Skip to main content
Top
Published in: Quantum Information Processing 6/2016

01-06-2016

Dynamical behavior of quantum correlations between two qubits coupled to an external environment

Authors: Jin-Long Wei, Xing-Li Li, Xi-Zheng Zhang, Jin-Liang Guo

Published in: Quantum Information Processing | Issue 6/2016

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We investigate the dynamics of quantum correlations of a two-qubit system coupled to an external environment. We have considered both cases: a spin environment and a bosonic environment. In all cases, we have chosen the Bell-diagonal state as the initial state and computed the evolution of quantum correlations in terms of entanglement, quantum discord and trace distance geometric quantum discord. Special attention is paid to the singular quantum phenomena, such as entanglement sudden death, sudden transition and double sudden transitions from classical to quantum decoherence, which all depend on the initial state and the parameters related to the system and the environment. We find the trace distance geometric quantum discord has a good robustness in resisting the spin and bosonic environmental noise.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature 404, 247 (2000)ADSCrossRef Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature 404, 247 (2000)ADSCrossRef
2.
go back to reference Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., O’Brien, J.L.: Quantum computers. Nature 464, 45 (2010)ADSCrossRef Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., O’Brien, J.L.: Quantum computers. Nature 464, 45 (2010)ADSCrossRef
3.
go back to reference Aolita, L., deMelo, F., Davidovich, L.: Open-system dynamics of entanglement:a key issues review. Rep. Prog. Phys. 78, 042001 (2015)ADSCrossRef Aolita, L., deMelo, F., Davidovich, L.: Open-system dynamics of entanglement:a key issues review. Rep. Prog. Phys. 78, 042001 (2015)ADSCrossRef
4.
go back to reference Orieux, A., D’Arrigo, A., Ferranti, A., Franco, G., Benenti, G., Paladino, E., Falci, G., Sciarrino, F., Mataloni, P.: Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics. Sci. Rep. 5, 8575 (2015)ADSCrossRef Orieux, A., D’Arrigo, A., Ferranti, A., Franco, G., Benenti, G., Paladino, E., Falci, G., Sciarrino, F., Mataloni, P.: Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics. Sci. Rep. 5, 8575 (2015)ADSCrossRef
5.
go back to reference Man, Z.X., Xia, Y.J., Franco, RLo: Cavity-based architecture to preserve quantum coherence and entanglement. Sci. Rep. 5, 13843 (2015)ADSCrossRef Man, Z.X., Xia, Y.J., Franco, RLo: Cavity-based architecture to preserve quantum coherence and entanglement. Sci. Rep. 5, 13843 (2015)ADSCrossRef
6.
go back to reference Franco, R.L.: Switching quantum memory on and off. New J. Phys 17, 081004 (2015)CrossRef Franco, R.L.: Switching quantum memory on and off. New J. Phys 17, 081004 (2015)CrossRef
7.
go back to reference Salles, A., de Melo, F., Almeida, M.P., Hor-Meyll, M., Walborn, S.P., Souto Ribeiro, P.H., Davidovich, L.: Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment. Phys. Rev. A 78, 022322 (2008)ADSCrossRef Salles, A., de Melo, F., Almeida, M.P., Hor-Meyll, M., Walborn, S.P., Souto Ribeiro, P.H., Davidovich, L.: Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment. Phys. Rev. A 78, 022322 (2008)ADSCrossRef
8.
go back to reference Franco, R.L., D’Arrigo, A., Falci, G., Compagno, G., Paladino, E.: Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling. Phys. Rev. B 90, 054304 (2014)ADSCrossRef Franco, R.L., D’Arrigo, A., Falci, G., Compagno, G., Paladino, E.: Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling. Phys. Rev. B 90, 054304 (2014)ADSCrossRef
9.
go back to reference D’Arrigo, A., Franco, R.L., Benenti, G., Paladino, E., Falci, G.: Recovering entanglement by loccal operations. Ann. Phys. 350, 211 (2014)ADSCrossRef D’Arrigo, A., Franco, R.L., Benenti, G., Paladino, E., Falci, G.: Recovering entanglement by loccal operations. Ann. Phys. 350, 211 (2014)ADSCrossRef
10.
