Characterizing correlation within multipartite quantum systems via local randomized measurements

Abstract

Given a quantum system on many qubits split into a few different parties, how much total correlations are there between these parties? Such a quantity -aimed to measure the deviation of the global quantum state from an uncorrelated state with the same local statistics -plays an important role in understanding multi-partite correlations within complex networks of quantum states. Yet, the experimental access of this quantity remains challenging as it tends to be non-linear, and hence often requires tomography which becomes quickly intractable as dimensions of relevant quantum systems scale. Here, we introduce a much more experimentally accessible quantifier of total correlations, which can be estimated using only single-qubit measurements. It requires far fewer measurements than state tomography, and obviates the need to coherently interfere multiple copies of a given state. Thus we provide a tool for proving multi-partite correlations that can be applied to near-term quantum devices.

Quantum separability criteria based on realignment moments

“…Although we have not yet found an example to show that the realignment moments based criteria work better than other criteria like the PT moments based ones, the approach may be used to to detect multipartite entanglement by using the generalized realignment criteria [36,37]. A scheme to experimentally measure the realignment moments via measuring the purity T r(ρ 2 AB ) [16,17] or by global random unitary matrices [22,23] or local randomized measurements [38] would also be of significance.…”