ea

codes/classical/bits/nonlinear/gray_map/gray.yml

@@ -34,6 +34,9 @@ notes:
 relations:
   parents:
     - code_id: bits_into_bits
+  cousins:
+    - code_id: qubits_into_qubits
+      detail: 'Gray codes are useful in optimizing qubit unitary circuits \cite{arxiv:quant-ph/0312218}.'
 
 
 # Begin Entry Meta Information

codes/eacq.yml

@@ -9,13 +9,24 @@ code_id: eacq
 
 name: 'Entanglement-assisted hybrid classical-quantum (EACQ) code'
 short_name: 'EACQ'
-introduced: '\cite{arxiv:0802.2414,arxiv:0807.2080,arxiv:1701.06963,arxiv:1911.12260,arxiv:2202.02184}'
+introduced: '\cite{arxiv:0802.2414,arxiv:0807.2080,arxiv:1911.12260}'
+
+description: |
+  Code that encodes quantum and classical information and requires pre-shared entanglement for transmission.
+
+  EACQ block quantum codes on \(n\) Galois qubits of dimensional \(q\) are denoted by \(((n,k:c,d;e))_q\), where \(k\) (\(c\)) is the number of encoded qubits (classical bits), where \(d\) is the distance, and where \(e\) is the required number of pre-shared ebits.
+  Similarly, block codes on \(n\) modular qudits are denoted by \(((n,k:c,d;e))_{\mathbb{Z}_q}\).
 
-description: 'Stub.'
 # arxiv:1701.06963,arxiv:1911.12260 uses union and CWS
 
+protection: |
+  The EACQ Singleton bound represents a triple trade-off region in the combined classical-bit, qubit, and e-bit space \cite{arxiv:2202.02184}.
+
+features:
+  rate: 'Tradeoff between classical communication, quantum communication, and entanglement distribution has been examined \cite{arxiv:0811.4227,arxiv:0901.3038,arxiv:0903.3920}; see also Ref. \cite{arXiv:quant-ph/0501045}.'
+
 relations:
-  parents:
+  cousins:
     - code_id: oaecc
       detail: 'EACQ codes utilize additional ancillary subsystems in a pre-shared entangled state, but reduce to operator-algebra QECCs when said subsystems are interpreted as noiseless physical subsystems.'
 

codes/oaecc.yml

@@ -28,6 +28,9 @@ 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}.'
+
 # Begin Entry Meta Information
 _meta:
   # Change log - most recent first

codes/quantum/eaoecc.yml

@@ -11,13 +11,18 @@ name: 'Entanglement-assisted (EA) operator QECC'
 short_name: 'EAOQECC'
 introduced: '\cite{arxiv:0708.2142,doi:10.1109/ISIT.2007.4557160}'
 
-description: 'Subsystem QECC whose encoding and decoding utilizes pre-shared entanglement between sender and receiver.'
+description: |
+  Subsystem QECC whose encoding and decoding utilizes pre-shared entanglement between sender and receiver.
+
+  
 
 relations:
   parents:
-    - code_id: oecc
-      detail: 'EQ operator QECCs utilize additional ancillary subsystems in a pre-shared entangled state, but reduce to subsystem QECCs when said subsystems are interpreted as noiseless physical subsystems.'
     - code_id: eacq
+  cousins:
+    - code_id: oecc
+      detail: 'EQOQECCs utilize additional ancillary subsystems in a pre-shared entangled state, but reduce to subsystem QECCs when said subsystems are interpreted as noiseless physical subsystems.'
+
 
 
 # Begin Entry Meta Information

codes/quantum/eaqecc.yml

@@ -9,15 +9,22 @@ code_id: eaqecc
 
 name: 'Entanglement-assisted (EA) QECC'
 short_name: 'EAQECC'
-introduced: '\cite{arxiv:quant-ph/0608027,arxiv:quant-ph/0610092}'
+introduced: '\cite{arXiv:quant-ph/0205117
+,arxiv:quant-ph/0608027,arxiv:quant-ph/0610092}'
 
 alternative_names:
   - 'Catalytic QECC'
 
 description: 'QECC whose encoding and decoding utilizes pre-shared entanglement between sender and receiver.'
 
