wigner refs

codes/quantum/oscillators/oscillators.yml

@@ -20,6 +20,9 @@ description: |
   States of a single oscillator correspond to \(L^2\)-normalizable functions on \(\mathbb{R}\) that have finite energy, finite variance, and finite values of all other moments (where the energy operator is defined to be the harmonic oscillator Hamiltonian); such functions form \textit{Schwartz space}, a subspace of Hilbert space \cite{arxiv:2211.05714}.
   Ideal codewords may not be normalizable because the space is infinite-dimensional, so approximate versions have to be constructed in practice.
 
+  States can be represented by a series via a basis expansion, such as that in the countable basis of Fock states \(|n\rangle\) with \(n\geq 0\).
+  Alternatively, states can be represented as functions over the reals by expanding in a continuous "basis" (more technically, set of tempered distributions in the space dual to Schwartz space), such as the position "basis" \(|y\rangle\) with \(y\in\mathbb{R}\) or the momentum "basis" \(|p\rangle\) with \(p\in\mathbb{R}\).
+  States can further be represented as functions over the joint position-momentum phase space in the Wigner function formalism \cite{doi:10.1103/PhysRev.40.749,doi:10.1103/PhysRevA.15.449}.
 
 protection: |
   \subsection{Displacement error basis}
@@ -84,7 +87,7 @@ relations:
       detail: 'Group quantum codes whose physical spaces are constructed using the group of the reals \(\mathbb{R}\) under addition are bosonic codes.'
   cousins:
     - code_id: t-designs
-      detail: 'The notion of quantum state designs has been extended to bosonic modes \cite{arxiv:2211.05127}.'
+      detail: 'The notion of quantum state designs has been extended to states of a bosonic mode \cite{arxiv:2211.05127}.'
 
 
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