term:ad, mceliece remove, ad refs

codes/classical/q-ary_digits/distributed_storage/mds.yml

@@ -27,9 +27,10 @@ description: |
 protection: 'Given \(n\) and \(k\), MDS codes have the highest distance possible of all codes and so have the best possible error-correction properties.'
 
 realizations:
-  - 'The McEliece Public Key Cryptosystem \cite{manual:{McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. DSN Progress Report pp. 114–116 (1978).}} uses algebraic coding theory to secure communications against eavesdropping attack, in which private keys are generator matrices of linear codes, i.e., \(G\). Public Keys shared to outside world are scrambled and permutated versions of \(G\), i.e., \(G^\prime=SGP\). Data to be encrypted, \(u\), is multiplied by public key and added intentional errors \(e\), i.e., \(x=uG^\prime+e\). Upon receiving encrypted data, private key owner can apply inverse permutation \(P^{-1}\) to \(x\), decode the scrambled message given the presence of \(e\) errors, and finally unscramble to obtain \(u\). Security parameters of the system are \(n\) and \(e\), hence MDS codes, such as GRS codes may provide the same security level for shorter key sizes, and the private key owner can decode arguably fast enough using known decoding algorithms.'
   - 'Automatic repeat request (ARQ) data transmission protocols (\cite{doi:10.1109/9780470546345}, Ch. 7).'
 
+# - 'The McEliece Public Key Cryptosystem \cite{manual:{McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. DSN Progress Report pp. 114–116 (1978).}} uses algebraic coding theory to secure communications against eavesdropping attack, in which private keys are generator matrices of linear codes, i.e., \(G\). Public Keys shared to outside world are scrambled and permutated versions of \(G\), i.e., \(G^\prime=SGP\). Data to be encrypted, \(u\), is multiplied by public key and added intentional errors \(e\), i.e., \(x=uG^\prime+e\). Upon receiving encrypted data, private key owner can apply inverse permutation \(P^{-1}\) to \(x\), decode the scrambled message given the presence of \(e\) errors, and finally unscramble to obtain \(u\). Security parameters of the system are \(n\) and \(e\), hence MDS codes, such as GRS codes may provide the same security level for shorter key sizes, and the private key owner can decode arguably fast enough using known decoding algorithms.'
+
 notes:
   - 'See Ref. \cite{doi:10.1016/j.ffa.2014.10.006} for a review of MDS codes and the MDS conjecture.'
 
@@ -55,6 +56,10 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: MarkusGrassl
+      date: '2024-07-11'
+    - user_id: VictorVAlbert
+      date: '2024-07-11'
     - user_id: VictorVAlbert
       date: '2022-08-09'
     - user_id: VictorVAlbert

codes/classical/spherical/modulation/bpsk.yml

@@ -22,7 +22,7 @@ description: |
 # in a PAM, PSK, or QAM scheme.
 
 features:
-  rate: 'Achieve capacity of AGWN in the low signal-to-noise regime \cite{doi:10.1109/ALLERTON.2010.5706965} (see also \cite{doi:10.1002/j.1538-7305.1948.tb00917.x}). BPSK concatenated with quantum-classical polar codes achieves the Holevo capacity for the pure-loss channel \cite{arxiv:1202.0533}.'
+  rate: 'Achieve capacity of AGWN in the low signal-to-noise regime \cite{doi:10.1109/ALLERTON.2010.5706965} (see also \cite{doi:10.1002/j.1538-7305.1948.tb00917.x}). BPSK concatenated with quantum-classical polar codes achieves the Holevo capacity for the \hyperref[topic:ad]{AD} channel \cite{arxiv:1202.0533}.'
 
