How much is a quantum controller controlled by the controlled system?
Abbreviated Journal Title
Appl. Algebr. Eng. Commun. Comput.
REFERENCE FRAME; INFORMATION; Computer Science, Interdisciplinary Applications; Computer Science, ; Theory & Methods; Mathematics, Applied
We consider unitary transformations on a bipartite system A x B. To what extent entails the ability to transmit information from A to B the ability to transfer information in the converse direction? We prove a dimension-dependent lower bound on the classical channel capacity C(A <- B) in terms of the capacity C(A -> B) for the case that the bipartite unitary operation consists of controlled local unitaries on B conditioned on basis states on A. If the local operations are given by the regular representation of a finite group G we have C(A -> B) = log vertical bar G vertical bar and C(A <- B) = log N where N is the sum over the degrees of all inequivalent representations. Hence the information deficit C(A -> B) -C(A <- B) between the forward and the backward capacity depends on the "non-abelianness" of the control group. For regular representations, the ratio between backward and forward capacities cannot be smaller than 1/2. The symmetric group S-n reaches this bound asymptotically. However, for the general case (without group structure) all bounds must depend on the dimensions since it is known that the ratio can tend to zero. Our results can be interpreted as statements on the strength of the inevitable backaction of a quantum system on its controller.
Applicable Algebra in Engineering Communication and Computing
"How much is a quantum controller controlled by the controlled system?" (2008). Faculty Bibliography 2000s. 485.