Title

How Much Is A Quantum Controller Controlled By The Controlled System?

Abstract

We consider unitary transformations on a bipartite system A × 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 |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. Our results can be interpreted as statements on the strength of the inevitable backaction of a quantum system on its controller. © 2008 Springer-Verlag.

Publication Date

6-1-2008

Publication Title

Applicable Algebra in Engineering, Communications and Computing

Volume

19

Issue

3

Number of Pages

241-258

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00200-008-0076-y

Socpus ID

44449141294 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/44449141294

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