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• W3102194711 startingPage "385306" @default.
• W3102194711 abstract "Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group $mathcal{U}(d)$ of arbitrary dimension $d$ which is constructed in a composite way. We show explicitly how any element of $mathcal{U}(d)$ can be composed of matrix exponential functions of generalized anti-symmetric $sigma$-matrices and one-dimensional projectors. The specific form makes it considerably easy to identify and discard redundant parameters in several cases. In this way, redundancy-free density matrices of arbitrary rank $k$ can be formulated. Our construction can also be used to derive an orthonormal basis of any $k$-dimensional subspaces of $mathbb{C}^d$ with the minimal number of parameters. As an example it will be shown that this feature leads to a significant reduction of parameters in the case of investigating distillability of quantum states via lower bounds of an entanglement measure (the $m$-concurrence)." @default.
• W3102194711 created "2020-11-23" @default.
• W3102194711 creator A5011840878 @default.
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• W3102194711 date "2010-08-17" @default.
• W3102194711 modified "2023-10-16" @default.
• W3102194711 title "A composite parameterization of unitary groups, density matrices and subspaces" @default.
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• W3102194711 doi "https://doi.org/10.1088/1751-8113/43/38/385306" @default.
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