Quantum Version of Wielandt’s Inequality Revisited
Quantum Version of Wielandt’s Inequality Revisited
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2019
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Shitov, Yaroslav
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IEEE Transactions on Information Theory (T-IT) ; 65 (2019), 8. - pp. 5239-5242. - Institute of Electrical and Electronics Engineers (IEEE). - ISSN 0018-9448. - eISSN 1557-9654
Abstract
Consider a linear space L of complex D-dimensional linear operators and assume that some power Lk of L is the whole set End(CD). Perez-Garcia, Verstraete, Wolf, and Cirac conjectured that the sequence L1, L2, . . . stablilizes after O(D2) terms; we prove that this happens after O(D2 log D) terms, improving the previously known bound of O(D4).
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MICHALEK, Mateusz, Yaroslav SHITOV, 2019. Quantum Version of Wielandt’s Inequality Revisited. In: IEEE Transactions on Information Theory (T-IT). Institute of Electrical and Electronics Engineers (IEEE). 65(8), pp. 5239-5242. ISSN 0018-9448. eISSN 1557-9654. Available under: doi: 10.1109/TIT.2019.2897772BibTex
@article{Michalek2019Quant-52489, year={2019}, doi={10.1109/TIT.2019.2897772}, title={Quantum Version of Wielandt’s Inequality Revisited}, number={8}, volume={65}, issn={0018-9448}, journal={IEEE Transactions on Information Theory (T-IT)}, pages={5239--5242}, author={Michalek, Mateusz and Shitov, Yaroslav} }
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