Is there a working rule to compute the capacity of a quantum channel described by a set of Kraus operators $\{K_i\}$?
$\begingroup$ $\endgroup$
3 
- 3$\begingroup$ Not a nice one no. The best result is the LSD theorem which says that the quantum channel capacity is the regularization of the coherent information, which means it involves a limit as $n\rightarrow \infty$, and so finding the capacity is generally an unbounded optimization problem. However if your Kraus operators satisfy certain conditions then it can be easier, for instance if the channel is degradable. $\endgroup$Condo– Condo2020-06-27 01:46:08 +00:00Commented Jun 27, 2020 at 1:46
- $\begingroup$ Thanks, @Connor. Similar question: How to check "degradability" knowing the Kraus operators? $\endgroup$Rob– Rob2020-06-29 11:56:25 +00:00Commented Jun 29, 2020 at 11:56
- 1$\begingroup$ It would be sufficient to show that $ker(T)\subseteq ket(T^C)$ where $T$ is your channel and $T^C$ is its complementary channel, both of which do have have nice formulas in terms of the Kraus operators for $T$. Though I am not sure how you could get a handle on characterizing the operators in the kernel of $T$... this (older) paper is a good starting point arxiv.org/pdf/0802.1360.pdf not sure what is state of the art these days though. $\endgroup$Condo– Condo2020-07-03 17:45:17 +00:00Commented Jul 3, 2020 at 17:45
Add a comment |