A tensor norm approach to quantum compatibility
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A tensor norm approach to quantum compatibility. / Bluhm, Andreas; Nechita, Ion.
I: Journal of Mathematical Physics, Bind 63, Nr. 6, 062201, 2022.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - A tensor norm approach to quantum compatibility
AU - Bluhm, Andreas
AU - Nechita, Ion
N1 - 18 pages, 1 figure
PY - 2022
Y1 - 2022
N2 - Measurement incompatibility is one of the most striking examples of how quantum physics is different from classical physics. Two measurements are incompatible if they cannot arise via classical post-processing from a third one. A natural way to quantify incompatibility is in terms of noise robustness. In the present article, we review recent results on the maximal noise robustness of incompatible measurements, which have been obtained by the present authors using free spectrahedra, and rederive them using tensor norms. In this way, we make them accessible to a broader audience from quantum information theory and mathematical physics and contribute to the fruitful interactions between Banach space theory and quantum information theory. We also describe incompatibility witnesses using tensor norm and matrix convex set duality, emphasizing the relation between the different notions of witnesses.
AB - Measurement incompatibility is one of the most striking examples of how quantum physics is different from classical physics. Two measurements are incompatible if they cannot arise via classical post-processing from a third one. A natural way to quantify incompatibility is in terms of noise robustness. In the present article, we review recent results on the maximal noise robustness of incompatible measurements, which have been obtained by the present authors using free spectrahedra, and rederive them using tensor norms. In this way, we make them accessible to a broader audience from quantum information theory and mathematical physics and contribute to the fruitful interactions between Banach space theory and quantum information theory. We also describe incompatibility witnesses using tensor norm and matrix convex set duality, emphasizing the relation between the different notions of witnesses.
KW - quant-ph
KW - math-ph
KW - math.MP
U2 - 10.1063/5.0089770
DO - 10.1063/5.0089770
M3 - Journal article
VL - 63
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 6
M1 - 062201
ER -
ID: 312631739