Construction of general symmetric-informationally-complete-positive-operator-valued measures by using a complete orthogonal basis

Autor:	Masakazu Yoshida, Gen Kimura
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	Quantum Physics FOS: Physical sciences Quantum Physics (quant-ph)
Popis:	A general symmetric-informationally-complete (GSIC)-positive-operator-valued measure (POVM) is known to provide an optimal quantum state tomography among minimal IC POVMs with a fixed average purity. In this paper we provide a general construction of a GSIC POVM by means of a complete orthogonal basis (COB), also interpreted as a normal quasiprobability representation. A spectral property of a COB is shown to play a key role in the construction of SIC POVMs and also for the bound of the mean-square error of the state tomography. In particular, a necessary and sufficient condition to construct a SIC POVM for any d is constructively given by the power of traces of a COB. We give three simple constructions of COBs from which one can systematically obtain GSIC POVMs. 10 pages, 1 figure
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::724c6efbe6166094e278f892aa94db28 http://arxiv.org/abs/2208.00578 Zobrazit plný text záznamu