Entanglement detection with trace polynomials

Abstract

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

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Cited by in corpus (10)

• Analysing quantum systems with randomised measurements
• Efficient witnessing and testing of magic in mixed quantum states
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Witness based nonlinear detection of quantum entanglement
• New Partial Trace Inequalities and Distillability of Werner States
• Refuting spectral compatibility of quantum marginals
• Entanglement and distillation from symmetric positive maps
• State-witness contraction
• Experimental measurement and a physical interpretation of quantum shadow enumerators
• Absolutely maximally entangled pure states of multipartite quantum systems