How many mutually unbiased bases are needed to detect bound entangled states?

Autor(en)

Joonwoo Bae, Anindita Bera, Dariusz Chruscinski, Beatrix C. Hiesmayr, Daniel McNulty

Abstrakt

From a practical perspective it is advantageous to develop methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of mutually unbiased bases (MUBs) needed to detect bound entanglement in bipartite $(d\times d)$-dimensional states, i.e. entangled states that are positive under partial transposition. In particular, we show that a class of entanglement witnesses (EWs) composed of MUBs can detect bound entanglement if the number of measurements is greater than $d/2+1$. This is a substantial improvement over other detection methods, requiring significantly fewer resources than either full quantum state tomography or measuring a complete set of d + 1 MUBs. Our approach is based on a partial characterisation of the (non-)decomposability of EWs. We show that non-decomposability is a universal property of MUBs, which holds regardless of the choice of complementary observables, and we find that both the number of measurements and the structure of the witness play an important role in the detection of bound entanglement.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Korea Advanced Institute of Science and Technology (KAIST), Nicolaus Copernicus University, Polish Academy of Sciences (PAS), Aberystwyth University

Journal

Journal of Physics A: Mathematical and Theoretical

Band

55

Anzahl der Seiten

19

ISSN

1751-8113

DOI

https://doi.org/10.1088/1751-8121/acaa16

Publikationsdatum

12-2022

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik, 103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Allgemeine Physik und Astronomie, Statistical and Nonlinear Physics, Statistics and Probability, Mathematical Physics, Modelling and Simulation

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/44cb5ffa-ff4f-479d-944e-695ef95d156a