Built on

W. Górecki, S. Zhou, L. Jiang, and R. Demkowicz-Dobrzański, Optimal probes and error-correction schemes in multi-parameter quantum metrology, Quantum 4
Original
1901
Earlier work this paper cites.
P. Faist, S. Nezami, V. V. Albert, G. Salton, F. Pastawski, P. Hayden, and J. Preskill, Continuous symmetries and approximate quantum error correction, Physical Review X 10
Original
1902
Earlier work this paper cites.
M. P. Woods and Á. M. Alhambra, Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames, Quantum 4
Original
1902
Earlier work this paper cites.
K. Chabuda, J. Dziarmaga, T. J. Osborne, and R. Demkowicz-Dobrzański, Tensor-network approach for quantum metrology in many-body quantum systems, Nature Communications 11
Original
1906
Earlier work this paper cites.
F. Albarelli, J. F. Friel, and A. Datta, Evaluating the Holevo Cramér-Rao bound for multiparameter quantum metrology, Physical Review Letters 123
Original
1906
Earlier work this paper cites.
L. Seveso, F. Albarelli, M. G. Genoni, and M. G. A. Paris, On the discontinuity of the quantum Fisher information for quantum statistical models with parameter dependent rank, Journal of Physics A: Mathematical and Theoretical 53
Original
1906
Earlier work this paper cites.
H. Zhou, J. Choi, S. Choi, R. Landig, A. M. Douglas, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, P. Cappellaro, H. S. Knowles, H. Park, and M. D. Lukin, Quantum metrology with strongly interacting spin systems, Physical Review X 10
Original
1907
Earlier work this paper cites.
Y. Ouyang, N. Shettell, and D. Markham, Robust quantum metrology with explicit symmetric states, IEEE Transactions on Information Theory 68
Original
1908
Earlier work this paper cites.
B. Koczor, S. Endo, T. Jones, Y. Matsuzaki, and S. C. Benjamin, Variational-state quantum metrology, New Journal of Physics 22
Original
1908
Earlier work this paper cites.
S. Zhou and L. Jiang, An exact correspondence between the quantum Fisher information and the Bures metric, ArXiv e-prints (2019), arXiv:1910.08473
Original
1910
Earlier work this paper cites.
S. Zhou and L. Jiang, Optimal approximate quantum error correction for quantum metrology, Physical Review Research 2
Original
1910
Earlier work this paper cites.
J. S. Sidhu, Y. Ouyang, E. T. Campbell, and P. Kok, Tight bounds on the simultaneous estimation of incompatible parameters, Physical Review X 11
Original
1912
Earlier work this paper cites.
L. Mandelstam and I. Tamm, The uncertainty relation between energy and time in nonrelativistic quantum mechanics, Journal of Physics (USSR) IX
1945
Earlier work this paper cites.
Y. Aharonov and D. Bohm, Time in the quantum theory and the uncertainty relation for time and energy, Physical Review 122
1961
Earlier work this paper cites.
C. Helstrom, Minimum mean-squared error of estimates in quantum statistics, Physics Letters A 25
1967
Earlier work this paper cites.
C. W. Helstrom, Quantum detection and estimation theory, Journal of Statistical Physics 1
1969
Earlier work this paper cites.
R. H. Bartels and G. W. Stewart, Solution of the matrix equation a x + x b = c ax+xb=c [F4], Communications of the ACM 15
1972
Earlier work this paper cites.
M. Reed and B. Simon, I: Functional Analysis , Methods of Modern Mathematical Physics, Vol. 1 (Elsevier Science, 1981)
1981
Earlier work this paper cites.
M. Hübner, Explicit computation of the Bures distance for density matrices, Physics Letters A 163
1992
Earlier work this paper cites.
A. S. Holevo, A note on covariant dynamical semigroups, Reports on Mathematical Physics 32
1993
Earlier work this paper cites.
S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Physical Review Letters 72
1994
Earlier work this paper cites.
C. A. Fuchs and C. M. Caves, Mathematical techniques for quantum communication theory, Open Systems & Information Dynamics 3
1995
Earlier work this paper cites.
S. L. Braunstein, C. M. Caves, and G. Milburn, Generalized uncertainty relations: Theory, examples, and Lorentz invariance, Annals of Physics 247
1996
Earlier work this paper cites.
A. M. Steane, Error correcting codes in quantum theory, Physical Review Letters 77
1996
Earlier work this paper cites.
S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Improvement of frequency standards with quantum entanglement, Physical Review Letters 79
1997
Earlier work this paper cites.
E. Knill and R. Laflamme, Theory of quantum error-correcting codes, Physical Review A 55
1997
Earlier work this paper cites.
A. Y. Kitaev, Quantum error correction with imperfect gates, in Proceedings of the Third International Conference on Quantum Communication and Measurement , edited by O. Hirota, A. S. Holevo, and C. M. Caves (Springer US, Boston, MA, 1997) pp. 181–188
1997
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.
V. Bužek, R. Derka, and S. Massar, Optimal quantum clocks, Physical Review Letters 82
1999
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000)
2000
Earlier work this paper cites.
R. D. Gill and S. Massar, State estimation for large ensembles, Physical Review A 61
2000
Earlier work this paper cites.
C. Bertoni, Y. Yang, and J. M. Renes, Entropic time–energy uncertainty relations: an algebraic approach, New Journal of Physics 22
Original
2001
Earlier work this paper cites.
R. Demkowicz-Dobrzański, W. Górecki, and M. Guţă, Multi-parameter estimation beyond quantum Fisher information, Journal of Physics A 53
Original
2001
Earlier work this paper cites.
I. Kull, P. A. Guérin, and F. Verstraete, Uncertainty and trade-offs in quantum multiparameter estimation, Journal of Physics A 53
Original
2002
Earlier work this paper cites.
S. Zhou and L. Jiang, Asymptotic theory of quantum channel estimation, PRX Quantum 2
Original
2003
Earlier work this paper cites.
A. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303
2003
Earlier work this paper cites.

