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@article{TM_2021_313_a1, author = {G. G. Amosov and A. S. Mokeev}, title = {On {Noncommutative} {Operator} {Graphs} {Generated} by {Resolutions} of {Identity}}, journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova}, pages = {14--22}, publisher = {mathdoc}, volume = {313}, year = {2021}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/TM_2021_313_a1/} }
TY - JOUR AU - G. G. Amosov AU - A. S. Mokeev TI - On Noncommutative Operator Graphs Generated by Resolutions of Identity JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 2021 SP - 14 EP - 22 VL - 313 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TM_2021_313_a1/ LA - ru ID - TM_2021_313_a1 ER -
G. G. Amosov; A. S. Mokeev. On Noncommutative Operator Graphs Generated by Resolutions of Identity. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematics of Quantum Technologies, Tome 313 (2021), pp. 14-22. http://geodesic.mathdoc.fr/item/TM_2021_313_a1/
[1] Amosov G.G., “On general properties of non-commutative operator graphs”, Lobachevskii J. Math., 39:3 (2018), 304–308 | DOI | MR | Zbl
[2] G. G. Amosov and A. S. Mokeev, “On construction of anticliques for noncommutative operator graphs”, J. Math. Sci., 234:3 (2018), 269–275 | DOI | MR | MR | Zbl
[3] Amosov G.G., Mokeev A.S., “On non-commutative operator graphs generated by covariant resolutions of identity”, Quantum Inf. Process., 17:12 (2018), 325 | DOI | MR | Zbl
[4] Amosov G.G., Mokeev A.S., “On linear structure of non-commutative operator graphs”, Lobachevskii J. Math., 40:10 (2019), 1440–1443 | DOI | MR | Zbl
[5] Amosov G.G., Mokeev A.S., “Non-commutative graphs in the Fock space over one-particle Hilbert space”, Lobachevskii J. Math., 41:4 (2020), 592–596 | DOI | MR | Zbl
[6] Amosov G.G., Mokeev A.S., “On non-commutative operator graphs generated by reducible unitary representation of the Heisenberg–Weyl group”, Int. J. Theor. Phys., 60:2 (2021), 457–463 | DOI | MR
[7] Amosov G.G., Mokeev A.S., Pechen A.N., “Non-commutative graphs and quantum error correction for a two-mode quantum oscillator”, Quantum Inf. Process., 19:3 (2020), 95 | DOI | MR
[8] G. G. Amosov and I. Yu. Zhdanovskii, “Structure of the algebra generated by a noncommutative operator graph which demonstrates the superactivation phenomenon for zero-error capacity”, Math. Notes, 99:5–6 (2016), 924–927 | DOI | MR | Zbl
[9] Choi M.-D., Effros E.G., “Injectivity and operator spaces”, J. Funct. Anal., 24:2 (1977), 156–209 | DOI | MR | Zbl
[10] Duan R., Super-activation of zero-error capacity of noisy quantum channels, E-print, 2009, arXiv: 0906.2527 [quant-ph]
[11] Duan R., Severini S., Winter A., “Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovász number”, IEEE Trans. Inf. Theory, 59:2 (2013), 1164–1174 | DOI | MR | Zbl
[12] Glauber R.J., “Coherent and incoherent states of the radiation field”, Phys. Rev., 131:6 (1963), 2766–2788 | DOI | MR | Zbl
[13] Gottesman D., “Theory of fault-tolerant quantum computation”, Phys. Rev. A, 57:1 (1998), 127–137 | DOI
[14] Knill E., Laflamme R., “Theory of quantum error-correcting codes”, Phys. Rev. A, 55:2 (1997), 900–911 | DOI | MR
[15] Knill E., Laflamme R., Viola L., “Theory of quantum error correction for general noise”, Phys. Rev. Lett., 84:11 (2000), 2525–2528 | DOI | MR | Zbl
[16] Laflamme R., Miquel C., Paz J.P., Zurek W.H., “Perfect quantum error correcting code”, Phys. Rev. Lett., 77:1 (1996), 198–201 | DOI
[17] Shirokov M.E., Shulman T., “On superactivation of zero-error capacities and reversibility of a quantum channel”, Commun. Math. Phys., 335:3 (2015), 1159–1179 | DOI | MR | Zbl
[18] Shor P.W., “Scheme for reducing decoherence in quantum computer memory”, Phys. Rev. A, 52:4 (1995), R2493–R2496 | DOI
[19] Steane A., “Multiple-particle interference and quantum error correction”, Proc. R. Soc. London A, 452:1954 (1996), 2551–2577 | DOI | MR | Zbl
[20] Sudarshan E.C.G., “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams”, Phys. Rev. Lett., 10:7 (1963), 277–279 | DOI | MR | Zbl
[21] Weaver N., “A “quantum” Ramsey theorem for operator systems”, Proc. Amer. Math. Soc., 145:11 (2017), 4595–4605 | DOI | MR | Zbl
[22] Weaver N., “The “quantum” Turán problem for operator systems”, Pac. J. Math., 301:1 (2019), 335–349 | DOI | MR | Zbl
[23] Yashin V.I., “Properties of operator systems, corresponding to channels”, Quantum Inf. Process., 19:7 (2020), 195 | DOI | MR