quantum states,
quantum channels,
the additivity problem,
the convex hull and the convex roof of a function,
entanglement monotone,
entanglement of formation,
convex stable set,
concave function,
weak convergence of probability measures,
barycenter map.
Quantum information theory. Mathematical physics. Convex analysis.
Main publications:
M. E. Shirokov, “The Holevo capacity of infinite dimensional channels and the additivity problem”, Comm. Math. Phys., 262 (2006), 137–159
M.E. Shirokov, “Continuity of the von Neumann entropy”, Comm. Math. Phys., 296:3 (2010), 625–654
V. Yu. Protasov, M. E. Shirokov, “Generalized compactness in linear spaces and its applications”, Sbornik:Mathematics, 200:5 (2009), 697–722
M. E. Shirokov, “Entropy reduction of quantum measurements”, Journal of Mathematical Physics, 52:5 (2011), 052202
M. E. Shirokov, “On channels with positive quantum zero-error capacity having vanishing n-shot capacity”, Quantum Inf. Process., 14:8 (2015), 3057–3074
S. W. Weis, M. E. Shirokov, Uspekhi Mat. Nauk (to appear)
2020
2.
M. E. Shirokov, “Advanced Alicki–Fannes–Winter method for energy-constrained quantum systems and its use”, Quantum Inf. Process., 19 (2020), 164 , 33 pp., arXiv: 1907.02458;
3.
M. E. Shirokov, “Operator E-norms and their use”, Mat. Sb. (to appear)
2019
4.
M. E. Shirokov, “Uniform continuity bounds for information characteristics of quantum channels depending on input dimension and on input energy”, J. Phys. A, 52:1 (2019), 014001 (cited: 3) (cited: 6)
5.
M. E. Shirokov, “Upper bounds for the Holevo quantity and their use”, Problems Inform. Transmission, 55:3 (2019), 201–217
6.
M. E. Shirokov, “On completion of the cone of completely positive linear maps with respect to the energy-constrained diamond norm”, Lobachevskii J. Math., 40:10 (2019), 1549–1568 , arXiv: 1810.10922
7.
M. E. Shirokov, A. S. Holevo, “Energy-constrained diamond norms and quantum dynamical semigroups”, Lobachevskii J. Math., 40:10 (2019), 1569–1586;
2010
8.
V. Yu. Protasov, M. E. Shirokov, “On Mutually Inverse Transforms of Functions on a Half-Line”, Dokl. Math., 100:3 (2010), 560–563
2018
9.
M. E. Shirokov, “On the Energy-Constrained Diamond Norm and Its Application in Quantum Information Theory”, Problems Inform. Transmission, 54:1 (2018), 20–33 , arXiv: 1706.00361 (cited: 17) (cited: 17)
10.
Noah Davis, Maksim E. Shirokov, Mark M. Wilde, “Energy-constrained two-way assisted private and quantum capacities of quantum channels”, Phys. Rev. A, 97:6 (2018), 62310 , 31 pp., arXiv: 1801.08102 (cited: 4) (cited: 4)
11.
M. E. Shirokov, “Uniform finite-dimensional approximation of basic capacities of energy-constrained channels”, Quantum Inf. Process., 17 (2018), 322 , 29 pp., arXiv: 1707.05641 (cited: 2) (cited: 3)
12.
M. E. Shirokov, “Adaptation of the Alicki–Fannes–Winter method for the set of states with bounded energy and its use”, Rep. Math. Phys., 81:1 (2018), 81–104 (cited: 5) (cited: 5)
13.
G. G. Amosov, Al. V. Bulinski, An. V. Bulinski, V. M. Buchstaber, I. A. Ibragimov, V. P. Maslov, A. Ya. Helemskii, A. M. Chebotarev, M. E. Shirokov, A. N. Shiryaev, “Alexander Semenovich Holevo (on his 75th birthday)”, Russian Math. Surveys, 73:6 (2018), 1131–1136
2017
14.
M. E. Shirokov, A. S. Holevo, “On lower semicontinuity of the entropic disturbance and its applications in quantum information theory”, Izv. Math., 81:5 (2017), 1044–1060 (cited: 2) (cited: 1)
15.
