Higher-Rank Numerical Ranges and Compression Problems
  We consider higher-rank versions of the standard numerical range for matrices. A central motivation for this investigation comes from quantum error correction. We develop the basic structure theory for the higher-rank numerical ranges, and give a complete description in the Hermitian case. We also consider associated projection compression problems. 
Man-Duen Choi, David W. Kribs, and Karol Zyczkowski