Preparing genuine multipartite entanglement verifiable from separable marginals

Inference of global properties of a composite quantum system in an unknown state from its parts underlies many tasks in quantum information theory. This includes quantum marginal problem, separability criteria based on spin... [ view full abstract ]

Inference of global properties of a composite quantum system in an unknown state from its parts underlies many tasks in quantum information theory. This includes quantum marginal problem, separability criteria based on spin squeezing, extendibility of quantum states or computation of certain entanglement measures.

If a reduced state of a composite quantum system carries an information resource, then the resource is inevitably present also in the global state of the system. Conversely, provided that the reduced states do not possess the resource, it is generally impossible to deduce unequivocally the presence or absence of the resource in the global state. Remarkably, there are instances of reduced states without the resource, which can nevertheless be a part of only a global state containing the resource [1]. This can be exemplified by the existence of multipartite quantum states with separable reductions which are compatible only with genuine multipartite entangled global states [2].

Following the proposal of Ref. [3] we have prepared experimentally a three-qubit quantum state σ exhibiting previous property, using correlated single photons and linear optical circuit. Owing to the closeness of separable two-qubit reductions to the set of entangled states, we prepared the mixture ϱ=pσ +(1-p)(1/8) with p=0.868. The experimental density matrix ϱ_exp has been tomographically reconstructed using the maximum likelihood estimation algorithm and the uncertainties in the quantities have been estimated with the help of the Monte Carlo simulation. Separability of all two-qubit reductions of ϱ_exp has been confirmed by partial transposition criterion and the results are summarized in Table I.

The Table reveals that partial transposes of all reduced states are positive-semidefinite and thus they are separable as required. For certification of genuine multipartite entanglement we found numerically a fully decomposable entanglement witness W [4] acting only on two-qubit reductions [3], for which Tr(ϱ_expW)=(-3±2) ∙ 10^-3. The target state has been prepared with the fidelity of F=0.939±0.008.

We have demonstrated the possibility to verify genuine multipartite entanglement of a global quantum state from its separable reductions. We believe that our result will stimulate further studies on detection of emerging global properties of complex quantum systems from their parts which lack the properties.

[1] G. Tóth et al., Phys. Rev. Lett. 99, 250405 (2007).

[2] L. Chen et al., Phys. Rev. A 90, 042314 (2014).

[3] N. Miklin et al., Phys. Rev. A 93, 020104(R) (2016).

[4] B. Jungnitsch et al., Phys. Rev. Lett. 106, 190502 (2011).