arXiv:2502.02868 · iScience

Witness-based nonlinear detection of quantum entanglement

Yiding Wang, Tinggui Zhang, Xiaofen Huang, Shao-Ming Fei

Published Mar 10, 2025• 3 citations

Abstract

We present a nonlinear entanglement detection strategy that detects entanglement that the linear detection strategy fails. We show that when the nonlinear entanglement detection strategy fails to detect the entanglement of an entangled state with two copies, it may succeed with three or more copies. Based on our strategy, a witness combined with a suitable quantum mechanical observable may detect the entanglement that cannot be detected by the witness alone. Moreover, our strategy can also be applied to detect multipartite entanglement by using the witnesses for bipartite systems, as well as to entanglement concentrations.

DOI: 10.1016/j.isci.2025.112174

Related papers

Entanglement Detection with Trace Polynomials

Albert Rico, Felix Huber

We provide a systematic method for nonlinear entanglement detection based on trace polynomial inequalities. In particular, this allows us to employ multipartite witnesses for the detection of bipartite states, and vice versa. We identify pairs of entangled states and witnesses for which linear detection fails, but for which nonlinear detection succeeds. With the trace polynomial formulation a great variety of witnesses arise from immanant inequalities, which can be implemented in the laboratory through the randomized measurements toolbox.

arXiv:2303.07761Physical Review LettersFeb 15, 202418 citations

On the Optimization and Self-Tensoring Construction of Nonlinear Entanglement Witnesses

Juan Yu, Lei Li, Ming Li +1 more

Nonlinear entanglement witnesses constructed from multiple linear entanglement witnesses and multiple copies of quantum states have recently been proposed as a powerful tool for entanglement detection. In this work, we show, via an explicit counterexample, that the fineness of linear witnesses generally fails to transfer to their tensor-product nonlinear counterparts. For the canonical family of nonlinear witnesses in the form of (αI-L)⊗(βI-T), we rigorously prove that the optimal nonlinear witness is uniquely attained with weakly optimal parameters of α=λmax(L) and β=λmax(T). Meanwhile, we analytically demonstrate that the self-tensor products of two representative linear witnesses fail to detect any entangled state. The question of whether a nonlinear entanglement witness capable of detecting entanglement can be constructed by tensoring a linear witness with itself remains open.

EntropyMay 28, 20260 citations

Experimental measurement of a nonlinear entanglement witness by hyperentangling two-qubit states

Vojtěch Trávníček, Karol Bartkiewicz, Antonín Černoch +1 more

We demonstrate that nonlinear entanglement witnesses can be made particularly useful for entanglement detection in hyperentangled or multilevel states. We test this idea experimentally on the platform of linear optics using a hyperentangled state of two photons. Instead of several simultaneous copies of two-photon entangled states, one can directly measure the witness on a single copy of a hyperentangled state. Our results indicate that hyperentanglement can be used for quick entanglement detection and it provides a practical test bed for experiments with nonlinear entanglement witnesses.

arXiv:1805.11337Physical Review ASep 7, 201811 citations

Nonlinear Entanglement Witnesses

Otfried Gühne, Norbert Lütkenhaus

Entanglement detection typically relies on linear inequalities for mean values of certain observables (entanglement witnesses), where violation indicates entanglement. We provide a general method to improve any of these inequalities for bipartite systems via nonlinear expressions. The nonlinearities are of different orders and can be directly measured in experiments, often without any extra effort.

arXiv:quant-ph/0512164Physical Review LettersMay 1, 2006121 citations

Mirrored entanglement witnesses

Joonwoo Bae, Dariusz Chruściński, Beatrix C. Hiesmayr

Abstract Entanglement detection, which signifies the task of distinguishing entangled states from separable states, can be generally performed by realizing entanglement witnesses via local measurements on a single-copy level and classical communication, and are known to be experimenter friendly. We introduce a framework of constructing mirrored entanglement witnesses by showing that an experimental observable is twice as effective since it generally provides bounds from above and below for separable states. Differently stated, a pair of witnesses, mirrored witnesses, exists for the characterization of the bounds, which are two faces of one observable. We show how to generally construct those witnesses and provide examples for bipartite and multipartite systems. We also show that both mirrored witnesses can be improved by introducing nonlinearities, by which a larger set of entangled states can be certified.

arXiv:1811.09896npj Quantum InformationFeb 3, 202027 citations

State–Entanglement-Witness Contraction

Albert Rico

We construct linear and nonlinear entanglement witnesses, by tensoring and partial tracing existing states and witnesses. We show that little shared quantum resources allow one to employ decomposable witnesses to obtain larger ones detecting locally undistillable states and find analytic witnesses for multipartite entangled states that are undistillable across all bipartitions. Crucially, we show how to efficiently optimize multicopy witnesses to desired states, which is a current challenge. As an example of both theoretical and experimental interest, existing trace polynomial witnesses are significantly improved while preserving their symmetries and implementability with randomized measurements. In addition to detecting entanglement, we also find new witnesses detecting k-copy distillability. A recipe for the single-copy case is shown to be effective for generic and Werner states.

arXiv:2502.17697Physical Review LettersSep 23, 20252 citations