How much is a quantum controller controlled by the controlled system?
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Publication:937226
DOI10.1007/S00200-008-0076-YzbMATH Open1241.81044arXiv0708.1505OpenAlexW2112940232MaRDI QIDQ937226
Author name not available (Why is that?)
Publication date: 20 August 2008
Published in: (Search for Journal in Brave)
Abstract: 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. This can be interpreted as a statement on the strength of the inevitable backaction of a quantum system on its controller. If the local operations are given by the regular representation of a finite group G we have C(A-->B)=log |G| 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.
Full work available at URL: https://arxiv.org/abs/0708.1505
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