RT Journal Article
T1 Least-bias state estimation with incomplete unbiased measurements
A1 Řeháček, Jaroslav
A1 Hradil, Zdenek
A1 Teo, Yong Siah
A1 Sánchez Soto, Luis Lorenzo
A1 Ng, Hui Khoon
A1 Chai, Jing Hao
A1 Englert, Berthold-Georg
AB Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing unbiasedness on the probabilities for the unmeasured bases does not generally yield the estimator with the largest von Neumann entropy, a popular figure of merit in this context. Furthermore, this imposition typically leads to mock density matrices that are not even positive definite. This provides a strong argument against perfunctory applications of linear estimation strategies. We propose to use instead the physical state estimators that maximize the Shannon entropy of the unmeasured outcomes, which quantifies our lack of knowledge fittingly and gives physically meaningful statistical predictions.
PB American Physical Society
SN 1050-2947
YR 2015
FD 2015-11
LK https://hdl.handle.net/20.500.14352/24289
UL https://hdl.handle.net/20.500.14352/24289
LA eng
NO ©2015 American Physical Society. Many of the ideas in this paper originated at the Workshop on Mathematical Methods of Quantum Tomography at Fields Institute (Toronto). Z.H., J.R., and Y.S.T. are grateful for the support of the European Social Fund and the state budget of the Czech Republic [Project No. CZ.1.07/2.3.00/30.0004 (POST-UP)], the Grant Agency of the Czech Republic (Grant No. 15-031945), the IGA Project of the Palacky University (Grant No. IGA PrF 2015-002), and the sustainability of postdoc positions at Palacky University. L.L. S.S. acknowledges the support from UCM-Banco Santander Program (Grant No. GR3/14) and helpful discussions with M. Grassl. H.K.N.'s, J.H.C.'s, and B.-G.E.'s work was funded by the Singapore Ministry of Education (partly through the Academic Research Fund Tier 3 MOE2012-T3-1-009) and the National Research Foundation of Singapore. H.K.N. was also funded by a Yale-NUS College start-up grant.
NO State Budget of the Czech Republic (República Checa)
NO Grant Agency of the Czech Republic (República Checa)
NO IGA Project of the Palacky University
NO Universidad Complutense de Madrid (UCM)
NO Ministerio de Educación (República de Singapur)
NO National Research Foundation (República de Singapur)
NO Banco Santander Central Hispano (BSCH)
DS Docta Complutense
RD 4 abr 2025