go back to reference D’Arrigo, A., Benenti, G., Franco, RLo, Falci, G., Paladino, E.: Hidden entanglement, system-environment information flow and non-Markovianity. Int. J. Quantum Inf. 12, 1461005 (2014)MathSciNetCrossRefMATH D’Arrigo, A., Benenti, G., Franco, RLo, Falci, G., Paladino, E.: Hidden entanglement, system-environment information flow and non-Markovianity. Int. J. Quantum Inf. 12, 1461005 (2014)MathSciNetCrossRefMATH
11.
go back to reference Yu, T., Eberly, J.H.: Finite-Time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)ADSCrossRef Yu, T., Eberly, J.H.: Finite-Time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)ADSCrossRef
12.
go back to reference Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefMATH Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefMATH
13.
go back to reference Ali, M., Rau, A.R.P., Alber, G.: Erratum: quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)ADSCrossRef Ali, M., Rau, A.R.P., Alber, G.: Erratum: quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)ADSCrossRef
14.
go back to reference Dakic, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSCrossRefMATH Dakic, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSCrossRefMATH
16.
go back to reference Zhou, T., Cui, J.X., Long, G.L.: Measure of nonclassical correlation in coherence-vector representation. Phys. Rev. A 84, 062105 (2011)ADSCrossRef Zhou, T., Cui, J.X., Long, G.L.: Measure of nonclassical correlation in coherence-vector representation. Phys. Rev. A 84, 062105 (2011)ADSCrossRef
17.
go back to reference Hassan, A.S.M., Lari, B., Joag, P.S.: Tight lower bound to the geometric measure of quantum discord. Phys. Rev. A 85, 024302 (2012)ADSCrossRef Hassan, A.S.M., Lari, B., Joag, P.S.: Tight lower bound to the geometric measure of quantum discord. Phys. Rev. A 85, 024302 (2012)ADSCrossRef
18.
go back to reference Xu, J.S., Sun, K., Li, C.F., Xu, X.Y., Guo, G.C.: Experimental recovery of quantum correlations in absence of system-enviroment back-action. Nat. Commun. 4, 2851 (2013)ADS Xu, J.S., Sun, K., Li, C.F., Xu, X.Y., Guo, G.C.: Experimental recovery of quantum correlations in absence of system-enviroment back-action. Nat. Commun. 4, 2851 (2013)ADS
19.
go back to reference Leggio, B., Franco, R.L., Soares-Pinto, D.O., Horodecki, P., Compagno, G.: Distributed correlations and information flows within a hybrid multipartite quantum-classical system. Phys. Rev. A 92, 032311 (2015)ADSCrossRef Leggio, B., Franco, R.L., Soares-Pinto, D.O., Horodecki, P., Compagno, G.: Distributed correlations and information flows within a hybrid multipartite quantum-classical system. Phys. Rev. A 92, 032311 (2015)ADSCrossRef
20.
go back to reference Bellomo, B., Compagno, G., Franco, R.L., Ridolfo, A., Savasta, S.: dynamics and extraction ofquantum discord in a multipartite open system. Int. J. Quantum Inf. 9, 1665 (2011)CrossRefMATH Bellomo, B., Compagno, G., Franco, R.L., Ridolfo, A., Savasta, S.: dynamics and extraction ofquantum discord in a multipartite open system. Int. J. Quantum Inf. 9, 1665 (2011)CrossRefMATH
21.
go back to reference Bellomo, B., Franco, R.L., Compagno, G.: Dynamics of geometric and entropic quantifiers of correlations in open quantum systems. Phys. Rev. A 86, 012312 (2012)ADSCrossRef Bellomo, B., Franco, R.L., Compagno, G.: Dynamics of geometric and entropic quantifiers of correlations in open quantum systems. Phys. Rev. A 86, 012312 (2012)ADSCrossRef
22.
go back to reference Lanyon, B.P., Barbieri, M., Almedia, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008)ADSCrossRef Lanyon, B.P., Barbieri, M., Almedia, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008)ADSCrossRef
23.
go back to reference Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)ADSCrossRef Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)ADSCrossRef
24.
go back to reference Mazzola, L., Piilo, J., Maniscalco, S.: Sudden transition between classical and quantum decoherence. Phys. Rev. Lett. 104, 200401 (2010)ADSMathSciNetCrossRef Mazzola, L., Piilo, J., Maniscalco, S.: Sudden transition between classical and quantum decoherence. Phys. Rev. Lett. 104, 200401 (2010)ADSMathSciNetCrossRef
25.
