Permutation-invariant quantum codes
Abstract: The quantum capacity of a quantum channel characterizes the optimal rate at which entanglement can be generated between two parties connected by the channel. The only known formula for the quantum capacity of a channel involves an unbounded, non-convex optimization problem that is generally intractable to solve. This talk will be about an approach to approximating the solution to this optimization problem for a fixed channel using symmetric input states, which involves the use of representation theory. For physically relevant 1-parameter families of channels, the use of symmetric codes significantly reduces the complexity of computing the parameter value at which the quantum capacity vanishes.
Student Information: Sujeet Bhalerao is a 4th year math graduate student working for Felix Leditzky researching quantum channels and their capacities.
