Zhu, Huangjun and Hayashi, Masahito (2018). Universally Fisher-Symmetric Informationally Complete Measurements. Phys. Rev. Lett., 120 (3). COLLEGE PK: AMER PHYSICAL SOC. ISSN 1079-7114

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Abstract

A quantum measurement is Fisher symmetric if it provides uniform and maximal information on all parameters that characterize the quantum state of interest. Using (complex projective) 2-designs, we construct measurements on a pair of identically prepared quantum states that are Fisher symmetric for all pure states. Such measurements are optimal in achieving the minimal statistical error without adaptive measurements. We then determine all collective measurements on a pair that are Fisher symmetric for the completely mixed state and for all pure states simultaneously. For a qubit, these measurements are Fisher symmetric for all states. The minimal optimal measurements are tied to the elusive symmetric informationally complete measurements, which reflects a deep connection between local symmetry and global symmetry. In the study, we derive a fundamental constraint on the Fisher information matrix of any collective measurement on a pair, which offers a useful tool for characterizing the tomographic efficiency of collective measurements.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Zhu, HuangjunUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Hayashi, MasahitoUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-198683
DOI: 10.1103/PhysRevLett.120.030404
Journal or Publication Title: Phys. Rev. Lett.
Volume: 120
Number: 3
Date: 2018
Publisher: AMER PHYSICAL SOC
Place of Publication: COLLEGE PK
ISSN: 1079-7114
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
COMPLETE QUANTUM MEASUREMENTS; PURE-STATE MODEL; TOMOGRAPHYMultiple languages
Physics, MultidisciplinaryMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/19868

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