26.
go back to reference Guo, J.L., Mi, Y.J., Song, H.S.: Quantum discord dynamics of two-qubit system in a quantum spin environment. Eur. Phys. J. D 66, 24 (2012)ADSCrossRef Guo, J.L., Mi, Y.J., Song, H.S.: Quantum discord dynamics of two-qubit system in a quantum spin environment. Eur. Phys. J. D 66, 24 (2012)ADSCrossRef
27.
go back to reference Guo, J.L., Mi, Y.J., Zhang, J., Song, H.S.: Thermal quantum discord of spins in an inhomogeneous magnetic field. J. Phys. B At. Mol. Opt. Phys. 44, 065504 (2011)ADSCrossRef Guo, J.L., Mi, Y.J., Zhang, J., Song, H.S.: Thermal quantum discord of spins in an inhomogeneous magnetic field. J. Phys. B At. Mol. Opt. Phys. 44, 065504 (2011)ADSCrossRef
28.
go back to reference Sarandy, M.S.: Classical correlation and quantum discord in critical systems. Phys. Rev. A 80, 022108 (2009)ADSCrossRef Sarandy, M.S.: Classical correlation and quantum discord in critical systems. Phys. Rev. A 80, 022108 (2009)ADSCrossRef
29.
go back to reference Mi, Y.J.: Classical correlation and quantum discord in a two qubit system under dissipation environments. Int. J. Theor. Phys. 51, 544 (2012)MathSciNetCrossRefMATH Mi, Y.J.: Classical correlation and quantum discord in a two qubit system under dissipation environments. Int. J. Theor. Phys. 51, 544 (2012)MathSciNetCrossRefMATH
30.
go back to reference He, Q.L., Xu, J.B., Yao, D.X., Zhang, Y.Q.: Sudden transition between classical and quantum decoherence in dissipative cavity QED and stationary quantum discord. Phys. Rev. A 84, 022312 (2011)ADSCrossRef He, Q.L., Xu, J.B., Yao, D.X., Zhang, Y.Q.: Sudden transition between classical and quantum decoherence in dissipative cavity QED and stationary quantum discord. Phys. Rev. A 84, 022312 (2011)ADSCrossRef
31.
go back to reference Luo, D.W., Lin, H.Q., Xu, J.B., Yao, D.X.: Pulse control of sudden transition for two qubits in XY spin baths and quantum phase transition. Phys. Rev. A 84, 062112 (2011)ADSCrossRef Luo, D.W., Lin, H.Q., Xu, J.B., Yao, D.X.: Pulse control of sudden transition for two qubits in XY spin baths and quantum phase transition. Phys. Rev. A 84, 062112 (2011)ADSCrossRef
32.
go back to reference Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)ADSMathSciNetCrossRef Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)ADSMathSciNetCrossRef
33.
go back to reference Bellomo, B., Giorgi, G.L., Galve, F., Franco, RLo, Compagno, G., Zambrini, R.: Unified view of correlations using the square-norm distance. Phys. Rev. A 85, 032104 (2012)ADSCrossRef Bellomo, B., Giorgi, G.L., Galve, F., Franco, RLo, Compagno, G., Zambrini, R.: Unified view of correlations using the square-norm distance. Phys. Rev. A 85, 032104 (2012)ADSCrossRef
34.
go back to reference Paula, F.M., de Oliveira, T.R., Sarandy, M.S.: Geometric quantum discord through the Schatten 1-norm. Phys. Rev. A 87, 064101 (2013)ADSCrossRef Paula, F.M., de Oliveira, T.R., Sarandy, M.S.: Geometric quantum discord through the Schatten 1-norm. Phys. Rev. A 87, 064101 (2013)ADSCrossRef
35.
