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Title: Minimax Quantum Tomography: Estimators and Relative Entropy Bounds

A minimax estimator has the minimum possible error (“risk”) in the worst case. Here we construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O (1/$$\sqrt{N}$$ ) —in contrast to that of classical probability estimation, which is O (1/N) —where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. Lastly, this makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states.
Authors:
 [1] ;  [2]
  1. Univ. of New Mexico, Albuquerque, NM (United States). Center for Quantum Information and Control; Univ. of Sydney, NSW (Australia). Centre for Engineered Quantum Systems, School of Physics
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
OSTI Identifier:
1341781
Report Number(s):
SAND-2015-1684J
Journal ID: ISSN 0031-9007; PRLTAO; 650745
Grant/Contract Number:
AC04-94AL85000; PHY-1212445; W911NF-14-1-0098; W911NF-14-1-0103
Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 116; Journal Issue: 9; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS