Fetching the paper…
Reading the bibliography…
In the quest to unlock the maximum potential of quantum sensors, it is of paramount importance to have practical measurement strategies that can estimate incompatible parameters with best precisions possible.
C. Helstrom, Minimum mean-squared error of estimates in quantum statistics, Physics Letters A 25
1967
Earlier work this paper cites.
R. M. Van Slyke and R. J.-B. Wets, A duality theory for abstract mathematical programs with applications to optimal control theory, Journal of Mathematical Analysis and Applications 22
1968
Earlier work this paper cites.
C. W. Helstrom, Quantum detection and estimation theory (Academic press, 1976)
1976
Earlier work this paper cites.
G. Lindblad, On the generators of quantum dynamical semigroups, Communications in Mathematical Physics 48
1976
Earlier work this paper cites.
P. Delsarte, J. Goethals, and J. Seidel, Spherical codes and designs, Geom Dedicata 6
1977
Earlier work this paper cites.
H. Nagaoka, A new approach to Cramér-Rao bounds for quantum state estimation, IEICE Tech Report IT 89-42
1989
Earlier work this paper cites.
A. Fujiwara and H. Nagaoka, Quantum fisher metric and estimation for pure state models, Physics Letters A 201
1995
Earlier work this paper cites.
M. Horodecki, P. Horodecki, and R. Horodecki, Separability of mixed states: necessary and sufficient conditions, Physics Letters A 223
1996
Earlier work this paper cites.
M. Hayashi, A linear programming approach to attainable Cramer-Rao type bound, in Quantum Communication, Computing, and Measurement , edited by O. Hirota, A. S. Holevo, and C. M. Caves (Plenum, New York, 1997)
1997
Earlier work this paper cites.
K. Fujisawa, M. Kojima, and K. Nakata, Exploiting sparsity in primal-dual interior-point methods for semidefinite programming, Mathematical Programming 79
1997
Earlier work this paper cites.
M. Hayashi and K. Matsumoto, Statistical model with measurement degree of freedom and quantum physics, in Asymptotic Theory Of Quantum Statistical Inference: Selected Papers , edited by M. Hayashi (World Scientific, 2005) pp. 162–169, originally published in Japanese in Surikaiseki Kenkyusho Kokyuroku No. 1055, 1998
1998
Earlier work this paper cites.
M. Hayashi, On simultaneous measurement of noncommutative observables. in development of infinite-dimensional non-commutative anaysis, in Surikaisekikenkyusho (RIMS), Kokyuroku No. 1099, In Japanese (Kyoto Univ., 1999) pp. 96–188
1999
Earlier work this paper cites.
A. Fujiwara and H. Nagaoka, An estimation theoretical characterization of coherent states, Journal of Mathematical Physics 40
1999
Earlier work this paper cites.
R. D. Gill and S. Massar, State estimation for large ensembles, Phys. Rev. A 61
2000
Earlier work this paper cites.
B. M. Terhal, A family of indecomposable positive linear maps based on entangled quantum states, Linear Algebra and its Applications 323
2001
Earlier work this paper cites.
M. Lewenstein, B. Kraus, P. Horodecki, and J. I. Cirac, Characterization of separable states and entanglement witnesses, Phys. Rev. A 63
2001
Earlier work this paper cites.
D. Bruß, Characterizing entanglement, Journal of Mathematical Physics 43
2002
Earlier work this paper cites.
K. Matsumoto, A new approach to the Cramér-Rao-type bound of the pure-state model, Journal of Physics A: Mathematical and General 35
2002
Earlier work this paper cites.
L. Gurvits, Classical deterministic complexity of Edmonds’ problem and quantum entanglement, STOC ’03, 10 (2003)
2003
Earlier work this paper cites.
A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Complete family of separability criteria, Phys. Rev. A 69
2004
Earlier work this paper cites.
H. Nagaoka, A generalization of the simultaneous diagonalization of hermitian matrices and its relation to quantum estimation theory, in Asymptotic Theory Of Quantum Statistical Inference: Selected Papers , edited by M. Hayashi (World Scientific, 2005) pp. 133–149
2005
Cited alongside, same era.
H. Masahito, ed., Asymptotic theory of quantum statistical inference: selected papers (World Scientific, 2005)
2005
Cited alongside, same era.
M. Hayashi, Quantum information theory: Mathematical Foundation (Springer, 2016) graduate Texts in Physics, First edition was published from Springer in 2006
2006
Cited alongside, same era.
M. Guţă and J. Kahn, Local asymptotic normality for qubit states, Physical Review A 73
2006
Cited alongside, same era.