 realizations:
   - 'Telephone-line modems throughout 1950s and 1960s: Bell 103 and 202, as well as international standards V.21 \cite{manual:{International Telecommunication Union-T, Recommendation V.21: 300 bits per second duplex modem standardized for use in the general switched telephone network, 1984}} and V.23 \cite{manual:{International Telecommunication Union-T, Recommendation V.23: 600/1200-baud modem standardized for use in the general switched telephone network, 1988}}.'
@@ -41,7 +41,7 @@ relations:
     - code_id: two-legged-cat
       detail: 'BPSK (two-component cat) codes are used to transmit classical (quantum) information using (superpositions of) antipodal coherent states over classical (quantum) channels.'
     - code_id: polar_for_quantum
-      detail: 'BPSK concatenated with quantum-classical polar codes achieves the Holevo capacity for the pure-loss channel \cite{arxiv:1202.0533}.'
+      detail: 'BPSK concatenated with quantum-classical polar codes achieves the Holevo capacity for the \hyperref[topic:ad]{AD} channel \cite{arxiv:1202.0533}.'
 
 
 # Begin Entry Meta Information

codes/quantum/oscillators/coherent_state/qsc.yml

@@ -43,29 +43,31 @@ protection: |
 
   The code also protects against general ladder errors, which are defined as
   \begin{align}
-    L_{\mathbf{p},\mathbf{q}}(\mathbf{a}^{\dagger},\mathbf{a})=\prod_{j=1}^{n}a_{j}^{\dagger p_{j}}a_{j}^{q_{j}}~.
+    E_{\mathbf{p},\mathbf{q}}(\mathbf{a}^{\dagger},\mathbf{a})=\prod_{j=1}^{n}a_{j}^{\dagger p_{j}}a_{j}^{q_{j}}~.
   \end{align}
-  Any pure-loss ladder error \(L_{\mathbf{p}=\boldsymbol{0},\mathbf{q}}\) with \(|\mathbf{q}|<d_{\downarrow}\) is detectable.
-  Any ladder error \(L_{\mathbf{p},\mathbf{q}}\) with \(|\mathbf{p}|,|\mathbf{q}|<t_{\downarrow}\) is detectable, implying that up to \(t_{\downarrow}-1\) losses are correctable.
+  Any \hyperref[topic:ad]{AD} ladder error \(E_{\mathbf{p}=\boldsymbol{0},\mathbf{q}}\) with \(|\mathbf{q}|<d_{\downarrow}\) is detectable.
+  Any ladder error \(E_{\mathbf{p},\mathbf{q}}\) with \(|\mathbf{p}|,|\mathbf{q}|<t_{\downarrow}\) is detectable, implying that up to \(t_{\downarrow}-1\) losses are correctable.
   Any ladder error with degree \(|\mathbf{p}+\mathbf{q}|<d_{\updownarrow}\) is detectable.
 
+features:
+  decoders:
+    - 'Lindbladian scheme stabilizing all points in the constellation and protecting from the \hyperref[topic:ad]{AD} operator \(E_{0}^{\otimes n}\) \cite{arxiv:2302.11593}.'
 
 relations:
   parents:
     - code_id: coherent_constellation
       detail: 'Coherent-state QSCs are coherent-state constellation codes constrained to lie on a sphere.'
+    - code_id: ampdamp
+      detail: 'QSC codewords are superpositions of coherent states with the same energy, but coherent states are not eigenstates of the energy Hamiltonian. The \hyperref[topic:ad]{AD} Kraus operator \(E_{0}^{\otimes n}\) acts identically on each coherent state by shrinking the radius of the QSC''s sphere.'
   cousins:
     - code_id: group_representation
-      detail: 'QSCs should be able to be formulated as group-representation codes whose group is that formed by the permutation representation of the code polytope symmetry group.
-      It remains to show that the permutation representation is irreducible.'
+      detail: 'QSCs should be able to be formulated as group-representation codes whose group is that formed by the permutation representation of the code polytope symmetry group, but this representation may be reducible.'
     - code_id: points_into_spheres
       detail: 'QSCs are quantum analogues of spherical and constant-energy codes because they store information in quantum superpositions of points on a sphere in quantum phase space.'
     - code_id: spherical
       detail: 'QSCs are quantum analogues of spherical and constant-energy codes because they store information in quantum superpositions of points on a sphere in quantum phase space.'
     - code_id: single_spin
       detail: 'Single-spin codes whose codewords are expressed in terms of discrete sets of spin-coherent states may also be interpreted as QSCs.'
-    - code_id: paircat
-      detail: 'Pair-cat codes are QSCs embedded into the configuration space of pair-coherent states.'
     - code_id: qubit_css
       detail: 'CSS codes concatenated with two-component cat codes form QSCs which have a weight-based notion of distance.'
     - code_id: oscillators_concatenated

codes/quantum/oscillators/fock_state/constant_excitation/chuang-leung-yamamoto.yml

