Isoentangled mutually unbiased bases, symmetric quantum measurements, and mixed-state designs
Jakub Czartowski , Dardo Goyeneche , Markus Grassl , Karol Życzkowski
AbstractDiscrete 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.
|Journal series||Physical Review Letters, ISSN 0031-9007, e-ISSN 1079-7114, (N/A 200 pkt)|
|Publication size in sheets||0.5|
|Score||= 200.0, 19-05-2020, ArticleFromJournal|
|Publication indicators||: 2017 = 2.464; : 2018 = 9.227 (2) - 2018=8.313 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.