3‐Spontaneous Emission Error Designs from PSL (2, q) or PGL (2, q)

Quantum jump codes are quantum codes that correct errors caused by quantum jumps. A spontaneous emission error design (SEED) was introduced by Beth et al. in 2003 to construct quantum jump codes. In this paper, we study the existence of 3‐SEEDs from PSL(2, q ) or PGL(2, q ). By doing this, a large number of 3‐ ( q + 1 , k ; m ) SEEDs are derived for prime powers q and all 3 ≤ k ≤ q + 1 .