2009/07/31 by Remigiusz Augusiak, Janusz Grabowski, Marek Kuś +1 · 27 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Biology #Cluster state #Combinatorics #Computer science #Mathematics #Peres–Horodecki criterion #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Qubit #Set (abstract data type) #State (computer science) #Theoretical physics #Type (biology) #quant-ph
paper · pdf · doi:10.1016/j.optcom.2009.10.050
published in Optics Communications 283(5), 805-813 (Elsevier BV) · 12 pages, 2 figures, revised version due to the partial overlap with results of arXiv:0704.3348, some new results on extremality in multi-qubit systems added, contribution to the special issue of Optics Communications in memory of Krzysztof Wodkiewicz
arxiv created 2009/11/25 · openalex publication_date 2009/11/28 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study extremality in various sets of states that have positive partial transposes. One of the tools we use for this purpose is the recently formulated criterion allowing to judge if a given state is extremal in the set of PPT states. First we investigate qubit--ququart states and show that the only candidates for extremal PPT entangled states (PPTES) have ranks of the state and its partial transposition (5,5) or (5,6) (equivalently (6,5)). Then, examples of extremal states of (5,5) type and the so--called edge states of type (5,6) are provided. We also make an attempt to explore the set of PPT states with ranks (5,6). Finally, we discuss what are the possible configurations of ranks of density matrices and their respective partial transposition in general three-qubit and four-qubit symmetric states for which there may exist extremal entangled PPT states. For instance in the first case we show that the only possibilities are (4,4,4) and (4,4,5).