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

Fuente: arXiv
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Main Author: Siudzińska, Katarzyna
Format: Preprint
Published: 2025
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author Siudzińska, Katarzyna
author_facet Siudzińska, Katarzyna
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_18807
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Families of $k$-positive maps and Schmidt number witnesses from generalized equiangular measurements
Siudzińska, Katarzyna
Quantum Physics
Mathematical Physics
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.
title Families of $k$-positive maps and Schmidt number witnesses from generalized equiangular measurements
topic Quantum Physics
Mathematical Physics
url https://arxiv.org/abs/2512.18807