2015/09/30 by Julien Deschamps, Ion Nechita, Clément Pellegrini +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Bipartite graph #Combinatorics #Dilation (metric space) #Dimension (graph theory) #Discrete mathematics #Hilbert space #Mathematics #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum channel #Quantum entanglement #Quantum information #Quantum mechanics #Tensor product #Unitary operator #Unitary state #Variety (cybernetics) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/49/33/335301
published as J. Phys. A: Math. Theor. 49 335301 (2016) · v2: references [14,15] added, as well as various comments and clarifications
arxiv created 2015/10/07 · openalex publication_date 2016/07/06 · arxiv updated 2016/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate unitary operators acting on a tensor product space, with the property that the quantum channels they generate, via the Stinespring dilation theorem, are of a particular type, independently of the state of the ancilla system in the Stinespring relation. The types of quantum channels we consider are those of interest in quantum information theory: unitary conjugations, constant channels, unital channels, mixed unitary channels, positive partial transpose channels, and entanglement breaking channels. For some of the classes of bipartite unitary operators corresponding to the above types of channels, we provide explicit characterizations, necessary and/or sufficient conditions for membership, and we compute the dimension of the corresponding algebraic variety. Inclusions between these classes are considered, and we show that for small dimensions, many of these sets are identical.