TY - JOUR

T1 - Compatibility of any pair of 2-outcome measurements characterizes the Choquet simplex

AU - Kuramochi, Yui

N1 - Funding Information:
This work was supported by Cross-ministerial Strategic Innovation Promotion Program (SIP) (Council for Science, Technology and Innovation (CSTI)).
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020/11/1

Y1 - 2020/11/1

N2 - For a compact convex subset K of a locally convex Hausdorff space, a measurement on A(K) is a finite family of positive elements in A(K) normalized to the unit constant 1 K, where A(K) denotes the set of continuous real affine functionals on K. It is proved that a compact convex set K is a Choquet simplex if and only if any pair of 2-outcome measurements are compatible, i.e. the measurements are given as the marginals of a single measurement. This generalizes the finite-dimensional result of Plávala (Phys Rev A 94:042108, 2016) obtained in the context of the foundations of quantum theory.

AB - For a compact convex subset K of a locally convex Hausdorff space, a measurement on A(K) is a finite family of positive elements in A(K) normalized to the unit constant 1 K, where A(K) denotes the set of continuous real affine functionals on K. It is proved that a compact convex set K is a Choquet simplex if and only if any pair of 2-outcome measurements are compatible, i.e. the measurements are given as the marginals of a single measurement. This generalizes the finite-dimensional result of Plávala (Phys Rev A 94:042108, 2016) obtained in the context of the foundations of quantum theory.

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U2 - 10.1007/s11117-020-00742-0

DO - 10.1007/s11117-020-00742-0

M3 - Article

AN - SCOPUS:85079708016

SN - 1385-1292

VL - 24

SP - 1479

EP - 1486

JO - Positivity

JF - Positivity

IS - 5

ER -