Compatibility of quantum measurements and inclusion constants for the matrix jewel
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Compatibility of quantum measurements and inclusion constants for the matrix jewel. / Bluhm, Andreas; Nechita, Ion.
I: SIAM Journal on Applied Algebra and Geometry, Bind 4, Nr. 2, 2020, s. 255-296.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Compatibility of quantum measurements and inclusion constants for the matrix jewel
AU - Bluhm, Andreas
AU - Nechita, Ion
PY - 2020
Y1 - 2020
N2 - In this work, we establish the connection between the study of free spectrahedra and the compatibility of quantum measurements with an arbitrary number of outcomes. This generalizes previous results by the authors for measurements with two outcomes. Free spectrahedra arise from matricial relaxations of linear matrix inequalities. A particular free spectrahedron which we define in this work is the matrix jewel. We find that the compatibility of arbitrary measurements corresponds to the inclusion of the matrix jewel into a free spectrahedron defined by the effect operators of the measurements under study. We subsequently use this connection to bound the set of (asymmetric) inclusion constants for the matrix jewel using results from quantum information theory and symmetrization. The latter translate to new lower bounds on the compatibility of quantum measurements. Among the techniques we employ are approximate quantum cloning and mutually unbiased bases.
AB - In this work, we establish the connection between the study of free spectrahedra and the compatibility of quantum measurements with an arbitrary number of outcomes. This generalizes previous results by the authors for measurements with two outcomes. Free spectrahedra arise from matricial relaxations of linear matrix inequalities. A particular free spectrahedron which we define in this work is the matrix jewel. We find that the compatibility of arbitrary measurements corresponds to the inclusion of the matrix jewel into a free spectrahedron defined by the effect operators of the measurements under study. We subsequently use this connection to bound the set of (asymmetric) inclusion constants for the matrix jewel using results from quantum information theory and symmetrization. The latter translate to new lower bounds on the compatibility of quantum measurements. Among the techniques we employ are approximate quantum cloning and mutually unbiased bases.
KW - Algebraic convexity
KW - Free spectrahedra
KW - Polytope
KW - Quantum cloning
KW - Quantum measurement
KW - Semidefinite relaxation
UR - https://www.mendeley.com/catalogue/801c874a-45ec-361e-9930-3422d49469ac/
U2 - 10.1137/19M123837X
DO - 10.1137/19M123837X
M3 - Journal article
VL - 4
SP - 255
EP - 296
JO - SIAM Journal on Applied Algebra and Geometry
JF - SIAM Journal on Applied Algebra and Geometry
SN - 2470-6566
IS - 2
ER -
ID: 255789501