Geodesic
On asymptotically optimal hypotheses testing in quantum statistics
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 2, pp. 429-432

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The mathematical formulation of a hypothesis testing problem in quantum statistics under consideration reduces to the following. Let $\{\psi_j\}$ be a given basis in a $d$-dimensional unitary space. Find an orthonormal basis $\{e_j\}$ which approximates the basis $\{\psi_j\}$ in the sense that the value of (1) is minimal. An asymptotic solution to this problem is given for «almost orthogonal» vectors $\psi_j$. An asymptotically optimal basis is $\widehat\psi_j=\Gamma^{-1/2}\psi_j$, where $\Gamma$ is the Gram operator of the system $\{\psi_j\}$. 
@article{TVP_1978_23_2_a20,
     author = {A. S. Holevo},
     title = {On asymptotically optimal hypotheses testing in quantum statistics},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {429--432},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a20/}
}
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A. S. Holevo. On asymptotically optimal hypotheses testing in quantum statistics. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 2, pp. 429-432. http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a20/