  An important topic in quantum information is the theory of error correction
codes. Practical situations often involve quantum systems with states in an
infinite dimensional Hilbert space, for example coherent states. Motivated by
these practical needs, we apply the theory of non-commutative graphs, which is
a tool to analyze error correction codes, to infinite dimensional Hilbert
spaces. As an explicit example, a family of non-commutative graphs associated
with the Schr\"odinger equation describing the dynamics of a two-mode quantum
oscillator is constructed and maximal quantum anticliques for these graphs are
found.
