refs

codes/classical/ecc.yml

@@ -11,11 +11,18 @@ short_name: 'ECC'
 description: |
   Code designed for transmission of classical information through classical channels in a robust way.
 
+features:
+  rate: 'The Shannon channel capacity (the maximum of the mutual information over input and output distributions) is the highest rate of information transmission through a classical (i.e., non-quantum) channel with arbitrarily small error rate \cite{doi:10.1002/j.1538-7305.1948.tb01338.x}.
+  Corrections to the capacity and tradeoff between decoding error, code rate and code length are determined using small \cite{manual:{V. Strassen, “Asymptotische Absch¨atzungen in Shannons Informationstheorie,” Trans. Third Prague Conference on Information Theory, Prague, 689–723, (1962)},arxiv:0801.2242,doi:10.1109/TIT.2010.2043769}, moderate \cite{arxiv:1208.1924,doi:10.1109/ALLERTON.2010.5707068,arxiv:1701.03114} and large \cite{doi:10.1007/978-3-7091-2945-6,doi:10.1017/CBO9780511921889,doi:10.1109/TIT.1973.1055007,doi:10.1109/TIT.1979.1056003} deviation analysis.
+  Sometimes the difference from the asymptotic rate at finite block length can be characterized by the \textit{channel dispersion} \cite{doi:10.1109/TIT.2010.2043769,doi:10.1109/TIT.2014.2341919}.'
+
 
 relations:
   parents:
     - code_id: oaecc
-      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. For example, a bit of information can be embedded into a two-dimensional vector space by associating the two bit values with two basis vectors for the space.'
+      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 what codewords are functions on the alphabet.
+      For example, a bit of information can be embedded into a two-dimensional vector space by associating the two bit values with two basis vectors for the space.'
 
 
 # Begin Entry Meta Information

codes/classical/properties/block/block.yml

@@ -24,8 +24,7 @@ protection: |
   Block codes protect from errors acting on a few of the \(n\) symbols. A block code with \textit{distance} \(d\) detects errors acting on up to \(d-1\) symbols, and corrects erasure errors on up to \(d-1\) symbols.
 
 features:
-  rate: 'The Shannon channel capacity (the maximum of the mutual information over input and output distributions) is the highest rate of information transmission through a classical (i.e., non-quantum) channel with arbitrarily small error rate \cite{doi:10.1002/j.1538-7305.1948.tb01338.x}.
-  Corrections to the capacity and tradeoff between decoding error, code rate and code length are determined using small \cite{manual:{V. Strassen, “Asymptotische Absch¨atzungen in Shannons Informationstheorie,” Trans. Third Prague Conference on Information Theory, Prague, 689–723, (1962)},arxiv:0801.2242,doi:10.1109/TIT.2010.2043769}, moderate \cite{arxiv:1208.1924,doi:10.1109/ALLERTON.2010.5707068,arxiv:1701.03114} and large \cite{doi:10.1007/978-3-7091-2945-6,doi:10.1017/CBO9780511921889,doi:10.1109/TIT.1973.1055007,doi:10.1109/TIT.1979.1056003} deviation analysis. Sometimes the difference from the asymptotic rate at finite block length can be characterized by the \textit{channel dispersion} \cite{doi:10.1109/TIT.2010.2043769,doi:10.1109/TIT.2014.2341919}.'
+  rate: 'Ideal decoding error scales is suppressed exponentially with the number of subsystems \(n\), and the exponent has been studied in Ref. \cite{doi:10.1002/j.1538-7305.1959.tb03905.x,10.1016/S0019-9958(67)90052-6,manual:{Fano, Robert M. The transmission of information. Vol. 65. Cambridge, MA, USA: Massachusetts Institute of Technology, Research Laboratory of Electronics, 1949.}}.'
   decoders:
     - 'Decoding an error-correcting code is equivalent to finding the ground state of some statistical mechanical model \cite{doi:10.1038/339693a0}.'
 

codes/classical_into_quantum/classical_into_quantum.yml

@@ -26,6 +26,8 @@ features:
     Corrections to the Holevo capacity and tradeoff between decoding error, code rate and code length are determined in quantum generalizations of small \cite{arxiv:1308.6503}, moderate \cite{arxiv:1701.03114,arxiv:1709.05258}, and large \cite{arxiv:1409.3562} deviation analysis.
     Bounds also exist on the one-shot capacity, i.e., the achievability of classical codes given only one use of the quantum channel \cite{arxiv:quant-ph/9703013,arxiv:quant-ph/0206186,arxiv:quant-ph/0611013,arxiv:1007.5456,arxiv:1312.3822,arxiv:2208.02132}; see \cite[Table 2]{arxiv:2208.02132} for a summary.
 
+    Ideal decoding error scales is suppressed exponentially with the number of subsystems \(n\) (for c-q block codes), and the exponent has been studied in Ref. \cite{arxiv:2310.09014}.
+
 relations:
   parents:
     - code_id: oaecc

codes/quantum/oscillators/stabilizer/lattice/gkp.yml

@@ -52,7 +52,7 @@ notes:
 
 realizations:
   - 'Motional degree of freedom of a trapped ion: square-lattice GKP encoding realized with the help of post-selection \cite{arxiv:1807.01033,arXiv:1907.06478}, followed by realization of reduced form of GKP error correction, where displacement error syndromes are measured to one bit of precision using an ion electronic state \cite{arxiv:2010.09681}.'
-  - 'Microwave cavity coupled to superconducting circuits: reduced form of square-lattice GKP error correction, where displacement error syndromes are measured to one bit of precision using an ancillary transmon \cite{arxiv:1907.12487}. Subsequent paper \cite{arxiv:2211.09116} uses reinforcement learning for error-correction cycle design and is the first to go beyond break-even error-correction, with the lifetime of a logical qubit exceeding the cavity lifetime by about a factor of two (see also \cite{arxiv:2211.09319}).'
+  - 'Microwave cavity coupled to superconducting circuits: reduced form of square-lattice GKP error correction, where displacement error syndromes are measured to one bit of precision using an ancillary transmon \cite{arxiv:1907.12487}. Subsequent paper by Devoret group \cite{arxiv:2211.09116} (see also \cite{arxiv:2310.11400}) uses reinforcement learning for error-correction cycle design and is the first to go beyond break-even error-correction, with the lifetime of a logical qubit exceeding the cavity lifetime by about a factor of two (see also \cite{arxiv:2211.09319}).'
   - 'GKP states and homodyne measurements have been realized in propagating telecom light by the Furusawa group \cite{arxiv:2309.02306}.'
   - 'Single-qubit \(Z\)-gate has been demonstrated in the single-photon subspace of an infinite-mode space \cite{arxiv:1904.01351}, in which time and frequency become bosonic conjugate variables of a single effective bosonic mode.'
   - 'In signal processing, GKP state position-state wavefunctions are related to Dirac combs \cite{doi:10.1007/978-1-4612-2016-9}.'