diff --git a/codes/classical/ecc.yml b/codes/classical/ecc.yml index b7e0f572a..695059068 100644 --- a/codes/classical/ecc.yml +++ b/codes/classical/ecc.yml @@ -25,7 +25,7 @@ relations: - 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. - Classical codes can be unified with quantum codes using an algebraic framework \cite{arxiv:1005.0353}.' + Classical codes can be unified with quantum codes using various algebraic frameworks \cite{arxiv:0910.1536,arxiv:1005.0353}.' # Begin Entry Meta Information diff --git a/codes/oaecc.yml b/codes/oaecc.yml index 071292e6c..42adce1d2 100644 --- a/codes/oaecc.yml +++ b/codes/oaecc.yml @@ -39,6 +39,7 @@ 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 \(\mathcal{A}\). + Tradeoffs between error correction and privacy have been studied \cite{arxiv:1811.10425}. relations: parents: diff --git a/codes/quantum/qubits/hybrid_qubits_into_qubits.yml b/codes/quantum/qubits/hybrid_qubits_into_qubits.yml index 18ad36968..01d074330 100644 --- a/codes/quantum/qubits/hybrid_qubits_into_qubits.yml +++ b/codes/quantum/qubits/hybrid_qubits_into_qubits.yml @@ -17,8 +17,9 @@ description: | protection: | Any qubit code can be converted into a hybrid qubit code by using some its qubits to store only classical information \cite{arxiv:0802.2414}. An \(((n,K:M))\) hybrid qubit code can detect more errors than an \(((n,KM))\) qubit code \cite{arxiv:1901.02913}. + A hybrid Hamming bound has been constructed \cite{arxiv:1806.03702}. - Quantum weight enumerators, quantum MacWilliams identities, and linear programming bounds have been extended to hybrid qubit codes \cite{arxiv:1701.06963,arxiv:1901.02913,arxiv:1911.12260} + Quantum weight enumerators, quantum MacWilliams identities, and linear programming bounds have been extended to hybrid qubit codes \cite{arxiv:1701.06963,arxiv:1901.02913,arxiv:1911.12260}. relations: diff --git a/codes/quantum/qubits/oa_stabilizer/hybrid_stabilizer.yml b/codes/quantum/qubits/oa_stabilizer/hybrid_stabilizer.yml index 2b72397c9..83b00302f 100644 --- a/codes/quantum/qubits/oa_stabilizer/hybrid_stabilizer.yml +++ b/codes/quantum/qubits/oa_stabilizer/hybrid_stabilizer.yml @@ -35,6 +35,12 @@ relations: detail: 'The Shor code can be modified to store three additional classical bits to yield a \([[9,1:3,3]]\) hybrid stabilizer code \cite{arxiv:0802.2414}.' - code_id: iceberg detail: 'The \([[2m+1,2m+2:1,2]]\) hybrid stabilizer code \cite{arxiv:1911.12260} (extendable to modular qudits \cite{arxiv:2002.11075}) is closely related to the \([[2m,2m-2,2]]\) qubit stabilizer code.' + - code_id: stab_4_2_2 + detail: 'The \([[4,2,2]]\) codewords can be modified by signs to yield a \([[4,1:1,2]]\) hybrid stabilizer code \cite{arxiv:1806.03702}.' + - code_id: subsystem_stabilizer + detail: 'Hybrid stabilizer codes can be constructed from qubit subsystem stabilizer codes by using the gauge qubits of the latter to store classical information \cite[Thm. 4]{arxiv:2012.05896}.' + - code_id: subsystem_quantum_parity + detail: 'Hybrid stabilizer codes can be constructed from SHP codes by using the gauge qubits of the latter to store classical information \cite[Sec. 4]{arxiv:2012.05896}.' # Begin Entry Meta Information