2016/12/31 by Michał Studziński, Sergii Strelchuk, Marek Mozrzymas +1 · 51 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Combinatorics #Computer science #Dimension (graph theory) #Homogeneous space #Mathematics #Permutation (music) #Physics #Polynomial #Port (circuit theory) #Protocol (science) #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum channel #Quantum entanglement #Quantum mechanics #Quantum optics and atomic interactions #Quantum teleportation #Representation (politics) #Teleportation #Theoretical computer science #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.1038/s41598-017-10051-4
published in Scientific Reports 7(1), 10871 (Nature Portfolio) · 30 pages, 5 figures
openalex publication_date 2017/09/01 · arxiv created 2017/09/25 · arxiv updated 2017/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Port-based teleportation (PBT), introduced in 2008, is a type of quantum teleportation protocol which transmits the state to the receiver without requiring any corrections on the receiver's side. Evaluating the performance of PBT was computationally intractable and previous attempts succeeded only with small systems. We study PBT protocols and fully characterize their performance for arbitrary dimensions and number of ports. We develop new mathematical tools to study the symmetries of the measurement operators that arise in these protocols and belong to the algebra of partially transposed permutation operators. First, we develop the representation theory of the mentioned algebra which provides an elegant way of understanding the properties of subsystems of a large system with general symmetries. In particular, we introduce the theory of the partially reduced irreducible representations which we use to obtain a simpler representation of the algebra of partially transposed permutation operators and thus explicitly determine the properties of any port-based teleportation scheme for fixed dimension in polynomial time.