[39] Bartosz Regula, Kaifeng Bu, Ryuji Takagi, and
Zi-Wen Liu. Benchmarking one-shot distillation
in general quantum resource theories. Phys. Rev.
A, 101:062315, Jun 2020. DOI: 10.1103/Phys-
RevA.101.062315. URL https://link.aps.
org/doi/10.1103/PhysRevA.101.062315.
[40] Madhav Krishnan Vijayan, Eric Chitambar,
and Min-Hsiu Hsieh. One-shot distillation
in a general resource theory. arXiv preprint
arXiv:1906.04959 [quant-ph], 2019. URL https:
//arxiv.org/abs/1906.04959.
[41] J. Eisert and M. M. Wolf. Gaussian
Quantum Channels, pages 23–42. DOI:
10.1142/9781860948169_0002. URL
https://www.worldscientific.com/doi/
abs/10.1142/9781860948169_0002.
[42] A. S. Holevo. One-mode quantum Gaus-
sian channels: Structure and quantum capac-
ity. Probl. Inf. Transm., 43, Mar 2007. DOI:
10.1134/S0032946007010012. URL https://
doi.org/10.1134/S0032946007010012.
[43] Anindita Bera, Tamoghna Das, Debasis Sad-
hukhan, Sudipto Singha Roy, Aditi Sen(De), and
Ujjwal Sen. Quantum discord and its allies:
a review of recent progress. Rep. Prog. Phys.,
81(2):024001, dec 2017. DOI: 10.1088/1361-
6633/aa872f. URL https://doi.org/10.1088%
2F1361-6633%2Faa872f.
[44] Stanley Gudder. Quantum markov chains.
J. Math. Phys., 49(7):072105, 2008. DOI:
10.1063/1.2953952. URL https://doi.org/10.
1063/1.2953952.
[45] Daniel Jonathan and Martin B. Plenio.
Entanglement-assisted local manipulation of
pure quantum states. Phys. Rev. Lett., 83:
3566–3569, Oct 1999. DOI: 10.1103/Phys-
RevLett.83.3566. URL https://link.aps.
org/doi/10.1103/PhysRevLett.83.3566.
[46] Charles H. Bennett, David P. DiVincenzo,
John A. Smolin, and William K. Woot-
ters. Mixed-state entanglement and quan-
tum error correction. Phys. Rev. A, 54:
3824–3851, Nov 1996. DOI: 10.1103/Phys-
RevA.54.3824. URL https://link.aps.org/
doi/10.1103/PhysRevA.54.3824.
[47] Patrick M Hayden, Michal Horodecki, and
Barbara M Terhal. The asymptotic en-
tanglement cost of preparing a quantum
state. J. Phys. A: Math. Gen., 34(35):
6891–6898, aug 2001. DOI: 10.1088/0305-
4470/34/35/314. URL https://doi.org/10.
1088%2F0305-4470%2F34%2F35%2F314.
[48] Andreas Winter and Dong Yang. Operational
resource theory of coherence. Phys. Rev. Lett.,
116:120404, Mar 2016. DOI: 10.1103/Phys-
RevLett.116.120404. URL https://link.aps.
org/doi/10.1103/PhysRevLett.116.120404.
[49] Matthew J. Donald, Michał Horodecki, and
Oliver Rudolph. The uniqueness theorem for
entanglement measures. J. Math. Phys., 43(9):
4252–4272, 2002. DOI: 10.1063/1.1495917. URL
https://doi.org/10.1063/1.1495917.
[50] Michael Reed and Barry Simon. Methods of
modern mathematical physics. vol. 1. Functional
analysis. Academic New York, 1980.
[51] Masamichi Takesaki. Theory of Opera-
tor Algebras I. Springer, 2012. ISBN
0387903917;9780387903910;. DOI: 10.1007/978-
1-4612-6188-9. URL https://doi.org/10.
1007/978-1-4612-6188-9.
[52] A Yu Kitaev. Quantum computations:
algorithms and error correction. Russ.
Math. Surv., 52(6):1191–1249, dec 1997.
DOI: 10.1070/rm1997v052n06abeh002155.
URL https://doi.org/10.1070%
2Frm1997v052n06abeh002155.
[53] Fernando G. S. L. Brandão and Martin Ple-
nio. Entanglement theory and the second law of
thermodynamics. Nat. Phys., 4:873–877, 2008.
DOI: 10.1038/nphys1100. URL https://doi.
org/10.1038/nphys1100.
[54] Patricia Contreras-Tejada, Carlos Palazuelos,
and Julio I. de Vicente. Resource theory
of entanglement with a unique multipartite
maximally entangled state. Phys. Rev. Lett.,
122:120503, Mar 2019. DOI: 10.1103/Phys-
RevLett.122.120503. URL https://link.aps.
org/doi/10.1103/PhysRevLett.122.120503.
[55] Eric Chitambar, Debbie Leung, Laura Mančin-
ska, Maris Ozols, and Andreas Winter. Every-
thing you always wanted to know about locc (but
were afraid to ask). Commun. Math. Phys., 328
(1):303–326, May 2014. ISSN 1432-0916. DOI:
10.1007/s00220-014-1953-9. URL https://doi.
org/10.1007/s00220-014-1953-9.
[56] Michael A. Nielsen and Isaac L. Chuang.
Quantum Computation and Quantum In-
formation: 10th Anniversary Edition.
Cambridge University Press, 2010. DOI:
10.1017/CBO9780511976667. URL https:
//doi.org/10.1017/CBO9780511976667.
[57] Berry Groisman, Sandu Popescu, and Andreas
Winter. Quantum, classical, and total amount
of correlations in a quantum state. Phys. Rev.
A, 72:032317, Sep 2005. DOI: 10.1103/Phys-
RevA.72.032317. URL https://link.aps.org/
doi/10.1103/PhysRevA.72.032317.
[58] Anurag Anshu, Min-Hsiu Hsieh, and Rahul
Jain. Quantifying resources in general re-
source theory with catalysts. Phys. Rev. Lett .,
121:190504, Nov 2018. DOI: 10.1103/Phys-
RevLett.121.190504. URL https://link.aps.
org/doi/10.1103/PhysRevLett.121.190504.
[59] S. Pirandola, U. L. Andersen, L. Banchi,
M. Berta, D. Bunandar, R. Colbeck, D. Englund,
T. Gehring, C. Lupo, C. Ottaviani, J. Pereira,
Accepted in Quantum 2020-10-21, click title to verify. Published under CC-BY 4.0. 29