Fetching the paper…

Reading the bibliography…

2022

Upper Bounds on the Distillable Randomness of Bipartite Quantum States

Lami, Ludovico, Regula, Bartosz, Wang, Xin et al.

Original
PDF
Post on X

Understand

The distillable randomness of a bipartite quantum state is an information-theoretic quantity equal to the largest net rate at which shared randomness can be distilled from the state by means of local operations and classical communication.

This quantity has been widely used as a measure of classical correlations, and one version of it is equal to the regularized Holevo information of the ensemble that results from measuring one share of the state.
However, due to the regularization, the distillable randomness is difficult to compute in general.
To address this problem, we define measures of classical correlations and prove a number of their properties, most importantly that they serve as upper bounds on the distillable randomness of an arbitrary bipartite state.

Upper Bounds on the Distillable Randomness of Bipartite Quantum States · Around

Built on

Z.-W. Liu, K. Bu, and R. Takagi, “One-Shot Operational Quantum Resource Theory,” Physical Review Letters , vol. 123, no. 2, p. 020401, Jul. 2019, arXiv:1904.05840
Original
1904
Earlier work this paper cites.
X. Wang and M. M. Wilde, “Resource theory of asymmetric distinguishability,” Physical Review Research , vol. 1, no. 3, p. 033170, Dec. 2019, arXiv:1905.11629
Original
1905
Earlier work this paper cites.
K. Fang and H. Fawzi, “Geometric Rényi divergence and its applications in quantum channel capacities,” Communications in Mathematical Physics , vol. 384, pp. 1615–1677, Jun. 2021, arXiv:1909.05758
Original
1909
Earlier work this paper cites.
K. Fang and Z.-W. Liu, “No-go theorems for quantum resource purification,” Physical Review Letters , vol. 125, no. 6, p. 060405, Aug. 2020, arXiv:1909.02540
Original
1909
Earlier work this paper cites.
B. Regula, K. Bu, R. Takagi, and Z.-W. Liu, “Benchmarking one-shot distillation in general quantum resource theories,” Physical Review A , vol. 101, no. 6, p. 062315, Jun. 2020, arXiv:1909.11677
Original
1909
Earlier work this paper cites.
H. Umegaki, “Conditional expectations in an operator algebra IV (entropy and information),” Kodai Mathematical Seminar Reports , vol. 14, pp. 59–85, 1962
1962
Earlier work this paper cites.
A. Uhlmann, “The “transition probability” in the state space of a *-algebra,” Reports on Mathematical Physics , vol. 9, pp. 273–279, 1976
1976
Earlier work this paper cites.
R. Ahlswede and I. Csiszár, “Common randomness in information theory and cryptography—part I: Secret sharing,” IEEE Transactions on Information Theory , vol. 39, no. 4, pp. 1121–1132, July 1993
1993
Earlier work this paper cites.
——, “Common randomness in information theory and cryptography—part II: CR capacity,” IEEE Transactions on Information Theory , vol. 44, no. 1, pp. 225–240, Jan. 1998
1998
Earlier work this paper cites.
E. M. Rains, “Bound on distillable entanglement,” Physical Review A , vol. 60, no. 1, pp. 179–184, Jul. 1999, arXiv:quant-ph/9809082
1999
Earlier work this paper cites.
L. Henderson and V. Vedral, “Classical, quantum and total correlations,” Journal of Physics A: Mathematical and General , vol. 34, no. 35, pp. 6899–6905, Sep. 2001, arXiv:quant-ph/0105028
2001
Earlier work this paper cites.
H. Ollivier and W. H. Zurek, “Quantum discord: A measure of the quantumness of correlations,” Physical Review Letters , vol. 88, no. 1, p. 017901, Dec. 2001, arXiv:quant-ph/0105072
2001
Earlier work this paper cites.
——, “A semidefinite program for distillable entanglement,” IEEE Transactions on Information Theory , vol. 47, no. 7, pp. 2921–2933, Nov. 2001, arXiv:quant-ph/0008047
2001
Earlier work this paper cites.
J. Oppenheim, M. Horodecki, P. Horodecki, and R. Horodecki, “Thermodynamical approach to quantifying quantum correlations,” Physical Review Letters , vol. 89, no. 18, p. 180402, Oct. 2002, arXiv:quant-ph/0112074
2002
Earlier work this paper cites.
K. Audenaert, B. De Moor, K. G. H. Vollbrecht, and R. F. Werner, “Asymptotic relative entropy of entanglement for orthogonally invariant states,” Physical Review A , vol. 66, no. 3, p. 032310, Sep. 2002, arXiv:quant-ph/0204143
2002
Earlier work this paper cites.