M. E. Shirokov, “Tight uniform continuity bounds for the quantum conditional mutual information, for the Holevo quantity, and for capacities of quantum channels”, J. Math. Phys., 58:10 (2017), 102202 , 29 pp., arXiv: 1512.09047 (cited: 17) (cited: 16)
2019
16.
M. E. Shirokov, A. V. Bulinski, “Lower estimates for distances from a given quantum channel to certain classes of quantum channels”, Journal of Mathematical Sciences, 241:2 (2019), 237–244 (cited: 1)
2016
17.
M. E. Shirokov, “Measures of correlations in infinite-dimensional quantum systems”, Sb. Math., 207:5 (2016), 724–768 , arXiv: 1506.06377 (cited: 11) (cited: 11)
18.
M. E. Shirokov, “Squashed entanglement in infinite dimensions”, J. Math. Phys., 57:3 (2016), 32203 , 22 pp., arXiv: 1507.08964 (cited: 8) (cited: 8)
19.
M. E. Shirokov, “On characterization of positive maps preserving continuity of the von Neumann entropy”, Russian Math. Surveys, 71:5 (2016), 965–966 , arXiv: 1704.01905
20.
M. E. Shirokov, “Estimates for discontinuity jumps of information characteristics of quantum systems and channels”, Problems of Information Transmission, 52:3 (2016), 239–264 , arXiv: 1602.05930
2015
21.
M. E. Shirokov, “On quantum zero-error capacity”, Russian Math. Surveys, 70:1 (2015), 176–178 (cited: 4) (cited: 2)
22.
M. E. Shirokov, T. Shulman, “On superactivation of zero-error capacities and reversibility of a quantum channels”, Comm. Math. Phys., 335:3 (2015), 1159–1179 , arXiv: 1309.2610 (cited: 2) (cited: 11) (cited: 4) (cited: 13)
23.
A. S. Holevo, M. E. Shirokov, “On the Gain of Entanglement Assistance in the Classical Capacity of Quantum Gaussian Channels”, Math. Notes, 97:6 (2015), 974–977 (cited: 1) (cited: 1)
24.
M. E. Shirokov, “On multipartite superactivation of quantum channel capacities”, Problems Inform. Transmission, 51:2 (2015), 87–102 , arXiv: 1411.5386 (cited: 1) (cited: 1)
2016
25.
A. S. Holevo, M. E. Shirokov, “Criterion of weak compactness for families of generalized quantum ensembles and its applications”, Theory Probab. Appl., 60:2 (2016), 320–325
2015
26.
M. E. Shirokov, “On channels with positive quantum zero-error capacity having vanishing $n$-shot capacity”, Quantum Inf. Process., 14:8 (2015), 3057–3074 , arXiv: 1407.8524 (cited: 1) (cited: 5) (cited: 3)
2014
27.
M. E. Shirokov, “Criteria for equality in two entropic inequalities”, Sb. Math., 205:7 (2014), 1045–1068 , arXiv: 1302.5336 (cited: 1) (cited: 1)
28.
M. E. Shirokov, T. V. Shulman, “On superactivation of one-shot zero-error quantum capacity and the related property of quantum measurements”, Problems Inform. Transmission, 50:3 (2014), 232–246 , arXiv: 1312.3586 (cited: 5) (cited: 3) (cited: 5)
2013
29.
M. E. Shirokov, “Schmidt Number and Partially Entanglement-Breaking Channels in Infinite-Dimensional Quantum Systems”, Math. Notes, 93:5 (2013), 766–779 , arXiv: 1110.4363 (cited: 3) (cited: 1) (cited: 1) (cited: 2)
30.
M. E. Shirokov, “Reversibility conditions for quantum channels and their applications”, Sb. Math., 204:8 (2013), 1215–1237 , arXiv: 1203.0262 (cited: 4) (cited: 3) (cited: 3) (cited: 4)
31.
A. S. Holevo, M. E. Shirokov, “On classical capacities of infinite-dimensional quantum channels”, Problems Inform. Transmission, 49:1 (2013), 15–31 , arXiv: 1210.6926 (cited: 12) (cited: 4) (cited: 11)
32.
M. E. Shirokov, “Reversibility of a quantum channel: General conditions and their applications to Bosonic linear channels”, J. Math. Phys., 54:11 (2013), 112201 , 19 pp., arXiv: 1212.2354 (cited: 4) (cited: 4)
33.
