On the structure of mirrored operators obtained from optimal entanglement witnesses

Anindita Bera (Corresponding author), Joonwoo Bae, Beatrix C. Hiesmayr, Dariusz Chruściński

Publications: Contribution to journalArticlePeer Reviewed


Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The framework of mirrored EW doubles the power of a given EW by introducing its twin—a mirrored EW—whereby two EWs related by mirroring can bound the set of separable states more efficiently. In this work, we investigate the relation between the EWs and its mirrored ones, and present a conjecture which claims that the mirrored operator obtained from an optimal EW is either a positive operator or a decomposable EW, which implies that positive-partial-transpose entangled states, also known as the bound entangled states, cannot be detected. This conjecture is reached by studying numerous known examples of optimal EWs. However, the mirrored EWs obtained from the non-optimal ones can be non-decomposable as well. We also show that mirrored operators obtained from the extremal decomposable witnesses are positive semi-definite. Interestingly, the witnesses that violate the well known conjecture of Structural Physical Approximation, do satisfy our conjecture. The intricate relation between these two conjectures is discussed and it reveals a novel structure of the separability problem.
Original languageEnglish
Article number10733
Number of pages15
JournalScientific Reports
Issue number1
Publication statusPublished - 3 Jul 2023

Austrian Fields of Science 2012

  • 103025 Quantum mechanics
  • 103019 Mathematical physics


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