go back to reference Nakano, T., Piani, M., Adesso, G.: Negativity of quantumness and its interpretations. Phys. Rev. A 88, 012117 (2013)ADSCrossRef Nakano, T., Piani, M., Adesso, G.: Negativity of quantumness and its interpretations. Phys. Rev. A 88, 012117 (2013)ADSCrossRef
37.
go back to reference Bromley, T.R., Cianciaruso, M., Franco, RLo, Adesso, G.: Unifying approach to the quantification of bipartite correlations by Bures distance. J. Phys. A 47, 405302 (2013)MathSciNetCrossRefMATH Bromley, T.R., Cianciaruso, M., Franco, RLo, Adesso, G.: Unifying approach to the quantification of bipartite correlations by Bures distance. J. Phys. A 47, 405302 (2013)MathSciNetCrossRefMATH
38.
go back to reference Hu, X., Fan, H., Zhou, D.L., Liu, W.M.: Quantum correlating power of local quantum channels. Phys. Rev. A 87, 032340 (2013)ADSCrossRef Hu, X., Fan, H., Zhou, D.L., Liu, W.M.: Quantum correlating power of local quantum channels. Phys. Rev. A 87, 032340 (2013)ADSCrossRef
40.
go back to reference Ciccarello, F., Tufarelli, T., Giovannetti, V.: Toward computability of trace distance discord. New J. Phys. 16, 013038 (2014)ADSCrossRef Ciccarello, F., Tufarelli, T., Giovannetti, V.: Toward computability of trace distance discord. New J. Phys. 16, 013038 (2014)ADSCrossRef
41.
go back to reference Montealegre, J.D., Paula, F.M., Saguia, A., Sarandy, M.S.: One-norm geometric quantum discord under decoherence. Phys. Rev. A 87, 042115 (2013)ADSCrossRef Montealegre, J.D., Paula, F.M., Saguia, A., Sarandy, M.S.: One-norm geometric quantum discord under decoherence. Phys. Rev. A 87, 042115 (2013)ADSCrossRef
42.
go back to reference Paula, F.M., Silva, I.A., Montealegre, J.D., Souza, A.M., deAzevedo, E.R., Sarthour, R.S., Saguia, A., Oliveira, I.S., Soares-Pinto, D.O., Adesso, G., Sarandy, M.S.: Observation of environment-induced double sudden transitions in geometric quantum correlations. Phys. Rev. Lett. 111, 250401 (2013)ADSCrossRef Paula, F.M., Silva, I.A., Montealegre, J.D., Souza, A.M., deAzevedo, E.R., Sarthour, R.S., Saguia, A., Oliveira, I.S., Soares-Pinto, D.O., Adesso, G., Sarandy, M.S.: Observation of environment-induced double sudden transitions in geometric quantum correlations. Phys. Rev. Lett. 111, 250401 (2013)ADSCrossRef
43.
go back to reference Luo, D.W., Xu, J.B.: Sudden transitions and scaling behavior of geometric quantum correlation for two qubits in quantum critical environments at finite temperature. J. Phys. A 47, 365302 (2014)MathSciNetCrossRefMATH Luo, D.W., Xu, J.B.: Sudden transitions and scaling behavior of geometric quantum correlation for two qubits in quantum critical environments at finite temperature. J. Phys. A 47, 365302 (2014)MathSciNetCrossRefMATH
44.
go back to reference Aaronson, B., Franco, RLo, Adesso, G.: Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence. Phys. Rev. A 88, 012120 (2013)ADSCrossRef Aaronson, B., Franco, RLo, Adesso, G.: Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence. Phys. Rev. A 88, 012120 (2013)ADSCrossRef
45.
go back to reference Aaronson, B., Franco, RLo, Compagno, G., Adesso, G.: Hierarchy and dynamics of trace distance correlations. New J. Phys. 15, 093022 (2014)CrossRef Aaronson, B., Franco, RLo, Compagno, G., Adesso, G.: Hierarchy and dynamics of trace distance correlations. New J. Phys. 15, 093022 (2014)CrossRef
46.