M. E. Shirokov, T. V. Shulman, On superactivation of one-shot zero-error quantum capacity and the related property of quantum measurements, 2013 , 16 pp., arXiv: 1312.3586
2012
34.
M. E. Shirokov, “Stability of convex sets and applications”, Izv. Math., 76:4 (2012), 840–856 (cited: 2) (cited: 1) (cited: 1) (cited: 2)
35.
M. E. Shirokov, “Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a quantum channel”, Problems Inform. Transmission, 48:2 (2012), 85–101 , arXiv: 1105.1040 (cited: 13) (cited: 6) (cited: 11)
2011
36.
M. E. Shirokov, “The continuity of the output entropy of positive maps”, Sb. Math., 202:10 (2011), 1537–1564 , arXiv: 1002.0230 (cited: 1) (cited: 1)
37.
M. E. Shirokov, “Entropy reduction of quantum measurements”, J. Math. Phys., 52:5 (2011), 052202 , 18 pp., arXiv: 1011.3127 (cited: 8) (cited: 7) (cited: 8)
38.
M. E. Shirokov, “O svoistvakh veroyatnostnykh mer na mnozhestve kvantovykh sostoyanii”, Trudy MFTI, 3:1 (2011), 162–167 , arXiv: math-ph/0607019
2010
39.
M. E. Shirokov, “On properties of the space of quantum states and their application to the construction of entanglement monotones”, Izv. Math., 74:4 (2010), 849–882 , arXiv: 0804.1515 (cited: 9) (cited: 3) (cited: 3) (cited: 7)
40.
M. E. Shirokov, “A Property of the Output Entropy of a Positive Map of Spaces of Nuclear Operators”, Math. Notes, 87:3 (2010), 449–451 , arXiv: 1002.0230
41.
A. S. Holevo, M. E. Shirokov, “Mutual and coherent information for infinite-dimensional quantum channels”, Problems Inform. Transmission, 46:3 (2010), 201–218 , arXiv: 1004.2495 (cited: 13) (cited: 8) (cited: 14)
42.
M. E. Shirokov, “Continuity of the von Neumann entropy”, Comm. Math. Phys., 296:3 (2010), 625–654 , arXiv: 0904.1963 (cited: 16) (cited: 12) (cited: 17)
2009
43.
V. Yu. Protasov, M. E. Shirokov, “Generalized compactness in linear spaces and its applications”, Sb. Math., 200:5 (2009), 697–722 , arXiv: 1002.3610 (cited: 6) (cited: 7) (cited: 7) (cited: 6)
44.
M. E. Shirokov, “On Channels with Finite Holevo Capacity”, Theory Probab. Appl., 53:4 (2009), 648–662 , arXiv: quant-ph/0602073 (cited: 1)
2008
45.
M. E. Shirokov, “Ob odnom klasse vypuklykh mnozhestv”, Sovremennye problemy fundamentalnoi i prikladnoi matematiki, MFTI, M., 2008, 193–203
46.
M. E. Shirokov, A. S. Holevo, “On Approximation of Infinite-Dimensional Quantum Channels”, Problems Inform. Transmission, 44:2 (2008), 73–90 , arXiv: 0711.2245 (cited: 37) (cited: 8) (cited: 8) (cited: 22)
47.
M. E. Shirokov, “Characterization of convex $\mu$-compact sets”, Russian Math. Surveys, 63:5 (2008), 981–982 , arXiv: 1004.3792 (cited: 2) (cited: 2) (cited: 2) (cited: 2)
2007
48.
M. E. Shirokov, “Entropy characteristics of subsets of states. II”, Izv. Math., 71:1 (2007), 181–218 , arXiv: quant-ph/0510073 (cited: 3) (cited: 1) (cited: 1) (cited: 1)
49.
M. E. Shirokov, “On the Strong CE-Property of Convex Sets”, Math. Notes, 82:3 (2007), 395–409 (cited: 4) (cited: 4) (cited: 4) (cited: 4)
2008
50.
M. E. Shirokov, “On properties of quantum channels related to their classical capacity”, Theory Probab. Appl., 52:2 (2008), 250–276 , arXiv: quant-ph/0411091 (cited: 6) (cited: 2) (cited: 2) (cited: 2)
2006
51.
