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arXiv:1509.00078 · Physical Review A

Entanglement detection via some classes of measurements

Shu‐Qian Shen, Ming Li, Xuefeng Duan

Published Jan 20, 2015• 27 citations
arXivHTMLPDF

Abstract

Based on the mutually unbiased bases, the mutually unbiased measurements and the general symmetric informationally complete positive-operator-valued measures, we propose three separability criteria for $d$-dimensional bipartite quantum systems, which are more powerful than the corresponding ones introduced previously [C. Spengler, M. Huber, S. Brierley, T. Adaktylos, and B. C. Hiesmayr, Phys. Rev. A 86, 022311 (2012); B. Chen, T. Ma, and S. M. Fei, Phys. Rev. A 89, 064302 (2014); and B. Chen, T. Li, and S. M. Fei, arXiv:1406.7820v1 [quant-ph] (2014)]. Some states such as Werner states and Bell-diagonal states are used to further illustrate the efficiency of the presented criteria.

DOI
10.1103/physreva.91.012326

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Mutually unbiased measurements (MUMs) are generalized from the concept of mutually unbiased bases (MUBs) and include the complete set of MUBs as a special case, but they are superior to MUBs as they do not need to be rank one projectors. We investigate entanglement detection using sets of MUMs and derive separability criteria for multipartite qudit systems, arbitrary high-dimensional bipartite systems of a d1-dimensional subsystem and a d2-dimensional subsystem, and multipartite systems of multi-level subsystems. These criteria are of the advantages of more effective and wider application range than previous criteria. They provide experimental implementation in detecting entanglement of unknown quantum states.
Mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete measurements are three related concepts in quantum information theory. We investigate multipartite systems using these notions and present some criteria detecting entanglement of arbitrary high dimensional multi-qudit systems and multipartite systems of subsystems with different dimensions. It is proved that these criteria can detect the k -nonseparability ( k is even) of multipartite qudit systems and arbitrary high dimensional multipartite systems of m subsystems with different dimensions. We show that they are more efficient and wider of application range than the previous ones. They provide experimental implementation in detecting entanglement without full quantum state tomography.
Abstract The detection of quantum entanglement represents a fundamental challenge in quantum measurement theory within the context of quantum information science. In this work, we propose a family of separability criteria based on mutually unbiased equiangular tight frames [IEEE Trans. Inf. Theory 67 , 1656–1667 (2021)], which constitute a natural generalization of both mutually unbiased bases and equiangular tight frames. The proposed criteria are applicable to a broad class of quantum systems, including bipartite systems with equal or unequal subsystem dimensions, as well as multipartite systems with heterogeneous dimensional components. In the examined cases, namely isotropic, Bell-diagonal, and Werner states, the proposed entanglement detection criteria demonstrate superior performance relative to several established methods. Crucially, these criteria rely solely on a small set of local measurements, which significantly enhances their experimental feasibility for the characterization of entanglement in unknown quantum states. Overall, the MUETF-based criteria provide more robust and versatile tools for entanglement verification across diverse quantum architectures.