Fetching the paper…
Reading the bibliography…
Computing the exact rate at which entanglement can be distilled from noisy quantum states is one of the longest-standing questions in quantum information.
M. Fekete, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. 17
1923
Earlier work this paper cites.
E. H. Lieb and M. B. Ruskai, Proof of the strong subadditivity of quantum mechanical entropy, J. Math. Phys. 14
1938
Earlier work this paper cites.
S. Kullback and R. A. Leibler, On information and sufficiency, Ann. Math. Statist. 22
1951
Earlier work this paper cites.
M. Sion, On general minimax theorems. Pacific J. Math. 8
1958
Earlier work this paper cites.
H. Umegaki, Conditional expectation in an operator algebra. IV. Entropy and information, Kodai Math. Sem. Rep. 14
1962
Earlier work this paper cites.
G. Lindblad, Completely positive maps and entropy inequalities, Commun. Math. Phys. 40
1975
Earlier work this paper cites.
M. J. Donald, On the relative entropy, Commun. Math. Phys. 105
1986
Earlier work this paper cites.
D. Petz, Sufficient subalgebras and the relative entropy of states of a von Neumann algebra, Commun. Math. Phys. 105
1986
Earlier work this paper cites.
R. F. Werner, Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Phys. Rev. A 40
1989
Earlier work this paper cites.
A. K. Ekert, Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett. 67
1991
Earlier work this paper cites.
F. Hiai and D. Petz, The proper formula for relative entropy and its asymptotics in quantum probability, Comm. Math. Phys. 143
1991
Earlier work this paper cites.
C. H. Bennett and S. J. Wiesner, Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70
1993
Earlier work this paper cites.
A. Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77
1996
Earlier work this paper cites.
S. Popescu and D. Rohrlich, Thermodynamics and the measure of entanglement, Phys. Rev. A 56
1997
Earlier work this paper cites.
V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Quantifying entanglement, Phys. Rev. Lett. 78
1997
Earlier work this paper cites.
S. Lloyd, Capacity of the noisy quantum channel, Phys. Rev. A 55
1997
Earlier work this paper cites.
B. Schumacher and M. D. Westmoreland, Sending classical information via noisy quantum channels, Phys. Rev. A 56
1997
Earlier work this paper cites.
P. Horodecki, Separability criterion and inseparable mixed states with positive partial transposition, Phys. Lett. A 232
1997
Earlier work this paper cites.
E. M. Rains, Entanglement purification via separable superoperators, preprint arXiv:quant-ph/9707002 (1997)
1997
Earlier work this paper cites.
V. Vedral and M. B. Plenio, Entanglement measures and purification procedures, Phys. Rev. A 57
1998
Earlier work this paper cites.
A. S. Holevo, The capacity of the quantum channel with general signal states, IEEE Trans. Inf. Theory 44
1998
Earlier work this paper cites.
G. Vidal and R. Tarrach, Robustness of entanglement, Phys. Rev. A 59
1999
Earlier work this paper cites.
M. Horodecki and P. Horodecki, Reduction criterion of separability and limits for a class of distillation protocols, Phys. Rev. A 59
1999
Earlier work this paper cites.
P. M. Hayden, M. Horodecki, and B. M. Terhal, The asymptotic entanglement cost of preparing a quantum state, J. Phys. A 34
2001
Earlier work this paper cites.
E. M. Rains, A semidefinite program for distillable entanglement, IEEE Trans. Inf. Theory 47
2001
Earlier work this paper cites.
K. G. H. Vollbrecht and R. F. Werner, Entanglement measures under symmetry, Phys. Rev. A 64
2001
Earlier work this paper cites.
G. Vidal and J. I. Cirac, Irreversibility in asymptotic manipulations of entanglement, Phys. Rev. Lett. 86
2001
Earlier work this paper cites.
K. Audenaert, J. Eisert, E. Jané, M. B. Plenio, S. Virmani, and B. De Moor, Asymptotic relative entropy of entanglement, Phys. Rev. Lett. 87
2001
Cited alongside, same era.
G. Vidal and R. F. Werner, Computable measure of entanglement, Phys. Rev. A 65
2002
Cited alongside, same era.
V. Vedral and E. Kashefi, Uniqueness of the entanglement measure for bipartite pure states and thermodynamics, Phys. Rev. Lett. 89
2002
Cited alongside, same era.
M. Horodecki, J. Oppenheim, and R. Horodecki, Are the laws of entanglement theory thermodynamical? Phys. Rev. Lett. 89
2002
Cited alongside, same era.
P. Shor, The quantum channel capacity and coherent information, Lecture notes, MSRI Workshop on Quantum Computation (2002)
2002
Cited alongside, same era.
E. Chitambar and M.-H. Hsieh, Asymptotic state discrimination and a strict hierarchy in distinguishability norms, J. Math. Phys. 55
2014
Later among the works it cites.
M. Tomamichel, Quantum Information Processing with Finite Resources: Mathematical Foundations , Vol. 5 (Springer, 2015)
2015
Later among the works it cites.
C. Lancien, S. Di Martino, M. Huber, M. Piani, G. Adesso, and A. Winter, Should entanglement measures be monogamous or faithful? Phys. Rev. Lett. 117
2016
Later among the works it cites.
