O.Gühne (Uni. Siegen): A complete hierarchy for the pure state marginal problem in quantum mechanics
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2021-04-18

Otfried Gühne  (University of Siegen)
A complete hierarchy for the pure state marginal problem in quantum mechanics
Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state for some given marginals. This problem arises in many contexts, ranging from quantum chemistry to entanglement theory and quantum error correcting codes. In this contribution, we prove a correspondence of the marginal problem to the separability problem. Based on this, we describe a sequence of semidefinite programs which can decide whether some given marginals are compatible with some pure global quantum state. As an application, we prove that the existence of multi-particle absolutely maximally entangled states for a given dimension is equivalent to the separability of an explicitly given two-party quantum state. Finally, we show that the existence of quantum codes with given parameters can also be interpreted as a marginal problem; hence, our complete hierarchy can also be used.
CTP Quantum Information Days (online), 22-24 February 2021.
Center for Theoretical Physics PAS (Warsaw, Poland)