Isoentangled mutually unbiased bases, symmetric quantum measurements, and mixed-state designs

Jakub Czartowski , Dardo Goyeneche , Markus Grassl , Karol Życzkowski

Abstract

Discrete structures in Hilbert space play a crucial role in finding optimal schemes for quantum measurements. We solve the problem of whether a complete set of five isoentangled mutually unbiased bases exists in dimension four, providing an explicit analytical construction. The reduced density matrices of these 20 pure states forming this generalized quantum measurement form a regular dodecahedron inscribed in a sphere of radius root 3/20 located inside the Bloch ball of radius 1/2. Such a set forms a mixed-state 2-design-a discrete set of quantum states with the property that the mean value of any quadratic function of density matrices is equal to the integral over the entire set of mixed states with respect to the flat Hilbert-Schmidt measure. We establish necessary and sufficient conditions mixed-state designs need to satisfy and present general methods to construct them. Furthermore, it is shown that partial traces of a projective design in a composite Hilbert space form a mixed-state design, while decoherence of elements of a projective design yields a design in the classical probability simplex. We identify a distinguished two-qubit orthogonal basis such that four reduced states are evenly distributed inside the Bloch ball and form a mixed-state 2-design.
Author Jakub Czartowski
Jakub Czartowski,,
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, Dardo Goyeneche
Dardo Goyeneche,,
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, Markus Grassl (ICTQT)
Markus Grassl,,
- International Centre for Theory of Quantum Technologies
, Karol Życzkowski
Karol Życzkowski,,
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Journal seriesPhysical Review Letters, ISSN 0031-9007, e-ISSN 1079-7114, (N/A 200 pkt)
Issue year2020
Vol124
No9
Pages1-6
Publication size in sheets0.5
Article number090503
ASJC Classification3100 General Physics and Astronomy
DOIDOI:10.1103/PhysRevLett.124.090503
Languageen angielski
Score (nominal)200
Score sourcejournalList
ScoreMinisterial score = 200.0, 19-05-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2017 = 2.464; WoS Impact Factor: 2018 = 9.227 (2) - 2018=8.313 (5)
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