Similar

L. Sun, X. He, C. You, C. Lv, B. Li, S. Lloyd, and X. Wang, Exponentially enhanced quantum metrology using resources of linear complexity, ArXiv e-prints (2020), arXiv:2004.01216
Original
2004
Cited alongside, same era.
A. Kubica and R. Demkowicz-Dobrzański, Using quantum metrological bounds in quantum error correction: A simple proof of the approximate Eastin-Knill theorem, Physical Review Letters 126
Original
2004
Cited alongside, same era.
S. P. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, UK, 2004)
2004
Cited alongside, same era.
V. Katariya and M. M. Wilde, Geometric distinguishability measures limit quantum channel estimation and discrimination, Quantum Information Processing 20
Original
2004
Cited alongside, same era.
S. Zhou, Z.-W. Liu, and L. Jiang, New perspectives on covariant quantum error correction, Quantum 5

Then

E. M. Kessler, P. Kómár, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin, Heisenberg-limited atom clocks based on entangled qubits, Physical Review Letters 112
Original
2014
Later among the works it cites.
I. Apellaniz, B. Lücke, J. Peise, C. Klempt, and G. Tóth, Detecting metrologically useful entanglement in the vicinity of Dicke states, New Journal of Physics 17
Original
2015
Later among the works it cites.
J. Preskill, Lecture Notes on Quantum Computation (Caltech, 2015)
2015
Later among the works it cites.
LIGO Scientific Collaboration and Virgo Collaboration, Observation of gravitational waves from a binary black hole merger, Physical Review Letters 116
Original
2016
Later among the works it cites.
S. Altenburg, S. Wölk, G. Tóth, and O. Gühne, Optimized parameter estimation in the presence of collective phase noise, Physical Review A 94

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

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Reading the bibliography…

2022

Time-energy uncertainty relation for noisy quantum metrology

Faist, Philippe, Woods, Mischa P., Albert, Victor V. et al.

Understand

Detection of weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology.

We consider a quantum system initialized in a pure state and whose evolution is governed by a Hamiltonian $H$; a measurement can later estimate the time $t$ for which the system has evolved.
In this work, we introduce and study a fundamental trade-off which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment.
Specifically, we consider an idealized scenario in which Alice prepares an initial pure state of the clock, allows the clock to evolve for a time $t$ that is not precisely known, and then transmits the clock through a noisy channel to Bob.

