2006/11/09 by Michael Nathanson, M. Nathanson, M. B. Ruskai +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Conjecture #Degree (music) #Diagonal #Dimension (graph theory) #Entropy (arrow of time) #Mathematical Analysis and Transform Methods #Multipartite #Mutually unbiased bases #Pauli exclusion principle #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Upper and lower bounds #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/28/s22
published as J. Phys. A: Math. Theor. 40 (2007) 8171-8204.
arxiv created 2006/11/09 · openalex publication_date 2007/06/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We define and study the properties of channels which are analogous to unital qubit channels in several ways. A full treatment can be given only when the dimension d = p m a prime power, in which case each of the d + 1 mutually unbiased bases (MUB) defines an axis. Along each axis the channel looks like a depolarizing channel, but the degree of depolarization depends on the axis. When d is not a prime power, some of our results still hold, particularly in the case of channels with one symmetry axis. We describe the convex structure of this class of channels and the subclass of entanglement breaking channels. We find new bound entangled states for d = 3. For these channels, we show that the multiplicativity conjecture for maximal output p -norm holds for p = 2. We also find channels with behaviour not exhibited by unital qubit channels, including two pairs of orthogonal bases with equal output entropy in the absence of symmetry. This provides new numerical evidence for the additivity of minimal output entropy.