Communications in Mathematical Physics

, Volume 332, Issue 1, pp 449–476 | Cite as

Impossibility of Local State Transformation via Hypercontractivity



Local state transformation is the problem of transforming an arbitrary number of copies of a bipartite resource state to a bipartite target state under local operations. That is, given two bipartite states, is it possible to transform an arbitrary number of copies of one of them into one copy of the other state under local operations only? This problem is a hard one in general since we assume that the number of copies of the resource state is arbitrarily large. In this paper we prove some bounds on this problem using the hypercontractivity properties of some super-operators corresponding to bipartite states. We measure hypercontractivity in terms of both the usual super-operator norms as well as completely bounded norms.


Maximal Correlation Local Operation Quantum Case Logarithmic Sobolev Inequality Bipartite State 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  2. 2.Department of Electrical EngineeringSharif University of TechnologyTehranIran

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