Role of correlations in the two-body-marginal problem

Abstract

Quantum properties of correlations have a key role in disparate fields of physics, from quantum information processing, to quantum foundations, to strongly correlated systems. We tackle a specific aspect of the fundamental quantum marginal problem: we address the issue of deducing the global properties of correlations of tripartite quantum states based on the knowledge of their bipartite reductions, focusing on relating specific properties of bipartite correlations to global correlation properties. We prove that strictly classical bipartite correlations may still require global entanglement and that unentangled-albeit not strictly classical-reductions may require global genuine multipartite entanglement, rather than simple entanglement. On the other hand, for three qubits, the strict classicality of the bipartite reductions rules out the need for genuine multipartite entanglement. Our work sheds new light on the relation between local and global properties of quantum states, and on the interplay between classical and quantum properties of correlations.

Entanglement marginal problems

“…Acknowledging the LTI and invariance under reflections over the vertical axis of the underlying distribution p(φ) generating the separable state ρ, we arrive, via (7), at a hierarchy of SDP relaxations whose L th level is:…”

“…This approach naturally leads to the entanglement marginal problem: deciding if an ensemble of density matrices could be the marginal states of a separable global state ρ. In this regard, and despite past research on the topic [3][4][5][6][7], to date there is no systematic and scalable method to detect entanglement from incomplete information. Note that most general methods for entanglement detection are tailor-made for scenarios where the whole state is available and therefore require an optimization over an, again, exponential number of parameters.…”

Verifying genuine multipartite entanglement of the whole from its separable parts

“…In Ref. [9] an example of a three-qubit state possessing all two-qubit marginals separable has been found using analytical tools, whose GME can be verified just from all the marginals. Only recently, a more systematic way of finding states with the sought property has been developed, which is based on the numerical finding of the GME witness acting only on two-qubit marginals of the state [10].…”

“…This resulted in the discovery of another three-qubit genuine multipartite entangled state with the desired property, which exhibits a larger robustness against addition of white noise compared to the original state of Ref. [9].…”

Multiparticle entanglement as an emergent phenomenon

“…If all particles are entangled the state is called genuine multiparticle entangled and this property is much more difficult to infer from the marginals. In fact, there has been only one recent example of a three-qubit state, where the genuine multiparticle entanglement can be concluded from separable marginals [9]. However, this example and the underlying techniques are tailored to a specific situation and are not straightforward to generalize in any direction.…”