کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5500410 1400075 2017 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Clifford tori and unbiased vectors
ترجمه فارسی عنوان
کلیفورد توری و بردارهای بی طرفانه
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
چکیده انگلیسی

The existence problem for mutually unbiased bases is an unsolved problem in quantum information theory. A related question is whether every pair of bases admits vectors that are unbiased to both. Mathematically this translates to the question whether two Lagrangian Clifford tori intersect, and a body of results exists concerning it. These results are however rather weak from the point of view of the first problem. We make a detailed study of how the intersections behave in the simplest nontrivial case, that of complex projective 2-space (the qutrit), for which the set of pairs of Clifford tori can be usefully parametrized by the unistochastic subset of Birkhoff's polytope. Pairs that do not intersect transversally are located. Some calculations in higher dimensions are included to see which results are special to the qutrit.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Reports on Mathematical Physics - Volume 79, Issue 1, February 2017, Pages 33-51
نویسندگان
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