(1) Department of Mathematics and Statistics, University of Guelph, Guelph; ON, Canada; (2) Institute for Quantum Computing, University of Waterloo, Waterloo; ON, Canada; (3) UTS-AMSS Joint Research Laboratory for Quantum Computation and Quantum Information Processing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China; (4) State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China; (5) Department of Physics and Astronomy, University of Waterloo, Waterloo; ON, Canada
Abstract:
A bipartite state ρAB is symmetric extendible if there exists a tripartite state ρABB′ whose AB and AB′ marginal states are both identical to ρAB. Symmetric extendibility of bipartite states is of vital importance in quantum information because of its central role in separability tests, one-way distillation of Einstein-Podolsky-Rosen pairs, one-way distillation of secure keys, quantum marginal problems, and antidegradable quantum channels. We establish a simple analytic characterization for symmetric extendibility of any two-qubit quantum state ρAB; specifically, tr(ρB2)≥tr(ρAB2)-4detρAB. As a special case we solve the bosonic three-representability problem for the two-body reduced density matrix.
English Abstract:
A bipartite state ρAB is symmetric extendible if there exists a tripartite state ρABB′ whose AB and AB′ marginal states are both identical to ρAB. Symmetric extendibility of bipartite states is of vital importance in quantum information because of its central role in separability tests, one-way distillation of Einstein-Podolsky-Rosen pairs, one-way distillation of secure keys, quantum marginal problems, and antidegradable quantum channels. We establish a simple analytic characterization for symmetric extendibility of any two-qubit quantum state ρAB; specifically, tr(ρB2)≥tr(ρAB2)-4detρAB. As a special case we solve the bosonic three-representability problem for the two-body reduced density matrix.
