Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 47, Issue 50, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1751-8113/47/50/505302
Keywords
quantum information; relative entropy; convex optimization
Categories
Funding
- NSERC
- NSF [DMS-1216393]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1216393] Funding Source: National Science Foundation
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Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices. In most cases, finding exact solutions to these problems is usually impossible. As inspired by earlier investigations into the relative entropy of entanglement (REE) (Miranowicz and Ishizaka 2008 Phys. Rev. A 78 032310), we introduce a general method to solve the converse problem rather than find explicit solutions. That is, given a matrix in a convex set, we determine a family of convex functions that are minimized at this point. This method allows us find explicit formulae for the REE and the Rains bound, two well-known upper bounds on the distillable entanglement, and yields interesting information about these quantities, such as the fact that they coincide in the case where at least one subsystem of a multipartite state is a qubit.
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