Eur. Phys. J. D 29, 293-299 (2004)
https://doi.org/10.1140/epjd/e2004-00029-y

Minimizing the loss of entanglement under dimensional reduction

¹ QUANTOP, Danish National Research Foundation Center for Quantum Optics, Denmark
² Department of Physics and Astronomy, University of Aarhus, 8000 Århus C, Denmark

Corresponding author: ^a vivip@phys.au.dk

Received: 26 September 2003
Revised: 21 January 2004
Published online: 2 March 2004

Abstract

We investigate the possibility of transforming, under local operations and classical communication, a general bipartite quantum state on a tensor-product space into a final state in  dimensions, while maintaining as much entanglement as possible. For pure states, we prove that Nielsen's theorem provides the optimal protocol, and we present quantitative results on the degree of entanglement before and after the dimensional reduction. For mixed states, we identify a protocol that we argue is optimal for isotropic and Werner states. In the literature, it has been conjectured that some Werner states are bound entangled and in support of this conjecture our protocol gives final states without entanglement for this class of states. For all other entangled Werner states and for all entangled isotropic states some degree of free entanglement is maintained. In this sense, our protocol may be used to discriminate between bound and free entanglement.