A1 Refereed original research article in a scientific journal
Obtaining conclusive information from incomplete experimental quantum tomography
Authors: Henri Lyyra, Tom Kuusela, Teiko Heinosaari
Publisher: AMER PHYSICAL SOC
Publication year: 2019
Journal: Physical Review A
Journal name in source: PHYSICAL REVIEW A
Journal acronym: PHYS REV A
Article number: ARTN 042335
Volume: 99
Issue: 4
Number of pages: 8
ISSN: 2469-9926
eISSN: 2469-9934
DOI: https://doi.org/10.1103/PhysRevA.99.042335
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/40407939
Abstract
We demonstrate that incomplete quantum tomography can give conclusive information in experimental realizations. We divide the state space into a union of multiple disjoint subsets and determine conclusively to which of the subsets a system, prepared in completely unknown state, belongs. In other words, we construct and solve membership problems. Our membership problems are partitions of the state space into a union of four disjoint sets formed by fixing two maximally entangled reference states and boundary values of a fidelity function "radius" between the reference states and the unknown preparation. We study the necessary and sufficient conditions of the measurements that solve these membership problems conclusively. We construct and experimentally implement such informationally incomplete measurement on two-photon polarization states with combined one-qubit measurements, and we solve the membership problem in example cases.
We demonstrate that incomplete quantum tomography can give conclusive information in experimental realizations. We divide the state space into a union of multiple disjoint subsets and determine conclusively to which of the subsets a system, prepared in completely unknown state, belongs. In other words, we construct and solve membership problems. Our membership problems are partitions of the state space into a union of four disjoint sets formed by fixing two maximally entangled reference states and boundary values of a fidelity function "radius" between the reference states and the unknown preparation. We study the necessary and sufficient conditions of the measurements that solve these membership problems conclusively. We construct and experimentally implement such informationally incomplete measurement on two-photon polarization states with combined one-qubit measurements, and we solve the membership problem in example cases.
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