King, Christopher; Koldan, Nilufer New multiplicativity results for qubit maps. (English) Zbl 1111.81036 J. Math. Phys. 47, No. 4, 042106, 9 p. (2006). Summary: Let \(\Phi\) be a trace-preserving, positivity-preserving (but not necessarily completely positive) linear map on the algebra of complex \(2\times 2\) matrices, and let \(\Omega\) be any finite-dimensional completely positive map. For \(p=2\) and \(p\geq 4\), we prove that the maximal \(p\)-norm of the product map \(\Phi\otimes\Omega\) is the product of the maximal \(p\)-norms of \(\Phi\) and \(\Omega\). Restricting \(\Phi\) to the class of completely positive maps, this settles the multiplicativity question for all qubit channels in the range of values \(p\geq 4\). Cited in 1 ReviewCited in 1 Document MSC: 81P68 Quantum computation 15A90 Applications of matrix theory to physics (MSC2000) 81P15 Quantum measurement theory, state operations, state preparations PDFBibTeX XMLCite \textit{C. King} and \textit{N. Koldan}, J. Math. Phys. 47, No. 4, 042106, 9 p. (2006; Zbl 1111.81036) Full Text: DOI arXiv References: [1] Amosov G. G., Theor. Probab. Appl. 47 (1) pp 143– (2002) [2] Amosov G. G., Problems in Information Transmission 36 pp 305– (2000) · Zbl 0998.47023 [3] DOI: 10.1007/BF01231769 · Zbl 0803.47037 [4] DOI: 10.1080/095003400148231 [5] DOI: 10.1016/S0375-9601(02)00735-1 · Zbl 0996.78002 [6] DOI: 10.1088/0305-4470/38/45/L02 · Zbl 1079.81011 [7] DOI: 10.1007/BF01610499 · Zbl 0337.52008 [8] DOI: 10.1063/1.1500791 · Zbl 1060.94006 [9] DOI: 10.1063/1.1433943 · Zbl 1059.81023 [10] DOI: 10.1007/s00220-003-0955-9 · Zbl 1049.15013 [11] DOI: 10.1016/j.laa.2004.03.006 · Zbl 1064.15022 [12] DOI: 10.1016/j.laa.2005.02.035 · Zbl 1082.15043 [13] DOI: 10.1109/18.904522 · Zbl 1016.94012 [14] DOI: 10.1063/1.1498000 · Zbl 1060.94004 [15] DOI: 10.1007/s00220-003-0981-7 · Zbl 1070.81030 [16] Watrous J., Quantum Information and Computation 5 (1) pp 58– (2005) · Zbl 1085.68052 [17] DOI: 10.1063/1.1498491 · Zbl 1060.94008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.