go back to reference Cianciaruso, M., Bromley, T.R., Roga, W., Franco, RLo, Adesso, G.: Universal freezing of quantum correlations within the geometric approach. Sci. Rep. 5, 10177 (2015)ADSCrossRef Cianciaruso, M., Bromley, T.R., Roga, W., Franco, RLo, Adesso, G.: Universal freezing of quantum correlations within the geometric approach. Sci. Rep. 5, 10177 (2015)ADSCrossRef
47.
go back to reference Silva, I.A., Souza, A.M., Bromley, T.R., Cianciaruso, M., Sarthour, R.S., Oliveira, I.S., Franco, R.Lo., deAzevedo, E.R., Soares-Pinto, D.O., Adesso, G.: Observation of time-invariant coherence in a room temperature quantum simulator. arXiv:1511.01971 (2015) Silva, I.A., Souza, A.M., Bromley, T.R., Cianciaruso, M., Sarthour, R.S., Oliveira, I.S., Franco, R.Lo., deAzevedo, E.R., Soares-Pinto, D.O., Adesso, G.: Observation of time-invariant coherence in a room temperature quantum simulator. arXiv:​1511.​01971 (2015)
48.
go back to reference Lombardo, F.C., Villar, P.I.: Environmentally induced effects on a bipartite two-level system: geometric phase and entanglement properties. Phys. Rev. A 81, 022115 (2010)ADSCrossRef Lombardo, F.C., Villar, P.I.: Environmentally induced effects on a bipartite two-level system: geometric phase and entanglement properties. Phys. Rev. A 81, 022115 (2010)ADSCrossRef
49.
go back to reference Franco, RLo, Bellomo, B., Maniscalco, S., Compagno, G.: dynamics of correlations in two-qubit systems within non-Markovian environments. Int. J. Mod. Phys. B 27, 1345053 (2013)ADSMathSciNetCrossRefMATH Franco, RLo, Bellomo, B., Maniscalco, S., Compagno, G.: dynamics of correlations in two-qubit systems within non-Markovian environments. Int. J. Mod. Phys. B 27, 1345053 (2013)ADSMathSciNetCrossRefMATH
50.
go back to reference Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRef Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRef
51.
go back to reference Obando, P.C., Paula, F.M., Sarandy, M.S.: Trace-distance correlations for X states and the emergence of the pointer basis in Markovian and non-Markovian regimes. Phys. Rev. A 92, 032307 (2015)ADSCrossRef Obando, P.C., Paula, F.M., Sarandy, M.S.: Trace-distance correlations for X states and the emergence of the pointer basis in Markovian and non-Markovian regimes. Phys. Rev. A 92, 032307 (2015)ADSCrossRef
52.
go back to reference Piani, M., Gharibian, S., Adesso, G., Calsamiglia, J.: All nonclassical correlations can be activated into distillable entanglement. Phys. Rev. Lett. 106, 220403 (2011)ADSCrossRef Piani, M., Gharibian, S., Adesso, G., Calsamiglia, J.: All nonclassical correlations can be activated into distillable entanglement. Phys. Rev. Lett. 106, 220403 (2011)ADSCrossRef
53.
go back to reference Silva, I.A., Girolami, D., Auccaise, R., Sarthour, R.S., Oliveira, I.S., Bonagamba, T.J., deAzevedo, E.R., Soares-Pinto, D.O., Adesso, G.: Measuring bipartite quantum correlations of an unknown state. Phys. Rev. Lett. 110, 140501 (2013)ADSCrossRef Silva, I.A., Girolami, D., Auccaise, R., Sarthour, R.S., Oliveira, I.S., Bonagamba, T.J., deAzevedo, E.R., Soares-Pinto, D.O., Adesso, G.: Measuring bipartite quantum correlations of an unknown state. Phys. Rev. Lett. 110, 140501 (2013)ADSCrossRef
Metadata
Title
Dynamical behavior of quantum correlations between two qubits coupled to an external environment
Authors
Jin-Long Wei
Xing-Li Li
Xi-Zheng Zhang
Jin-Liang Guo
Publication date
01-06-2016
Publisher
Springer US
Published in
Quantum Information Processing / Issue 6/2016
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-016-1277-0

Other articles of this Issue 6/2016

Quantum Information Processing 6/2016 Go to the issue