Free versus Bound Entanglement in High Dimensional Systems

Erwin Schrödinger, an Austrian Nobel Prize winner, introduced the German word ``Verschränkung (Englisch: entanglement) for a phenomenon that cannot be explained classically. The Austrian Anton Zeilinger got this year (2022) the Nobel Prize for his experimental studies of this phenomenon. Mathematically, entanglement can be defined exactly, but surprisingly given a quantum state, i.e. the full information available, it is not generally possible to find out whether this state is entangled or not. Those states, that allow no simple detection, are also physically relevant as their entanglement cannot be increased to the maximal entanglement. This kind of entanglement is called ``bound entanglement, in contrast to the ``free entanglement. This project wants on one hand to find novel methods to detect those states, e.g. by utilizing machine learning, a kind of weak artificial intelligence (AI), on the other hand we will explore the structure of bound entanglement and its potential for applications to quantum technologies.

Information needed to describe, process, or store quantum systems is fundamentally different from classical information. A striking example is bound entanglement: a form of entanglement that may require maximal entanglement to create but from which no maximal entanglement can be extracted-its entanglement is effectively "bound." In this project, we show that bound entanglement is not rare; it is simply difficult to detect. Specifically, within a family of two quantum particles, about 14% are bound entangled. We also uncover a substructure within the set of boundentangled states. Complementing this, we develop a protocol FIMAX that certifies when a given state can be "freed" (distilled). For the family under study, our distillation method is currently the best-performing, successfully identifying approximately 80% of the distillable states.