NBIA/QDev Seminar: Matthias Christandl

Matthias Christandl, ETH Zurich
Entanglement Polytopes

Entangled many-body systems are an essential resource for quantum computing and interferometry. The exponential complexity inherent in such systems however is a major challenge for its systematic understanding. We show that in the case of pure multi-particle quantum states, significant features of the global entanglement can be extracted from local information alone. This is achieved by associating to each class of entanglement an entanglement polytope, which describes geometrically the constraints on the eigenvalues of the single-particle reduced states imposed by the class. The study of these polytopes, which can be constructed for quantum systems of arbitrary size and statistics, unveils an intriguing new perspective on multi-particle entanglement with applications ranging from the experimental detection of entanglement to the understanding of fermionic occupation numbers.