Quantum diagonalization of Hermitean matrices
نویسندگان
چکیده
منابع مشابه
Quantum Diagonalization of Hermitean Matrices
To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource. It allows one, in principle, to diagonalize hermitean (N × N) matrices by quantum mechanical measurements only. To do so, one considers the given matrix as an observable of a single spin wit...
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An entirely quantum mechanical approach to diagonalize hermitean matrices has been presented recently. Here, the genuinely quantum mechanical approach is considered in detail for (2× 2) matrices. The method is based on the measurement of quantum mechanical observables which provides the computational resource. In brief, quantum mechanics is able to directly address and output eigenvalues of her...
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A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real-quaternion) stochastic time series representing two ‘remote’ complex systems. The first paper in a series provides a detailed spectral theory of non-Hermitean Wishart random matrices composed of complex valued entries. The great em...
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The two-by-two Sp(2) matrix has three parameters with unit determinant. Yet, there are no established procedures for diagonalizing this matrix. It is shown that this matrix can be written as a similarity transformation of the two-by-two Wigner matrix, derivable from Wigner’s little group which dictates the internal space-time symmetries of relativistic particles. The Wigner matrix can be diagon...
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The Ginibre ensemble of nonhermitean random Hamiltonian matrices K is considered. Each quantum system described byK is a dissipative system and the eigenenergies Zi of the Hamiltonian are complex-valued random variables. The second difference of complex eigenenergies is viewed as discrete analog of Hessian with respect to labelling index. The results are considered in view of Wigner and Dyson’s...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2001
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/34/27/312