Genuine N -partite entanglement without N -partite correlation functions

Abstract

A genuinely N -partite entangled state may display vanishing N -partite correlations measured for arbitrary local observables. In such states the genuine entanglement is noticeable solely in correlations between subsets of particles. A straightforward way to obtain such states for odd N is to design an 'anti-state' in which all correlations between an odd number of observers are exactly opposite. Evenly mixing a state with its anti-state then produces a mixed state with no N -partite correlations, with many of them genuinely multiparty entangled. Intriguingly, all known examples of 'entanglement without correlations' involve an odd number of particles. Here we further develop the idea of anti-states, thereby shedding light on the different properties of even and odd particle systems. We conjecture that there is no anti-state to any pure even-N -party entangled state making the simple construction scheme unfeasable. However, as we prove by construction, higherrank examples of 'entanglement without correlations' for arbitrary even N indeed exist. These classes of states exhibit genuine entanglement and even violate an N -partite Bell inequality, clearly demonstrating the non-classical features of these states as well as showing their applicability for quantum communication complexity tasks.

Characterizing quantum states via sector lengths

“…This already yields an entanglement criterion which can detect states not detectable by known criteria using the sector lengths [5], an example being again the highly entangled state |χ = 1 √ 6 (|0001 + |0010 + |0100 + |1000 + √ 2 |1111 ) with sector length configuration (A 1 , A 2 , A 3 , A 4 ) = (0, 2, 8, 5). Note that it is known that even vanishing highest order correlations do not exclude multipartite entanglement [29][30][31][32]. Finally, let us note that while sector lengths are quadratic expressions in the quantum state, the additional knowledge of similar quantities of higher order, i.e.…”

A Moment for Random Measurements

“…Also note that it is common that entanglement criteria are sufficient, but not necessary. For example, any method, whether based on random measurements or on fully controlled ones, that is only using full correlations, i.e., correlations between all n parties without inspecting correlations between subsets of parties, will miss some entangled states: There are genuinely n-partite entangled states without any correlations between all n parties [31][32][33], which therefore will result in a Dirac-delta peak for the full distribution and are on that level indistinguishable from white noise.…”

Cooperation and dependencies in multipartite systems

“…-An intriguing question in the theory of multipartite entanglement asks whether entanglement can exist without classical multipartite correlations [10]. The examples of N -party entangled states with vanishing N -party classical correlations are known in the literature [36][37][38][39][40], though the corresponding notions of classical correlations do not satisfy all the postulates of Refs. [11,13].…”