Built on

W. Górecki, S. Zhou, L. Jiang, and R. Demkowicz-Dobrzański, Optimal probes and error-correction schemes in multi-parameter quantum metrology, Quantum 4
Original
1901
Earlier work this paper cites.
P. Faist, S. Nezami, V. V. Albert, G. Salton, F. Pastawski, P. Hayden, and J. Preskill, Continuous symmetries and approximate quantum error correction, Physical Review X 10
Original
1902
Earlier work this paper cites.
M. P. Woods and Á. M. Alhambra, Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames, Quantum 4
Original
1902
Earlier work this paper cites.
K. Chabuda, J. Dziarmaga, T. J. Osborne, and R. Demkowicz-Dobrzański, Tensor-network approach for quantum metrology in many-body quantum systems, Nature Communications 11
Original
1906
Earlier work this paper cites.
F. Albarelli, J. F. Friel, and A. Datta, Evaluating the Holevo Cramér-Rao bound for multiparameter quantum metrology, Physical Review Letters 123
Original
1906
Earlier work this paper cites.
L. Seveso, F. Albarelli, M. G. Genoni, and M. G. A. Paris, On the discontinuity of the quantum Fisher information for quantum statistical models with parameter dependent rank, Journal of Physics A: Mathematical and Theoretical 53
Original
1906
Earlier work this paper cites.
H. Zhou, J. Choi, S. Choi, R. Landig, A. M. Douglas, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, P. Cappellaro, H. S. Knowles, H. Park, and M. D. Lukin, Quantum metrology with strongly interacting spin systems, Physical Review X 10
Original
1907
Earlier work this paper cites.
Y. Ouyang, N. Shettell, and D. Markham, Robust quantum metrology with explicit symmetric states, IEEE Transactions on Information Theory 68
Original
1908
Earlier work this paper cites.
B. Koczor, S. Endo, T. Jones, Y. Matsuzaki, and S. C. Benjamin, Variational-state quantum metrology, New Journal of Physics 22
Original
1908
Earlier work this paper cites.
S. Zhou and L. Jiang, An exact correspondence between the quantum Fisher information and the Bures metric, ArXiv e-prints (2019), arXiv:1910.08473
Original
1910
Earlier work this paper cites.
S. Zhou and L. Jiang, Optimal approximate quantum error correction for quantum metrology, Physical Review Research 2
Original
1910
Earlier work this paper cites.
J. S. Sidhu, Y. Ouyang, E. T. Campbell, and P. Kok, Tight bounds on the simultaneous estimation of incompatible parameters, Physical Review X 11
Original
1912
Earlier work this paper cites.
L. Mandelstam and I. Tamm, The uncertainty relation between energy and time in nonrelativistic quantum mechanics, Journal of Physics (USSR) IX
1945
Earlier work this paper cites.
Y. Aharonov and D. Bohm, Time in the quantum theory and the uncertainty relation for time and energy, Physical Review 122
1961
Earlier work this paper cites.
C. Helstrom, Minimum mean-squared error of estimates in quantum statistics, Physics Letters A 25
1967
Earlier work this paper cites.
C. W. Helstrom, Quantum detection and estimation theory, Journal of Statistical Physics 1
1969
Earlier work this paper cites.
R. H. Bartels and G. W. Stewart, Solution of the matrix equation a x + x b = c ax+xb=c [F4], Communications of the ACM 15
1972
Earlier work this paper cites.
M. Reed and B. Simon, I: Functional Analysis , Methods of Modern Mathematical Physics, Vol. 1 (Elsevier Science, 1981)
1981
Earlier work this paper cites.
M. Hübner, Explicit computation of the Bures distance for density matrices, Physics Letters A 163
1992
Earlier work this paper cites.
A. S. Holevo, A note on covariant dynamical semigroups, Reports on Mathematical Physics 32
1993
Earlier work this paper cites.
S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Physical Review Letters 72
1994
Earlier work this paper cites.
C. A. Fuchs and C. M. Caves, Mathematical techniques for quantum communication theory, Open Systems & Information Dynamics 3
1995
Earlier work this paper cites.
S. L. Braunstein, C. M. Caves, and G. Milburn, Generalized uncertainty relations: Theory, examples, and Lorentz invariance, Annals of Physics 247
1996
Earlier work this paper cites.
A. M. Steane, Error correcting codes in quantum theory, Physical Review Letters 77
1996
Earlier work this paper cites.
S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Improvement of frequency standards with quantum entanglement, Physical Review Letters 79
1997
Earlier work this paper cites.
E. Knill and R. Laflamme, Theory of quantum error-correcting codes, Physical Review A 55
1997
Earlier work this paper cites.
A. Y. Kitaev, Quantum error correction with imperfect gates, in Proceedings of the Third International Conference on Quantum Communication and Measurement , edited by O. Hirota, A. S. Holevo, and C. M. Caves (Springer US, Boston, MA, 1997) pp. 181–188
1997
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.
V. Bužek, R. Derka, and S. Massar, Optimal quantum clocks, Physical Review Letters 82
1999
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000)
2000
Earlier work this paper cites.
R. D. Gill and S. Massar, State estimation for large ensembles, Physical Review A 61
2000
Earlier work this paper cites.
C. Bertoni, Y. Yang, and J. M. Renes, Entropic time–energy uncertainty relations: an algebraic approach, New Journal of Physics 22
Original
2001
Earlier work this paper cites.
R. Demkowicz-Dobrzański, W. Górecki, and M. Guţă, Multi-parameter estimation beyond quantum Fisher information, Journal of Physics A 53
Original
2001
Earlier work this paper cites.
I. Kull, P. A. Guérin, and F. Verstraete, Uncertainty and trade-offs in quantum multiparameter estimation, Journal of Physics A 53
Original
2002
Earlier work this paper cites.
S. Zhou and L. Jiang, Asymptotic theory of quantum channel estimation, PRX Quantum 2
Original
2003
Earlier work this paper cites.
A. Kitaev, Fault-tolerant quantum computation by anyons, Annals of Physics 303
2003
Earlier work this paper cites.

