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This research introduces a new family of $k$-positive linear maps derived from generalized equiangular measurements to construct Schmidt number witnesses for detecting quantum entanglement. The proposed method offers more efficient quantification of bipartite mixed states compared to existing symmetric measurement operators, advancing the toolkit for characterizing resources in quantum communication and computation.

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Families of $k$-positive maps and Schmidt number witnesses from generalized equiangular measurements

arXiv22 iulie 20262 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2512.18807v4 Announce Type: replace Abstract: Quantum entanglement is an important resource in many modern technologies, like quantum computation or quantum communication and information processing. Therefore, most interest is given to detect and quantify entangled states. Entanglement degree of bipartite mixed quantum states can be measured using the Schmidt number. Witnesses of the Schmidt number are closely related to $k$-positive linear maps, for which there is no general construction. Here, we use the generalized equiangular measurements to define a family of $k$-positive linear maps and the corresponding Schmidt number witnesses. We present examples of witnesses that detect two-parameter entangled states with Schmidt number $k+1$ in any dimension. Our approach allows for a more efficient entanglement quantification than other known Schmidt number witnesses constructed from symmetric measurement operators.

Abstract:Quantum entanglement is an important resource in many modern technologies, like quantum computation or quantum communication and information processing. Therefore, most interest is given to detect and quantify entangled states. Entanglement degree of bipartite mixed quantum states can be measured using the Schmidt number. Witnesses of the Schmidt number are closely related to $k$-positive linear maps, for which there is no general construction. Here, we use the generalized equiangular measurements to define a family of $k$-positive linear maps and the corresponding Schmidt number witnesses. We present examples of witnesses that detect two-parameter entangled states with Schmidt number $k+1$ in any dimension. Our approach allows for a more efficient entanglement quantification than other known Schmidt number witnesses constructed from symmetric measurement operators.

arXiv:2512.18807 [quant-ph]

(or arXiv:2512.18807v4 [quant-ph] for this version)

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