Multiparticle entanglement as an emergent phenomenon

Abstract

The question whether global entanglement of a multiparticle quantum system can be inferred from local properties is of great relevance for the theory of quantum correlations as well as for experimental implementations. We present a method to systematically find quantum states, for which the two- or three-body marginals do not contain any entanglement, nevertheless, the knowledge of these reduced states is sufficient to prove genuine multiparticle entanglement of the global state. With this, we show that the emergence of global entanglement from separable local quantum states occurs frequently and for an arbitrary number of particles. We discuss various extensions of the phenomenon and present examples where global entanglement can be proven from marginals, even if entanglement cannot be localized in the marginals with measurements on the other parties.Comment: 7+\varepsilon pages, 3 figures, v3: final versio

Proving genuine multiparticle entanglement from separable nearest-neighbor marginals

“…In order to study different marginal configurations for higher particle numbers the numerical tools used in Ref. [18] are not sufficient and improved optimization methods are required. The extension to more particles, however, gives new insights: for the minimal configurations of five (see Fig.…”

Experimental demonstration of a fully inseparable quantum state with nonlocalizable entanglement

“…Thus we have arrived to the finding that for state (3) it is impossible to probabilistically localize entanglement between any pair of qubits by any projective measurement on the third qubit if and only if p ≤ 1/3. Since nonlocalizability of entanglement by any projective measurement implies its nonlocalizability by any generalized measurement (or even operation) 29 we can conclude, that states (3), where parameter p lies in the interval 1/5 < p ≤ 1/3 are fully inseparable and their entanglement cannot be localized by any measurement. A larger set of three-qubit fully inseparable states with nonlocalizable entanglement is obtained if the GHZ state on the RHS of Eq.…”

“…1). Very recently, an example of such a state has been constructed 29 in the context of determination of genuine multipartite entanglement only from two-qubit reductions of the state. The state of ref.…”

Relating correlation measures: The importance of the energy gap

“…The nonclassical nature of quantum correlations and entanglement has enormous implications for quantum cryptography or quantum computation. Yet, quantifying correlations and entanglement for systems of identical particles is a part of an ongoing debate [19][20][21][22][23]. From a practical viewpoint, measuring correlation is even more challenging for identical particles since typically only oneand possibly two-particle properties are experimentally accessible.…”