Nonexistence of some quantum jump codes with specified parameters.

Quantum jump codes (JC) are quantum codes which correct errors caused by quantum jumps. A spontaneous emission error design (SEED) has been introduced to construct quantum JC. In this paper the nonexistence of some $$(n,m,t)_k$$ -JCs is proved, where $$m={n-t\atopwithdelims ()k-t},\, k\ge t+1,\, \text{ and }\, (n,t,k)=(2k+1,1,k), (2k,2,k),(7,2,3),(8,3,4)$$ . It is also shown that, for these parameters with $$t=1,2$$ , the existence of an $$(n,m,t)_k$$ -JC is equivalent to that of a $$t-(n,k;m)$$ -SEED. [ABSTRACT FROM AUTHOR]