M. Hayashi, Quantum Information Theory: Mathematical Foundation , 2nd ed., Graduate Texts in Physics (Springer Berlin Heidelberg, 2017)
2017
Later among the works it cites.
M. Berta, O. Fawzi, and M. Tomamichel, On variational expressions for quantum relative entropies, Lett. Math. Phys. 107
2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
K. Audenaert, M. B. Plenio, and J. Eisert, Entanglement cost under positive-partial-transpose-preserving operations, Phys. Rev. Lett. 90
2003
Cited alongside, same era.
M. Steiner, Generalized robustness of entanglement, Phys. Rev. A 67
2003
Cited alongside, same era.
P. W. Shor, Equivalence of additivity questions in quantum information theory, Commun. Math. Phys. 246
2004
Cited alongside, same era.
R. Renner, Security of quantum key distribution , Ph.D. thesis , ETH Zurich (2005)
2005
Cited alongside, same era.
I. Devetak and A. Winter, Distillation of secret key and entanglement from quantum states, Proc. Royal Soc. A 461
2005
Cited alongside, same era.
I. Devetak, The private classical capacity and quantum capacity of a quantum channel, IEEE Trans. Inf. Theory 51
2005
Cited alongside, same era.
M. Christandl, The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography , Ph.D. thesis , University of Cambridge (2006)
2006
Cited alongside, same era.
A. Müller-Hermes and D. Reeb, Monotonicity of the quantum relative entropy under positive maps, Ann. Henri Poincaré 18
2017
Later among the works it cites.
E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys. 91
2019
Later among the works it cites.
A. Anshu, M. Berta, R. Jain, and M. Tomamichel, A minimax approach to one-shot entropy inequalities, J. Math. Phys. 60
2019
Later among the works it cites.
E. Chitambar, J. I. de Vicente, M. W. Girard, and G. Gour, Entanglement manipulation beyond local operations and classical communication, J. Math. Phys. 61
2020
Later among the works it cites.
F. G. S. L. Brandão, A. W. Harrow, J. R. Lee, and Y. Peres, Adversarial hypothesis testing and a quantum Stein’s lemma for restricted measurements, IEEE Trans. Inf. Theory 66
2020
Later among the works it cites.
X. Wang and M. M. Wilde, Cost of quantum entanglement simplified, Phys. Rev. Lett. 125
2020
Later among the works it cites.
L. Lami, B. Regula, R. Takagi, and G. Ferrari, Framework for resource quantification in infinite-dimensional general probabilistic theories, Phys. Rev. A 103
2021
Later among the works it cites.
B. Regula, L. Lami, R. Takagi, and G. Ferrari, Operational quantification of continuous-variable quantum resources, Phys. Rev. Lett. 126
2021
Later among the works it cites.
P. Horodecki, Ł. Rudnicki, and K. Życzkowski, Five Open Problems in Quantum Information Theory, PRX Quantum 3
2022
Later among the works it cites.
Open quantum problems, https://oqp.iqoqi.oeaw.ac.at/open-quantum-problems , accessed: 2023-06-12
2023
Closest in time.
L. Lami and B. Regula, No second law of entanglement manipulation after all, Nat. Phys. 19
2023
Closest in time.
M. Berta, F. G. S. L. Brandão, G. Gour, L. Lami, M. B. Plenio, B. Regula, and M. Tomamichel, On a gap in the proof of the generalised quantum Stein’s lemma and its consequences for the reversibility of quantum resources, Quantum 7
2023
Closest in time.
X. Wang and M. M. Wilde, Exact entanglement cost of quantum states and channels under positive-partial-transpose-preserving operations, Phys. Rev. A 107
2023
Closest in time.
H.-C. Cheng, A. Winter, and N. Yu, Discrimination of Quantum States Under Locality Constraints in the Many-Copy Setting, Commun. Math. Phys. 404
2023
Closest in time.
G. Ferrari, L. Lami, T. Theurer, and M. B. Plenio, Asymptotic state transformations of continuous variable resources, Commun. Math. Phys. 398
2023
Closest in time.
L. Lami and M. E. Shirokov, Attainability and lower semi-continuity of the relative entropy of entanglement and variations on the theme, Ann. Henri Poincaré (2023)
2023
Closest in time.
M. Berta and M. Tomamichel, Entanglement monogamy via multivariate trace inequalities, Commun. Math. Phys. 405
2024
Closest in time.
L. Lami, B. Regula, and A. Streltsov, No-go theorem for entanglement distillation using catalysis, Phys. Rev. A 109
2024
Closest in time.
M. Berta, F. G. S. L. Brandão, G. Gour, L. Lami, M. B. Plenio, B. Regula, and M. Tomamichel, The tangled state of quantum hypothesis testing, Nat. Phys. 20
2024
Closest in time.
B. Regula and L. Lami, Reversibility of quantum resources through probabilistic protocols, Nat. Commun. 15
2024
Closest in time.
2024
Closest in time.
L. Lami, A solution of the generalised quantum stein’s lemma, preprint arXiv:2408.06410 (2024)
2024
Closest in time.
C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Concentrating partial entanglement by local operations, Phys. Rev. A 53
2046
Closest in time.