@@ -26,7 +26,7 @@ description: |
 
 
 protection: |
-  Protects against amplitude damping for up to \(t = d-1\) excitation losses. Defining the \textit{spacing} between two Fock states \(|u_1\cdots u_n\rangle\) and \(|v_1\cdots v_n\rangle\),
+  Protects against \hyperref[topic:ad]{AD} for up to \(t = d-1\) excitation losses. Defining the \textit{spacing} between two Fock states \(|u_1\cdots u_n\rangle\) and \(|v_1\cdots v_n\rangle\),
   \begin{align}
   \text{Spacing}(u,v) = \frac{1}{2}\sum_{i=1}^n |u_i - v_i|,
   \end{align}

codes/quantum/oscillators/fock_state/constant_excitation/dual_rail.yml

@@ -29,7 +29,7 @@ features:
     - 'Error-detecting \(CCZ\) and \(cSWAP\) gates using three-level ancilla \cite{arxiv:2212.11196}.'
 
   fault_tolerance:
-    - 'Dual-rail qubits can be used to convert leakage and amplitude damping noise into erasure noise \cite{arxiv:0710.1052,arxiv:2208.05461}.'
+    - 'Dual-rail qubits can be used to convert leakage and \hyperref[topic:ad]{AD} noise into erasure noise \cite{arxiv:0710.1052,arxiv:2208.05461}.'
 
   threshold:
     - 'Between \(1.78\%\) and \(11.5\%\) with faulty photon detectors when repeatedly concatenating with the Steane code \cite{arxiv:quant-ph/0502101}.'
@@ -52,13 +52,13 @@ relations:
   cousins:
     - code_id: quantum_concatenated
       detail: 'The KLM protocol, one of the first protocols for fault-tolerant quantum computation, utilizes concatenations of the dual-rail with a stabilizer code \cite{doi:10.1038/35051009}.
-      Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code \cite{arxiv:2010.00538} that protects against \(d-1\) amplitude damping errors \cite{arxiv:1001.2356}.'
+      Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code \cite{arxiv:2010.00538} that protects against \(d-1\) \hyperref[topic:ad]{AD} errors \cite{arxiv:1001.2356}.'
     - code_id: ampdamp
-      detail: 'Dual-rail qubits can be used to convert leakage and amplitude damping noise into erasure noise \cite{arxiv:0710.1052,arxiv:2208.05461}. Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code \cite{arxiv:2010.00538} that protects against \(d-1\) amplitude damping errors \cite{arxiv:1001.2356}.'
+      detail: 'Dual-rail qubits can be used to convert leakage and \hyperref[topic:ad]{AD} noise into erasure noise \cite{arxiv:0710.1052,arxiv:2208.05461}. Concatenating the dual-rail code with an \([[n,k,d]]\) stabilizer code yields an \([[2n,k,d]]\) constant-excitation code \cite{arxiv:2010.00538} that protects against \(d-1\) \hyperref[topic:ad]{AD} errors \cite{arxiv:1001.2356}.'
     - code_id: quantum_parity
-      detail: 'An \([[8,1,2]]\) QPC correcting a single amplitude damping error is equivalent to a concatenation of the \(\{|\overline{01}\rangle,|\overline{11}\rangle\}\) (constant-excitation) subcode of the \([[4,2,2]]\) code with the dual-rail code \cite{arxiv:quant-ph/0103042,arxiv:quant-ph/0501184,arxiv:2010.00538}. More generally, an \([[m^2,1,m]]\) QPC corrects \(m-1\) amplitude damping errors \cite{arxiv:1001.2356}.'
+      detail: 'An \([[8,1,2]]\) QPC correcting a single \hyperref[topic:ad]{AD} error is equivalent to a concatenation of the \(\{|\overline{01}\rangle,|\overline{11}\rangle\}\) (constant-excitation) subcode of the \([[4,2,2]]\) code with the dual-rail code \cite{arxiv:quant-ph/0103042,arxiv:quant-ph/0501184,arxiv:2010.00538}. More generally, an \([[m^2,1,m]]\) QPC corrects \(m-1\) \hyperref[topic:ad]{AD} errors \cite{arxiv:1001.2356}.'
     - code_id: stab_4_2_2
-      detail: 'An \([[8,1,2]]\) QPC correcting a single amplitude damping error is equivalent to a concatenation of the \(\{|\overline{01}\rangle,|\overline{11}\rangle\}\) (constant-excitation) subcode of the \([[4,2,2]]\) code with the dual-rail code \cite{arxiv:quant-ph/0103042,arxiv:quant-ph/0501184,arxiv:2010.00538}. More generally, an \([[m^2,1,m]]\) QPC corrects \(m-1\) amplitude damping errors \cite{arxiv:1001.2356}.'
+      detail: 'An \([[8,1,2]]\) QPC correcting a single \hyperref[topic:ad]{AD} error is equivalent to a concatenation of the \(\{|\overline{01}\rangle,|\overline{11}\rangle\}\) (constant-excitation) subcode of the \([[4,2,2]]\) code with the dual-rail code \cite{arxiv:quant-ph/0103042,arxiv:quant-ph/0501184,arxiv:2010.00538}. More generally, an \([[m^2,1,m]]\) QPC corrects \(m-1\) \hyperref[topic:ad]{AD} errors \cite{arxiv:1001.2356}.'
     - code_id: cluster_state
       detail: 'The KLM protocol can be combined cluster states in various ways \cite{arxiv:quant-ph/0303008,arxiv:quant-ph/0402005,arxiv:quant-ph/0405157}.'
 

