Multipartite entanglement detection with nonsymmetric probing

Abstract

We show that spin squeezing criteria commonly used for entanglement detection can be erroneous, if the probe is not symmetric. We then derive a lower bound on squeezing for separable states in spin systems probed asymmetrically. Using this we further develop a procedure that allows us to verify the degree of entanglement of a quantum state in the spin system. Finally, we apply our method for entanglement verification to existing experimental data, and use it to prove the existence of tri-partite entanglement in a spin squeezed atomic ensemble.Entanglement is a fundamental resource for proving nonclassicality of nature, and is a key feature for developing quantum technologies. It was first used experimentally for proving the breakdown of local realism [1,2], and has now become a practical ingredient in quantum information science and metrology [3]. As such, it is crucial to discern between separable and entangled systems. Unfortunately, this is not always straightforward; even though several criteria exist [4][5][6], it may be hard to experimentally verify that a state is entangled. Hence, there is a need for simple, practical procedures for proving that a system is entangled. An example of such a criterion is spin squeezing [7][8][9], which has often been used to probe entanglement in multi-particle systems [10]. One of its major advantages is that it relies on measuring only two observables: the mean spin and the fluctuations perpendicular to it. This makes it ideally suited for systems where complete control over all degrees of freedom is hard to achieve. Measuring that the noise is squeezed below a certain bound is then a sufficient criterion for proving entanglement [11][12][13][14][15][16][17][18][19]. Due to the simplicity of this approach, it has been employed to show even multi-partite entanglement in a wide range of experiments [20][21][22][23][24]. However, an inherent assumption in the entanglement criteria based on spin squeezing is that all particles are probed with equal strength. In many practical situations this is a very good approximation [21,23], but in others this is far from reality. As an example, consider a Gaussian beam probing a collection of trapped atoms. If the waist of the laser beam is much smaller than the size of the cloud, the atoms will have an asymmetric interaction with the light. This asymmetry leads to minor modifications of the interaction dynamics if suitable weighted operators are introduced [25,26]. For entanglement detection in the ensemble, however, the effect of such asymmetry may be much more severe and has so far not been investigated.In this article, we consider the effect of asymmetric probing on the entanglement criteria. We first consider a simple generalization of the standard squeezing criterion and show that it is no longer a suitable method for verifying entanglement. To overcome this problem we develop new entanglement criteria, that can accommodate the asymmetric probing of the particles. We show that our criteria are sufficient for detection of bi-partite...

Phononic-waveguide-assisted steady-state entanglement of silicon-vacancy centers

“…Multiparticle entanglement has attracted great attention for its diverse applications in quantum metrology and quantum computing [1][2][3][4][5][6][7][8][9][10]. Efforts along this direction have lead to a plenty of proposals for generating entangled states with particles as many as possible [11][12][13], such as spin squeezing states [14][15][16] and GHZ states [17][18][19][20]. So far, multiparticle entanglement has been realized involving up to 20 qubits in trapped-ion systems [21], and 12 qubits in superconducting circuits [22].…”

Bell Correlations in Spin-Squeezed States of 500 000 Atoms

“…The largest entanglement depth obtained in this analysis is approximately 500. However, using a more optimal entanglement depth criterion tailored for nonsymmetric probing [24], the best entanglement depth becomes 1590(130) [25].…”

Multiparticle entanglement criteria for nonsymmetric collective variances

“…the one axis twisting plus external field, that has been shown to be an enhancement over the simple oneaxis twisting. Experimentally, the bound has been able to confirm multiparticle entanglement in various setups [24,25,[30][31][32][33].…”

“…Experimentally, in different setups the presence of k-party entanglement has been verified, see e.g. [14,[22][23][24][25][26][27][28][29][30][31][32][33]. k-party entanglement provides a multiparticle entanglement hierarchy that can be verified for a large system even if only a subset of spins can be accessed: the number of parties that may be confirmed to be entangled on the subset also gives a lower bound to the entanglement of full system [20].…”

“…[6], see e.g. [14,15,24,25,[30][31][32][33], and paves the way for the detection of larger, potentially macroscopic, numbers of entangled particles.…”