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

Joonwoo Bae, Anindita Bera, Dariusz Chruściński, Beatrix C Hiesmayr, Daniel McNulty*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (SciVal)
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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.
Original languageEnglish
Article number505303
Number of pages19
JournalJournal of Physics A: Mathematical and Theoretical
Issue number50
Publication statusPublished - 28 Dec 2022


  • Paper
  • Quantum mechanics and quantum information theory
  • entanglement detection
  • bound entanglement
  • mutually unbiased bases
  • non-decomposable witnesses


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