codes/quantum/oscillators/fock_state/fock_state.yml

@@ -10,7 +10,7 @@ logical: qudits
 name: 'Fock-state bosonic code'
 #introduced: '\cite{arxiv:quant-ph/9505011,arxiv:quant-ph/9610043}'
 
-description: 'Qudit-into-oscillator code whose protection against amplitude damping (i.e., photon loss) stems from the use of disjoint sets of Fock states for the construction of each code basis state. The simplest example is the dual-rail code, which has codewords consisting of single Fock states \(|10\rangle\) and \(|01\rangle\). This code can detect a single loss error since a loss operator in either mode maps one of the codewords to a different Fock state \(|00\rangle\). More involved codewords consist of several well-separated Fock states such that multiple loss events can be detected and corrected.'
+description: 'Qudit-into-oscillator code whose protection against \hyperref[topic:ad]{AD} noise (i.e., photon loss) stems from the use of disjoint sets of Fock states for the construction of each code basis state. The simplest example is the dual-rail code, which has codewords consisting of single Fock states \(|10\rangle\) and \(|01\rangle\). This code can detect a single loss error since a loss operator in either mode maps one of the codewords to a different Fock state \(|00\rangle\). More involved codewords consist of several well-separated Fock states such that multiple loss events can be detected and corrected.'
 
 protection: 'Code distance \(d\) is the minimum distance (assuming some metric) between any two labels of Fock states corresponding to different code basis states. For a single mode, \(d\) is the minimum absolute value of the difference between any two Fock-state labels; such codes can detect up to \(d-1\) loss events. Multimode distances can be defined analogously; see, e.g., \hyperref[code:chuang-leung-yamamoto]{Chuang-Leung-Yamamoto codes}. There are tradeoffs in how well a Fock-state code protects against loss/gain errors and dephasing noise \cite{arxiv:2008.12576}.'
 
