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The quantum information and the Bures metric are equivalent to each other, except at points where the rank of the density matrix changes.
L. Mirsky, Symmetric gauge functions and unitarily invariant norms, The quarterly journal of mathematics 11
1960
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C. W. Helstrom, Quantum detection and estimation theory (Academic press 1976)
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M. Hübner, Explicit computation of the bures distance for density matrices, Physics Letters A 163
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S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Physical Review Letters 72
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H.-J. Sommers and K. Zyczkowski, Bures volume of the set of mixed quantum states, Journal of Physics A: Mathematical and General 36
2003
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A. S. Holevo, Probabilistic and statistical aspects of quantum theory , volume 1 (Springer Science & Business Media 2011)
2011
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B. Escher, R. de Matos Filho, and L. Davidovich, General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nature Physics 7
2011
Cited alongside, same era.
W. Zhong, Z. Sun, J. Ma, X. Wang, and F. Nori, Fisher information under decoherence in bloch representation, Physical Review A 87
2013
Cited alongside, same era.
H. Yuan, Sequential feedback scheme outperforms the parallel scheme for hamiltonian parameter estimation, Physical review letters 117
2016
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D. Šafránek, Discontinuities of the quantum fisher information and the bures metric, Physical Review A 95
2017
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P. Del Moral and A. Niclas, A taylor expansion of the square root matrix function, Journal of Mathematical Analysis and Applications 465
2018
Later among the works it cites.
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