Non-Distillable Entanglement of Mixed States

M. Horodecki, P. Horodecki, R. Horodecki


A mixed state of a two-component quantum system is called inseparable (entangled), if it is not a mixture of product states. It is called distillable, if it can be brought to the singlet form by means of local quantum operations and classical communication. We provide examples of states which are entangled, but cannot be distilled. We also provide a characterization of distillable states which indicates that distillable entanglement is in fact two-bit entanglement. The results are discussed by use of analogy with thermodynamics.