+protection: |
+  The original EAQECC Singleton bound \cite{arxiv:quant-ph/0608027,arxiv:quant-ph/0610092} was shown to be erroneous \cite{arxiv:2007.01249} and corrected in Ref. \cite{arxiv:2010.07902}.
+
+features:
+  rate: 'Bounds on the minimum entanglement required to achieve the entanglement-assisted channel capacity are derived \cite{arXiv:quant-ph/0205117}.'
+
 notes:
-  - 'See Ref. \cite{doi:10.1017/CBO9781139034807.009} for an introduction to EA QEC.'
+  - 'See Ref. \cite{doi:10.1017/CBO9781139034807.009} for an introduction to EAQECCs.'
 
 relations:
   parents:

codes/quantum/oecc.yml

@@ -9,8 +9,8 @@ name: 'Subsystem QECC'
 introduced: '\cite{arxiv:quant-ph/0412076,arxiv:quant-ph/0504189}'
 
 alternative_names:
-  - 'Operator quantum error-correcting code'
-  - 'Gauge quantum error-correcting code'
+  - 'Operator QECC (OQECC)'
+  - 'Gauge QECC'
 
 description: |
   Quantum code encoding information in a subsystem \(\mathsf{A}\) of the code space \(\mathsf{C}\), which is part of the system Hilbert space \(\mathsf{H}\), as

codes/quantum/properties/block/ea_mds.yml

@@ -10,7 +10,7 @@ name: 'EA MDS code'
 introduced: '\cite{arxiv:quant-ph/0610092,arxiv:1008.2598}'
 
 description: |
-  EA code that satisfies the generalization of the quantum Singleton bound to EA codes \cite[Thm. 6]{arxiv:2010.07902}.
+  EA code whose parameters make the EA quantum Singleton bound \cite[Thm. 6]{arxiv:2010.07902} become an equality.
 
 
 relations:

codes/quantum/quantum_into_quantum.yml

@@ -10,11 +10,12 @@ code_id: quantum_into_quantum
 name: 'Quantum code'
 
 description: |
-  Code designed for transmission of quantum information through a quantum channel for the purposes of robust storage, communication, or sensing. Transmission can be performed with side information or entanglement.
+  Code designed for transmission of quantum and, optionally, classical information through a quantum channel for the purposes of robust storage, communication, or sensing. 
+  Transmission can be performed with side information or entanglement.
 
-relations:
-  parents:
-    - code_id: eacq
+# relations:
+# parents:
+#   - code_id: eacq
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/qubits_into_qubits.yml

@@ -139,6 +139,7 @@ relations:
       detail: 'Spin codes with spin \(\ell=1/2\) correspond to qubit codes.'
 
 
+
 # Begin Entry Meta Information
 _meta:
   # Change log - most recent first

codes/quantum/qubits/subsystem/subsystem_stabilizer.yml

@@ -15,7 +15,8 @@ alternative_names:
 
 description: |
   A stabilizer code with some of its logical qubits denoted as \textit{gauge} qubits and not used for storage of logical information.
-  Note that this doesnt lead to new codes but does lead to new error correction and fault tolerance procedures. Subsystem codes are denoted by \([[n,k,r,d]]\), similar to stabilizer codes, but with an extra parameter \(r\) denoting the number of gauge qubits.
+  Note that this doesnt lead to new codes but does lead to new error correction and fault tolerance procedures.
+  Subsystem codes are denoted by \([[n,k,r,d]]\), similar to stabilizer codes, but with an extra parameter \(r\) denoting the number of gauge qubits.
 
   To create these codes proceed as follows.
   Choose \(2n\) operators \(\{ \tilde{X}_j,\tilde{Z}_j\}_{j=1}^n\) from \(\mathsf{P}_n\), the Pauli group on \(n\) qubits, such that they obey the same commutation relations as the regular \(n\)-qubit Pauli generators \( \{X_j,Z_j\}_{j=1}^n \) (the subscript on these latter operators indicates the single qubit the Pauli matrix acts on).