M. E. Shirokov, “The Holevo capacity of infinite dimensional channels and the additivity problem”, Comm. Math. Phys., 262:1 (2006), 137–159 , arXiv: quant-ph/0408009 (cited: 26) (cited: 20) (cited: 24)
52.
M. E. Shirokov, “Entropy characteristics of subsets of states. I”, Izv. Math., 70:6 (2006), 1265–1292 , arXiv: quant-ph/0510073 (cited: 18) (cited: 11) (cited: 11) (cited: 16)
53.
M. E. Shirokov, “On the Structure of Optimal Sets for a Quantum Channel”, Problems Inform. Transmission, 42:4 (2006), 282–297 , arXiv: quant-ph/0402178 (cited: 1) (cited: 1) (cited: 2)
54.
M. E. Shirokov, “Superadditivity of the convex closure of the output entropy of a quantum channel”, Russian Math. Surveys, 61:6 (2006), 1186–1188 , arXiv: quant-ph/0608090 (cited: 2) (cited: 1) (cited: 1)
2005
55.
R. F. Werner, A. S. Holevo, M. E. Shirokov, “On the notion of entanglement in Hilbert spaces”, Russian Math. Surveys, 60:2 (2005), 359–360 , arXiv: quant-ph/0504204 (cited: 28) (cited: 26)
56.
A. S. Holevo, M. E. Shirokov, “Continuous ensembles and the capacity of infinite-dimensional quantum channels”, Theory Probab. Appl., 50:1 (2005), 86–98 , arXiv: quant-ph/0408176 (cited: 34) (cited: 22) (cited: 22) (cited: 30)
2004
57.
A. S. Holevo, M. E. Shirokov, “On Shor's channel extension and constrained channels”, Comm. Math. Phys., 249:2 (2004), 417–430 , arXiv: quant-ph/0306196 (cited: 27) (cited: 29) (cited: 29)
58.
A. S. Holevo, M. E. Shirokov, “The additivity problem for constrained quantum channels”, Russian Math. Surveys, 59:2 (2004), 385–387 , arXiv: quant-ph/0306196
59.
A. S. Dmitriev, M. E. Shirokov, “Vybor generatora dlya pryamokhaoticheskoi sistemy svyazi”, Radiotekhnika i elektronika, 49:7 (2004), 840–849 (cited: 16)
2001
60.
G. G. Amosov, A. V. Bulinski, M. E. Shirokov, “Regular Semigroups of Endomorphisms of von Neumann Factors”, Math. Notes, 70:5 (2001), 583–598 (cited: 3) (cited: 1) (cited: 3)
1999
61.
M. E. Shirokov, “Mnogopolzovatelskaya sistema svyazi na khaoticheskikh nesuschikh”, Radiotekhnika i elektronika, 44:5 (1999), 583–590
1997
62.
A. S. Dmitriev, M. Shirokov, S. O. Starkov, “Chaotic synchronization in ensembles of coupled maps”, Special issue on chaos synchronization, control, and applications, IEEE Trans. Circuits Systems I Fund. Theory Appl., 44:10 (1997), 918–926 (cited: 26) (cited: 25) (cited: 29)
1996
63.
A. S. Dmitriev, S. O. Starkov, M. E. Shirokov, “Sinkhronizatsiya ansamblei svyazannykh otobrazhenii”, Izv. vuzov. Prikladnaya nelineinaya dinamika, 4:4-5 (1996), 40–58
1995
64.
A. S. Dmitriev, M. E. Shirokov, “Sinkhronizatory khaoticheskikh signalov”, Radiotekhnika i elektronika, 40:11 (1995), 1667–1676
65.
A. S. Dmitriev, M. E. Shirokov, “Dinamika sinkhronizatora dlya khaoticheskikh signalov s nepreryvnym vremenem”, Radiotekhnika i elektronika, 40:11 (1995), 1660–1666
1994
66.
A. S. Dmitriev, S. O. Starkov, M. E. Shirokov, “Struktura periodicheskikh orbit khaoticheskoi avtokolebatelnoi sistemy, opisyvaemoi raznostnymi uravneniyami 2-go poryadka”, Radiotekhnika i elektronika, 39:9 (1994), 1392–1397
2020
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