Multipartite entanglement analysis from random correlations

Abstract

Quantum entanglement is usually revealed via a well aligned, carefully chosen set of measurements. Yet, under a number of experimental conditions, for example in communication within multiparty quantum networks, noise along the channels or fluctuating orientations of reference frames may ruin the quality of the distributed states. Here, we show that even for strong fluctuations one can still gain detailed information about the state and its entanglement using random measurements. Correlations between all or subsets of the measurement outcomes and especially their distributions provide information about the entanglement structure of a state. We analytically derive an entanglement criterion for two-qubit states and provide strong numerical evidence for witnessing genuine multipartite entanglement of three and four qubits. Our methods take the purity of the states into account and are based on only the second moments of measured correlations. Extended features of this theory are demonstrated experimentally with four photonic qubits. As long as the rate of entanglement generation is sufficiently high compared to the speed of the fluctuations, this method overcomes any type and strength of localized unitary noise.

Entanglement characterization using quantum designs

“…Similar insights have been reached in Ref. [26] where the detection and characterization of multipartite entanglement based on second moments was studied experimentally with entangled photons.…”

“…It is important to note that one can gain more information about ρ by considering also moments of smaller qubit sectors, i.e., the respective reduced states, as has been investigated for t = 2 in Refs. [24][25][26][27][28][29][30]. However, in the remainder of this manuscript we will focus on the characterization of multipartite entanglement based on full N -qubit moments (2).…”

“…In several recent works it has been shown how to go beyond such procedures by relaxing also the assumption of being able to measure a fixed set of local observables and instead allow only for local measurements with settings drawn uniformly at random [19][20][21][22][23][24][25][26][27]. The common idea of these approaches is to measure a certain correlation function, and average the result over random local unitaries applied to the state.…”

Mixed-State Entanglement from Local Randomized Measurements

“…Thus, data processing is cheap-both in memory and runtime-and can be massively parallelized. Similar to previous measurement [10,15,16,18,34,35,[47][48][49] and entanglement detection [50][51][52][53][54] protocols based on randomized measurements, this is another distinct advantage over tomography which typically requires expensive data-processing algorithms [41] or training a neural network [43].…”

Machine learning discovery of new phases in programmable quantum simulator snapshots

“…Given a mixed state ρ, nonzero connected correlations can emerge either by entanglement, or by "classical" correlations between the pure states comprising ρ [48]. Efficient means for unambiguously revealing entanglement in experimental settings without full tomography is an active field of research [49][50][51][52][53][54][55].…”