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codes/quantum/properties/block/tensor_network/single_tensor/ame.yml

@@ -52,7 +52,9 @@ relations:
     - code_id: galois_grs
       detail: 'GRS codes can yield perfect tensors via a generalized Hermitian construction \cite{arxiv:1801.09623,arxiv:1812.04057}.'
     - code_id: quantum_secret_sharing
-      detail: 'Perfect tensors are useful for quantum secret sharing \cite{arxiv:1204.2289}.'
+      detail: 'Perfect tensors are useful for quantum secret sharing and state teleportation \cite{arxiv:1204.2289}.'
+    - code_id: qubit_stabilizer
+      detail: 'The codespace of a qubit stabilizer code with \hyperref[topic:quantum-weight-enumerator]{pure distance} \(d_{\smallsetminus}\) is a \((d_{\smallsetminus}-1)\)-uniform space.'
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/qubits_into_qubits.yml

@@ -77,11 +77,11 @@ protection: |
   The weight enumerator and its dual satisfy the \textit{quantum MacWilliams identity} \cite{arxiv:quant-ph/9610040}; see \cite[Ch. 7]{preset:GottesmanBook}.
   It gives rise to quantum linear programming (LP) bounds \cite{arxiv:quant-ph/9611001,arxiv:quant-ph/9709049}; see the book \cite{preset:GottesmanBook}.
 
-  The distance \(d\) of a code is the smallest \(j=d\) at which \(A_j \neq B_j\) \cite{arxiv:quant-ph/9906126}.
+  The distance \(d\) of a code is the smallest \(1<j=d\) at which \(A_j \neq B_j\) \cite{arxiv:quant-ph/9906126}.
   A code is called \textit{pure} if \(A_j = 0\) for all \(1 < j < d\); otherwise, the code is called \textit{impure}.
   The \textit{pure distance} \cite{arxiv:2107.14252} (a.k.a. diagonal distance \cite{arxiv:0712.1979}) \(d_{\smallsetminus}\) is the smallest \(1 < j=d_{\smallsetminus}\) at which \(A_j > 0\).
   Codes for which \(d_{\smallsetminus} < d\) are impure, otherwise they are pure.
-  For impure codes, there exists a Pauli error of weight less than the code distance that has a non-zero expectation value with respect to a code state.
+  For impure codes, there exists a Pauli error of weight less than the \(d\) that has a non-zero expectation value with respect to a code state.
 
   Degenerate qubit codes are impure, but impure codes may not be degenerate \cite{preset:GottesmanBook}.
   There are subtleties with defining \hyperref[topic:degeneracy]{degeneracy} for non-stabilizer qubit codes with even distance \cite{preset:GottesmanBook}.

codes/quantum/qubits/stabilizer/data_syndrome.yml

@@ -34,6 +34,9 @@ features:
   fault_tolerance:
     - 'Shor error correction \cite{arxiv:quant-ph/9605011,arxiv:quant-ph/9605031}, in which fault tolerance against syndrome extraction errors is ensured by simply repeating syndrome measurements \(\ell\) times, can be recast as a QDS code whose underlying matrix \(A\) is the identity matrix \(I_m\) repeated \(\ell\) times \cite{arxiv:1907.01393}.'
 
+notes:
+  - 'QDS codes can be used to estimate physical Pauli noise up to their \hyperref[topic:quantum-weight-enumerator]{pure distance} \cite{arxiv:2107.14252}, and logical Pauli noise for any correctable physical noise \cite{arxiv:2209.09267}.'
+
 
 relations:
   parents:

codes/quantum/qubits/stabilizer/qubit_stabilizer.yml

@@ -111,7 +111,7 @@ protection: |
   A stabilizer code is a \hyperref[topic:degeneracy]{degenerate} with respect to \(\mathcal{E}\) if and only if \(E^\dagger F \in \mathsf{N(S)}\) for some Pauli strings \(E,F \in \mathcal{E}\).
   As a distance-\(d\) code, a stabilizer code is degenerate if it admits a non-identity stabilizer whose weight is lower than the distance \cite{preset:GottesmanBook}.
   Since that stabilizer is in the normalizer, a stabilizer code is degenerate if and only if it is \hyperref[topic:quantum-weight-enumerator]{impure}.
-  The \hyperref[topic:quantum-weight-enumerator]{pure distance} of a stabilizer code is the minimum weight of a non-identity stabilizer. 
+  The \hyperref[topic:quantum-weight-enumerator]{pure distance} of a qubit stabilizer code is the minimum weight of a non-identity stabilizer. 
 
   \begin{defterm}{Cleaning lemma}
   \label{topic:cleaning-lemma}
@@ -212,7 +212,7 @@ notes:
   - 'See Quantum Codes qubit stabilizer database, maintained by N. Aydin, P. Liu, and B. Yoshino \cite{arxiv:2106.12065,arxiv:2108.03567}, at this \href{https://quantumcodes.info/}{website}.'
   - 'Entanglement purification protocols with qubit stabilizer codes are related to quantum key distribution (QKD) \cite{arxiv:quant-ph/0209091}. There is a correspondence between stabilizer codes and bilocal Clifford entanglement distillation circuits \cite{arxiv:2303.11465}.'
   - 'The overlap between any stabilizer codeword and any \(n\)-qubit product state is at most \(2/2^d\) \cite[Thm. 2]{arxiv:2405.01332}.'
-  - 'Qubit stabilizer codes can be used to estimate Pauli noise \cite{arxiv:2107.14252}.'
+  - 'Qubit stabilizer codes can be used to estimate physical Pauli noise up to their \hyperref[topic:quantum-weight-enumerator]{pure distance} \cite{arxiv:2107.14252}, and logical Pauli noise for any correctable physical noise \cite{arxiv:2209.09267}.'
   - 'The stabilizer formalism has been gamified \cite{arxiv:2405.06795}.'
   - 'Codes can be found via genetic algorithms \cite{arxiv:2409.13017}.'
 

codes/quantum/qubits/subsystem/subsystem_stabilizer.yml

@@ -76,6 +76,8 @@ features:
 
 notes:
   - 'See Ref. \cite{arxiv:1009.2203} for algorithms and lists of possible tilings of particular subsystem codes.'
+  - 'Subsystem qubit stabilizer codes can be used to estimate logical Pauli noise for any correctable physical noise \cite{arxiv:2209.09267}.'
+
 
 relations:
   parents: