Optimal entanglement witnesses from limited local measurements

Year: 2020

Authors: Ricciardi A., Chruscinski D., Macchiavello C.

Autors Affiliation: Univ Pavia, Dipartimento Fis, Via Bassi 6, I-27100 Pavia, Italy; Nicolaus Copernicus Univ, Fac Phys Astron & Informat, Inst Phys, Grudziadzka 5-7, PL-87100 Torun, Poland; Ist Nazl Fis Nucl, Sez Pavia, Via Bassi 6, I-27100 Pavia, Italy; CNR INO, Largo E Fermi 6, I-50125 Florence, Italy.

Abstract: We address the problem of optimizing entanglement witnesses when a limited fixed set of local measurements can be performed on a bipartite system, thus providing a procedure, feasible also for experiments, to detect entangled states using only the statistics of these local measurements. We completely characterize the class of entanglement witnesses of the form W = P-Gamma, where Gamma denotes partial transposition, that can be constructed from the measurements of the bipartite operators sigma(x) circle times sigma(x), sigma(y) circle times sigma(y), and sigma(z) circle times sigma(z) in the case of two-qubit systems. In particular, we consider all possible extremal decomposable witnesses within the considered class that can be defined from this set of measurements. Finally, we discuss possible extensions to higher-dimension bipartite systems when the set of available measurements is characterized by the generalized Gell-Mann matrices. We provide several examples of entanglement witnesses, both decomposable and indecomposable, that can be constructed with these limited resources.

Journal/Review: PHYSICAL REVIEW A

Volume: 101 (6)      Pages from: 062319  to: 062319

More Information: We thank O. Guhne for useful discussions and comments. D.C. was supported by the Polish National Science Centre Project No. 2015/19/B/ST1/03095
KeyWords: POSITIVE LINEAR-MAPS; SEPARABILITY
DOI: 10.1103/PhysRevA.101.062319

Citations: 7
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