S.-I. Amari and H. Nagaoka, Methods of information geometry (American Mathematical Soc., 2007)
2007
M. Hayashi, Group Representation for Quantum Theory (Springer, 2017)
2017
Later among the works it cites.
M. S. Baladram, On explicit construction of simplex t t -designs, Interdisciplinary Information Sciences 24
2018
Later among the works it cites.
Y. Yang, G. Chiribella, and M. Hayashi, Quantum stopwatch: how to store time in a quantum memory, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474
2018
Later among the works it cites.
F. Albarelli, J. F. Friel, and A. Datta, Evaluating the Holevo Cramér-Rao bound for multiparameter quantum metrology, Phys. Rev. Lett. 123
2019
Later among the works it cites.
R. Uola, T. Kraft, J. Shang, X.-D. Yu, and O. Gühne, Quantifying quantum resources with conic programming, Phys. Rev. Lett. 122
2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
D. Petz, Quantum information theory and quantum statistics (Springer Science & Business Media, 2007)
2007
Cited alongside, same era.
A. Ambainis and J. Emerson, Quantum t-designs: t-wise independence in the quantum world, in Twenty-Second Annual IEEE Conference on Computational Complexity (CCC’07) (2007) pp. 129–140, quant-ph/0701126
2007
Cited alongside, same era.
M. Hayashi and K. Matsumoto, Asymptotic performance of optimal state estimation in qubit system, Journal of Mathematical Physics 49
2008
Cited alongside, same era.
M. Navascués, Pure state estimation and the characterization of entanglement, Phys. Rev. Lett. 100
2008
Cited alongside, same era.
J. Kahn and M. Guţă, Local asymptotic normality for finite dimensional quantum systems, Communications in Mathematical Physics 289
2009
Cited alongside, same era.
E. Bannai and E. Bannai, A survey on spherical designs and algebraic combinatorics on spheres, European Journal of Combinatorics 30
2009
Cited alongside, same era.
A. S. Holevo, Probabilistic and statistical aspects of quantum theory (Edizioni della Normale, 2011)
2011
Cited alongside, same era.
R. Takagi, B. Regula, K. Bu, Z.-W. Liu, and G. Adesso, Operational advantage of quantum resources in subchannel discrimination, Phys. Rev. Lett. 122
2019
Later among the works it cites.
R. Takagi and B. Regula, General resource theories in quantum mechanics and beyond: Operational characterization via discrimination tasks, Phys. Rev. X 9
2019
Later among the works it cites.
Y. Yang, G. Chiribella, and M. Hayashi, Attaining the ultimate precision limit in quantum state estimation, Communications in Mathematical Physics 36 8
2019
Later among the works it cites.
Y. Ouyang, Computing spectral bounds of the heisenberg ferromagnet from geometric considerations, Journal of Mathematical Physics 60
2019
Later among the works it cites.
R. Demkowicz-Dobrzański, W. Górecki, and M. Guţă, Multi-parameter estimation beyond quantum fisher information, Journal of Physics A: Mathematical and Theoretical 53
2020
Later among the works it cites.
J. S. Sidhu and P. Kok, Geometric perspective on quantum parameter estimation, AVS Quantum Science 2
2020
Later among the works it cites.
J. Suzuki, Y. Yang, and M. Hayashi, Quantum state estimation with nuisance parameters, Journal of Physics A: Mathematical and Theoretical 53
2020
Later among the works it cites.
C. An and Y. Xiao, Numerical construction of spherical t t -designs by Barzilai-Borwein method, Applied Numerical Mathematics 150
2020
Later among the works it cites.
J. S. Sidhu, Y. Ouyang, E. T. Campbell, and P. Kok, Tight bounds on the simultaneous estimation of incompatible parameters, Phys. Rev. X 11
2021
Later among the works it cites.
L. O. Conlon, J. Suzuki, P. K. Lam, and S. M. Assad, Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements, npj Quantum Information 7
2021
Later among the works it cites.
X.-M. Lu and X. Wang, Incorporating heisenberg’s uncertainty principle into quantum multiparameter estimation, Phys. Rev. Lett. 126
2021
Later among the works it cites.
Review of Holevo’s research in the 1980s, private paper submitted for review, and to appear on arxiv soon (2023)
2023
Closest in time.
E. Chitambar, I. George, B. Doolittle, and M. Junge, The communication value of a quantum channel, IEEE Transactions on Information Theory 69
2023
Closest in time.
H. Arai and M. Hayashi, Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure, New Journal of Physics 25
2023
Closest in time.