Similar

G. Vidal and R. F. Werner, “Computable measure of entanglement,” Physical Review A , vol. 65, no. 3, p. 032314, Feb. 2002, arXiv:quant-ph/0102117
2002
Cited alongside, same era.
I. Devetak and A. Winter, “Distilling common randomness from bipartite quantum states,” IEEE Transactions on Information Theory , vol. 50, no. 12, pp. 3183–3196, Dec. 2004, arXiv:quant-ph/0304196
2004
Cited alongside, same era.
M. Koashi and A. Winter, “Monogamy of quantum entanglement and other correlations,” Physical Review A , vol. 69, no. 2, p. 022309, Feb. 2004, arXiv:quant-ph/0310037
2004
Cited alongside, same era.
I. Devetak, “Distillation of local purity from quantum states,” Physical Review A , vol. 71, no. 6, p. 062303, June 2005, arXiv:quant-ph/0406234
2005
Cited alongside, same era.
J. A. Smolin, F. Verstraete, and A. Winter, “Entanglement of assistance and multipartite state distillation,” Physical Review A , vol. 72, no. 5, p. 052317, Nov. 2005, arXiv:quant-ph/0505038

Then

F. Leditzky, M. M. Wilde, and N. Datta, “Strong converse theorems using Rényi entropies,” Journal of Mathematical Physics , vol. 57, no. 8, p. 082202, August 2016, arXiv:1506.02635
Original
2016
Later among the works it cites.
M. M. Wilde, Quantum Information Theory , 2nd ed. Cambridge University Press, 2017, arXiv:1106.1445
Original
2017
Later among the works it cites.
G. Manzano, F. Plastina, and R. Zambrini, “Optimal work extraction and thermodynamics of quantum measurements and correlations,” Physical Review Letters , vol. 121, no. 12, p. 120602, Sep. 2018, arXiv:1805.08184
Original
2018
Later among the works it cites.
X. Wang, W. Xie, and R. Duan, “Semidefinite programming strong converse bounds for classical capacity,” IEEE Transactions on Information Theory , vol. 64, no. 1, pp. 640–653, Jan. 2018, arXiv:1610.06381
Original
2018
Later among the works it cites.

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

2005

Cited alongside, same era.

H. Krovi and I. Devetak, “Local purity distillation with bounded classical communication,” Physical Review A , vol. 76, no. 1, p. 012321, July 2007, arXiv:0705.4089

2007

Cited alongside, same era.

R. König, R. Renner, A. Bariska, and U. Maurer, “Small accessible quantum information does not imply security,” Physical Review Letters , vol. 98, no. 14, p. 140502, Apr. 2007, arXiv:quant-ph/0512021

2007

Cited alongside, same era.

I. Devetak, A. W. Harrow, and A. Winter, “A resource framework for quantum Shannon theory,” IEEE Transactions on Information Theory , vol. 54, no. 10, pp. 4587–4618, October 2008, arXiv:quant-ph/0512015

2008

Cited alongside, same era.

F. Salek and A. Winter, “Multi-user distillation of common randomness and entanglement from quantum states,” Aug. 2020, arXiv:2008.04964

2008

Cited alongside, same era.

D. Ding, S. Khatri, Y. Quek, P. W. Shor, X. Wang, and M. M. Wilde, “Bounding the forward classical capacity of bipartite quantum channels,” IEEE Transactions on Information Theory (to appear) , 2023, arXiv:2010.01058

2010

Cited alongside, same era.

S. Khatri and M. M. Wilde, Principles of Quantum Communication Theory: A Modern Approach , Nov. 2020, arXiv:2011.04672v1

2011

Cited alongside, same era.

K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures,” Reviews of Modern Physics , vol. 84, pp. 1655–1707, Nov. 2012, arXiv:1112.6238

2012

Cited alongside, same era.

H. Fawzi and O. Fawzi, “Efficient optimization of the quantum relative entropy,” Journal of Physics A: Mathematical and Theoretical , vol. 51, no. 15, p. 154003, Mar. 2018, arXiv:1705.06671

2018

Later among the works it cites.

B. Morris, L. Lami, and G. Adesso, “Assisted work distillation,” Physical Review Letters , vol. 122, no. 13, p. 130601, Apr. 2019, arXiv:1811.12329

2019

Later among the works it cites.

X. Wang, K. Fang, and M. Tomamichel, “On converse bounds for classical communication over quantum channels,” IEEE Transactions on Information Theory , vol. 65, no. 7, pp. 4609–4619, Jul. 2019, arXiv:1709.05258

2019

Later among the works it cites.

P. Vrana and M. Christandl, “Distillation of Greenberger–Horne–Zeilinger states by combinatorial methods,” IEEE Transactions on Information Theory , vol. 65, no. 9, pp. 5945–5958, Sep. 2019, arXiv:1805.09096

2019

Later among the works it cites.

S. Huber, R. König, and M. Tomamichel, “Jointly constrained semidefinite bilinear programming with an application to Dobrushin curves,” IEEE Transactions on Information Theory , vol. 66, no. 5, pp. 2934–2950, May 2020, arXiv:1808.03182

2020

Later among the works it cites.

M. M. Wilde et al. , “Bounding the randomness distribution capacity of quantum states and channels,” unpublished notes, Sep. 2020, available upon request

2020

Later among the works it cites.

K. Horodecki, M. Studziński, R. P. Kostecki, O. Sakarya, and D. Yang, “Upper bounds on the leakage of private data and an operational approach to Markovianity,” Physical Review A , vol. 104, no. 5, p. 052422, Nov. 2021, arXiv:2107.10737

2021

Later among the works it cites.

L. Lami and B. Regula, “No second law of entanglement manipulation after all,” Nov. 2021, arXiv:2111.02438

Original

2021

Later among the works it cites.

S. Chakraborty, A. Nema, and F. Buscemi, “One-shot purity distillation with local noisy operations and one-way classical communication,” Aug. 2022, arXiv:2208.05628

2022

Closest in time.

J. Eisert and M. M. Wilde, “A smallest computable entanglement monotone,” in Proceedings of the 2022 International Symposium on Information Theory , Espoo, Finland, June 2022, pp. 2439–2444, arXiv:2201.00835

2022

Closest in time.