Minimax Quantum Tomography: Estimators and Relative Entropy Bounds

Journal Article · Fri Mar 04 00:00:00 EST 2016 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.116.090407· OSTI ID:1341781

Ferrie, Christopher ^[1]; Blume-Kohout, Robin ^[2]

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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)

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.

• Research Organization: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000; PHY-1212445; W911NF-14-1-0098; W911NF-14-1-0103
• OSTI ID: 1341781
• Alternate ID(s): OSTI ID: 1240449
• Report Number(s): SAND-2015-1684J; PRLTAO; 650745
• Journal Information: Physical Review Letters, Vol. 116, Issue 9; ISSN 0031-9007
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS