Non-commutative graphs and quantum error correction for a two-mode quantum oscillator
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 develop 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 Schrödinger equation describing the dynamics of a two-mode quantum oscillator is constructed and maximal quantum anticliques for these graphs are found.