Modifying method of constructing quantum codes from highly entangled states

Understand

There is a connection between classical codes, highly entangled pure states (called k-uniform or absolutely maximally entangled (AME) states), and quantum error correcting codes (QECCs).

• This leads to a systematic method to construct stabilizer QECCs by starting from a k-uniform state or the corresponding classical code and tracing out one party at each step.
• We provide explicit constructions for codewords, encoding procedure and stabilizer formalism of the QECCs by describing the changes that partial traces cause on the corresponding generator matrix of the classical codes.
• We then modify the method to produce another set of stabilizer QECCs that encode a logical qudit into a subspace spanned by AME states.