@@ -21,7 +21,7 @@ relations:
   parents:
     - code_id: qudits_into_oscillators
     - code_id: ampdamp
-      detail: 'Fock-state codes are designed to protect against bosonic AD noise.'
+      detail: 'Fock-state codes are designed to protect against bosonic \hyperref[topic:ad]{AD} noise.'
   cousins:
     - code_id: bits_into_bits
       detail: 'Fock-state code distance is a natural extension of Hamming distance between binary strings.'

codes/quantum/oscillators/fock_state/rotation/binomial.yml

@@ -32,7 +32,7 @@ description: |
     \end{align}
     The extended binomial coefficients \( \binom{n}{m}_q \) are also the coefficients of \( x^m \) in the polynomial \( (1 + x + \cdots + x^{q-1})^n \).
 
-protection: 'An \((N, S)\) binomial code protects against \(L\) boson losses, \(G\) boson gains, and dephasing up to \(\hat{n}^{D}\), where \(S=L+G\) and \(N = \mathrm{max}(L,G,2D)\).  Binomial codes approximately protect against continuous-time amplitude damping, boson loss and gain, and dephasing.'
+protection: 'An \((N, S)\) binomial code protects against \(L\) boson losses, \(G\) boson gains, and dephasing up to \(\hat{n}^{D}\), where \(S=L+G\) and \(N = \mathrm{max}(L,G,2D)\).  Binomial codes approximately protect against continuous-time \hyperref[topic:ad]{AD}, boson loss and gain, and dephasing.'
 
 features:
   general_gates:

codes/quantum/oscillators/oscillators.yml

@@ -45,7 +45,7 @@ protection: |
 
   \subsection{Loss and gain operators}
 
-  An error set relevant to \hyperref[code:fock_state]{Fock-state bosonic} codes is the set of loss operators associated with the \hyperref[code:ampdamp]{amplitude damping channel}, a common form of physical noise in bosonic systems. 
+  An error set relevant to \hyperref[code:fock_state]{Fock-state bosonic} codes is the set of loss operators associated with the \hyperref[topic:ad]{AD} channel, a common form of physical noise in bosonic systems. 
   For a single mode, loss operators are proportional to powers of the mode's annihilation operator \(a=(\hat{x}+i\hat{p})/\sqrt{2}\), where \(\hat x\) (\(\hat p\)) is the mode's position (momentum) operator, and with the power signifying the number of particles lost during the error. 
   For multiple modes, error set elements are tensor products of elements of the single-mode error set. 
 
@@ -55,9 +55,9 @@ protection: |
   These can also be obtained from qudit Pauli matrices through a limiting procedure \cite{arxiv:quant-ph/0109066} and allow one to expand trace-class operators despite not forming an orthonormal set \cite{arxiv:2211.05714}. These operators are correspong to the \textit{number-phase interpretation}, a polar-like decomposition of a single mode, complementing the cartesian-like decomposition in terms of position and momentum displacements.
 
 features:
-  rate: 'The quantum capacity of the pure-loss channel \cite{arxiv:quant-ph/0606132} and the dephasing noise channel \cite{arxiv:2205.05736} are both known.
+  rate: 'The quantum capacity of the \hyperref[topic:ad]{AD} channel \cite{arxiv:quant-ph/0606132} and the dephasing noise channel \cite{arxiv:2205.05736} are both known.
   The capacity of the displacement noise channel, the quantum analogue of AGWN, has been bounded using GKP codes \cite{arxiv:quant-ph/0105058,arxiv:1801.07271}.
-  Exact two-way assisted capacities have been obtained for the pure-loss channels and quantum limited amplifiers in what is known as the PLOB bound \cite{arxiv:1510.08863}.
+  Exact two-way assisted capacities have been obtained for the \hyperref[topic:ad]{AD} channels and quantum limited amplifiers in what is known as the PLOB bound \cite{arxiv:1510.08863}.
   These are examples of Gaussian channels, i.e., channels that map Gaussian states to Gaussian states \cite{doi:10.1016/0034-4877(79)90049-1,arxiv:quant-ph/0505151,arxiv:0707.0604,arxiv:0804.0511,arxiv:1004.0196,arxiv:1009.1108,arxiv:1012.4266}.'
 
   general_gates: