TY - JOUR

T1 - How many mutually unbiased bases are needed to detect bound entangled states?

AU - Bae, Joonwoo

AU - Bera, Anindita

AU - Chruściński, Dariusz

AU - Hiesmayr, Beatrix C

AU - McNulty, Daniel

N1 - Funding Information:
J B is supported by the National Research Foundation of Korea (Grant Nos. NRF-2021R1A2C200 6309, NRF-2022M1A3C2069728) and the Institute for Information & Communication Technology Promotion (IITP) (the ITRC Program/IITP-2022-2018-0-01402). A B and D C were supported by the Polish National Science Centre Project 2018/30/A/ST2/00837. B C H acknowledges gratefully that this research was funded in whole, or in part, by the Austrian Science Fund (FWF) Project P36102-N. D M has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 663830. D M also acknowledges financial support by the TEAM-NET project co-financed by the E U within the Smart Growth Operational Programme (Contract No. POIR.04.04.00-00-17C1/18-00).
Publisher Copyright:
© 2022 The Author(s).

PY - 2022/12/28

Y1 - 2022/12/28

N2 - 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×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.

AB - 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×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.

KW - Paper

KW - Quantum mechanics and quantum information theory

KW - entanglement detection

KW - bound entanglement

KW - mutually unbiased bases

KW - non-decomposable witnesses

UR - http://www.scopus.com/inward/record.url?scp=85146378559&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/acaa16

DO - 10.1088/1751-8121/acaa16

M3 - Article

SN - 1751-8113

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 50

M1 - 505303

ER -