کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897659 | 1631038 | 2018 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Operator Schmidt ranks of bipartite unitary matrices
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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چکیده انگلیسی
The operator Schmidt rank of an operator acting on the tensor product CnâCm is the number of terms in a decomposition of the operator as a sum of simple tensors with factors forming orthogonal families in their respective matrix algebras. It has been known that for unitary operators acting on two copies of C2, the operator Schmidt rank can only take the values 1, 2, and 4, the value 3 being forbidden. In this paper, we settle an open question, showing that the above obstruction is the only one occurring. We do so by constructing explicit examples of bipartite unitary operators of all possible operator Schmidt ranks, for arbitrary dimensions (n,m)â (2,2).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 557, 15 November 2018, Pages 174-187
Journal: Linear Algebra and its Applications - Volume 557, 15 November 2018, Pages 174-187
نویسندگان
Alexander Müller-Hermes, Ion Nechita,