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@article{1199784,
author = {Haapasalo, Erkka and Sedlák, Michal and Ziman, Mário},
article_number = {6},
doi = {http://dx.doi.org/10.1103/PhysRevA.89.062303},
keywords = {quantum information theory - quantum discrimination - convex analysis},
language = {eng},
issn = {1050-2947},
journal = {Physical Review A},
title = {Distance to boundary and minimum-error discrimination},
url = {http://dx.doi.org/10.1103/PhysRevA.89.062303},
volume = {89},
year = {2014}
}
TY - JOUR
ID - 1199784
AU - Haapasalo, Erkka - Sedlák, Michal - Ziman, Mário
PY - 2014
TI - Distance to boundary and minimum-error discrimination
JF - Physical Review A
VL - 89
IS - 6
SP - 1-12
EP - 1-12
SN - 10502947
KW - quantum information theory - quantum discrimination - convex analysis
UR - http://dx.doi.org/10.1103/PhysRevA.89.062303
L2 - http://dx.doi.org/10.1103/PhysRevA.89.062303
N2 - We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any explicit topology) how far the given element is from the boundary. It is shown that one of the elements from the boundary can be always chosen to be an extremal element. We focus on evaluation of this quantity for quantum sets of states, channels, and observables. We show that boundariness is intimately related to (semi)norms that provide an operational interpretation of this quantity. In particular, the minimum error probability for discrimination of a pair of quantum devices is lower bounded by the boundariness of each of them. We proved that for states and observables this bound is saturated and conjectured this feature for channels. The boundariness is zero for infinite-dimensional quantum objects as in this case all the elements are boundary elements.
ER -
HAAPASALO, Erkka, Michal SEDLÁK a Mário ZIMAN. Distance to boundary and minimum-error discrimination. \textit{Physical Review A}. 2014, roč.~89, č.~6, s.~1-12. ISSN~1050-2947. Dostupné z: https://dx.doi.org/10.1103/PhysRevA.89.062303.
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