Similar

L. Sun, X. He, C. You, C. Lv, B. Li, S. Lloyd, and X. Wang, Exponentially enhanced quantum metrology using resources of linear complexity, ArXiv e-prints (2020), arXiv:2004.01216
Original
2004
Cited alongside, same era.
A. Kubica and R. Demkowicz-Dobrzański, Using quantum metrological bounds in quantum error correction: A simple proof of the approximate Eastin-Knill theorem, Physical Review Letters 126
Original
2004
Cited alongside, same era.
S. P. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, UK, 2004)
2004
Cited alongside, same era.
V. Katariya and M. M. Wilde, Geometric distinguishability measures limit quantum channel estimation and discrimination, Quantum Information Processing 20
Original
2004
Cited alongside, same era.
S. Zhou, Z.-W. Liu, and L. Jiang, New perspectives on covariant quantum error correction, Quantum 5

Then

E. M. Kessler, P. Kómár, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin, Heisenberg-limited atom clocks based on entangled qubits, Physical Review Letters 112
Original
2014
Later among the works it cites.
I. Apellaniz, B. Lücke, J. Peise, C. Klempt, and G. Tóth, Detecting metrologically useful entanglement in the vicinity of Dicke states, New Journal of Physics 17
Original
2015
Later among the works it cites.
J. Preskill, Lecture Notes on Quantum Computation (Caltech, 2015)
2015
Later among the works it cites.
LIGO Scientific Collaboration and Virgo Collaboration, Observation of gravitational waves from a binary black hole merger, Physical Review Letters 116
Original
2016
Later among the works it cites.
S. Altenburg, S. Wölk, G. Tóth, and O. Gühne, Optimized parameter estimation in the presence of collective phase noise, Physical Review A 94

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2005

Cited alongside, same era.

R. A. Horn and F. Zhang, Basic properties of the Schur complement, in The Schur Complement and Its Applications , Numerical Methods and Algorithms, edited by F. Zhang (Springer US, Boston, MA, 2005) pp. 17–46

2005

Cited alongside, same era.

D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, Matrix product state representations, Quantum Information and Computation 7

2006

Cited alongside, same era.

J. J. Meyer, J. Borregaard, and J. Eisert, A variational toolbox for quantum multi-parameter estimation, npj Quantum Information 7

Original

2006

Cited alongside, same era.

Y. Yang, Y. Mo, J. M. Renes, G. Chiribella, and M. P. Woods, Optimal universal quantum error correction via bounded reference frames, Physical Review Research 4

Original

2007

Cited alongside, same era.

G. A. Durkin and J. P. Dowling, Local and global distinguishability in quantum interferometry, Physical Review Letters 99

2007

Cited alongside, same era.

P. Hayden, M. Horodecki, A. Winter, and J. Yard, A decoupling approach to the quantum capacity, Open Systems & Information Dynamics 15

2008

Cited alongside, same era.

A. Fujiwara and H. Imai, A fibre bundle over manifolds of quantum channels and its application to quantum statistics, Journal of Physics A 41

2008

Cited alongside, same era.

Original

2016