an alphabet, while quantum codewords are functions on the alphabet.'
+      In other words, classical codewords are elements of an alphabet, while quantum codewords are functions on the alphabet.
+      Classical codes can be unified with quantum codes using an algebraic framework \cite{arxiv:1005.0353}.'
 
 
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codes/oaecc.yml

@@ -7,7 +7,7 @@ code_id: oaecc
 
 name: 'Operator-algebra QECC'
 short_name: 'OAQECC'
-introduced: '\cite{arxiv:quant-ph/0203105,arxiv:quant-ph/0608071,arxiv:0705.1574,arxiv:1005.0353,doi:10.1142/S0219749908003839,arxiv:2012.14001}'
+introduced: '\cite{arxiv:quant-ph/0608071,arxiv:0705.1574,arxiv:1005.0353,doi:10.1142/S0219749908003839,arxiv:2012.14001}'
 
 description: |-
   A code that encompasses both subsystem codes and hybrid codes using an operator-algebraic framework.
@@ -39,8 +39,6 @@ protection: |
   Indeed, \(\mathcal{A}\) is correctable for \(\mathcal{E}\) if \begin{align}P_{\mathcal{A}} E_j^\dagger E_k P_{\mathcal{A}} \in \mathcal{A}'\end{align}
   for all \(j,k\), where \(\mathcal{A}'\) is the commutant of \(\mathcal{A}\).
 
-features:
-  rate: 'The quantum capacity for simultaneous transmission of classical and quantum information has been derived \cite{arXiv:quant-ph/0311131}.'
 
 relations:
   parents:

codes/quantum/hybridqecc.yml

@@ -8,7 +8,7 @@ physical: qubits
 logical: qubits
 
 name: 'Hybrid QECC'
-introduced: '\cite{arxiv:quant-ph/0608071,arxiv:0802.2414}'
+introduced: '\cite{arxiv:quant-ph/0203105,arXiv:quant-ph/0311131,arxiv:quant-ph/0608071,arxiv:0802.2414}'
 
 description: |
   A quantum code which encodes both quantum and classical information.
@@ -25,7 +25,9 @@ description: |
 
 
 features:
-  rate: 'The existence of a hybrid code protecting against a channel depends on certain matricial ranges \cite{arxiv:1911.12744}.'
+  rate: 'The capacity of a hybrid quantum memory is determined by a convex region in the classical-quantum entropy plane \cite{arxiv:quant-ph/0203105}.
+  The quantum capacity for simultaneous transmission of classical and quantum information has been derived \cite{arXiv:quant-ph/0311131}.
+  The existence of a hybrid code protecting against a channel depends on certain matricial ranges \cite{arxiv:1911.12744}.'
 
 # 20240704 subsystem QECC, hybrid QECC, and QECC are three children of OAQECC
 relations:

codes/quantum/properties/block/holographic.yml

@@ -24,7 +24,7 @@ relations:
     - code_id: approximate_qecc
       detail: 'Universal subspace approximate error correction is used to model black holes \cite{arxiv:1807.06041}.'
     - code_id: approximate_oaecc
-      detail: 'Properties of holographic codes are often quantified in the Heisenberg picture, i.e., in terms of operator algebras \cite{arxiv:1411.7041,arxiv:1612.00017}.'
+      detail: 'Properties of holographic codes are often quantified in the Heisenberg picture, i.e., in terms of operator algebras \cite{arxiv:1411.7041,arxiv:1612.00017,arxiv:2012.14001}.'
 
 
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codes/quantum/qubits/oa_stabilizer/qubit_stabilizer_oaqecc.yml

@@ -10,7 +10,7 @@ logical: qubits
 # Allowed children only subsystem and OA codes; no quantum code children within kingdom
 name: 'Operator-algebra (OA) qubit stabilizer code'
 short_name: 'OA qubit stabilizer'
-introduced: '\cite{arxiv:1701.06963,arxiv:2304.11442}'
+introduced: '\cite{arxiv:2304.11442}'
 
 description: |-
   An OAQECC in which the commutant \(\mathcal{A}'\) of the logical algebra \(\mathcal{A}\) arises as the \hyperref[topic:group-algebra]{group algebra} of a subgroup \(\mathsf{G}\) of the \(n\)-qubit Pauli group \(\mathsf{P}_n\).
@@ -29,6 +29,9 @@ protection: |-
 relations:
   parents:
     - code_id: oaecc
+  cousins:
+    - code_id: bacon_shor
+      detail: 'The OA qubit stabilizer formalism yields hybrid Bacon-Shor codes \cite{arxiv:2304.11442}.'
 
 
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