نتایج جستجو برای: joint matrix higher rank numerical range

تعداد نتایج: 2350093  

2008
Chi-Kwong Li

For a noisy quantum channel, a quantum error correcting code exists if and only if the joint higher rank numerical ranges associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint higher rank numerical ranges are obtained and their implications to quantum computing are discussed. It is shown that if the dimension of the underlying Hilbert ...

Journal: :AL-Rafidain Journal of Computer Sciences and Mathematics 2009

Journal: :Journal of Mathematical Analysis and Applications 2012

‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...

Journal: :bulletin of the iranian mathematical society 2013
h. r. afshin m. a. mehrjoofard a. salemi

in this note we characterize polynomial numerical hulls of matrices $a in m_n$ such that$a^2$ is hermitian. also, we consider normal matrices $a in m_n$ whose $k^{th}$ power are semidefinite. for such matriceswe show that $v^k(a)=sigma(a)$.

Journal: :SIAM J. Matrix Analysis Applications 2011
Hwa-Long Gau Chi-Kwong Li Yiu-Tung Poon Nung-Sing Sze

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix A ∈ Mn has eigenvalues a1, . . . , an, then its higher rank numerical range Λk(A) is the intersection of convex polygons with vertices aj1 , . . . , ajn−k+1 , where 1 ≤ j1 < · · · < jn−k+1 ≤ n. In this paper, it is shown that ...

2009
CHI-KWONG LI

For a noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the joint rank-k numerical range associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint rank k-numerical range are obtained and their implications to quantum computing are discussed. It is shown that for a given k if the dimension of the un...

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