Skip to main content
Erschienen in: Quantum Information Processing 2/2021

01.02.2021

Distinguishability of generalized Bell states in arbitrary dimension system via one-way local operations and classical communication

verfasst von: Ying-Hui Yang, Gao-Feng Mu, Jiang-Tao Yuan, Cai-Hong Wang

Erschienen in: Quantum Information Processing | Ausgabe 2/2021

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We investigate the distinguishability of generalized Bell states (GBSs) in arbitrary dimension system by one-way local operations and classical communication (LOCC). Firstly, by analyzing three local unitary transformations, we define two concepts for each set \(\mathcal {L}\) of GBSs, i.e., an admissible solutions set \(\mathcal {S}_{\mathcal {A}}\) and a genuinely nonadmissible solutions set \(\mathcal {S}_{\mathcal {L}}\). Then, we show that a set \({\mathcal {L}}\) of any GBSs can be distinguished by one-way LOCC if \({\mathcal {S}}_{\mathcal {A}}\backslash {\mathcal {S}}_{\mathcal {L}}\) is nonempty. Fan’s and Wang et al.’s results (Phys Rev Lett 92:177905, 2004: Phys Rev A 99:022307, 2019) can be covered by our result. Comparing with Wang et al.’s result, our successful ratio of local distinguishability improves markedly, especially for even dimension system. In some cases, it can increase by nearly \(42\%\). However, there are still some cases where our method cannot work. For the uncovered cases, we define an uncovered set and present that there is no method which is more powerful than ours for local discrimination of GBSs if the uncovered set is a subset of the different set of GBSs.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

Literatur
1.
Zurück zum Zitat Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shor, P.W., Smolin, J.A., Wootters, W.K.: Quantum nonlocality without entanglement. Phys. Rev. A 59, 1070 (1999)ADSMathSciNetCrossRef Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shor, P.W., Smolin, J.A., Wootters, W.K.: Quantum nonlocality without entanglement. Phys. Rev. A 59, 1070 (1999)ADSMathSciNetCrossRef
2.
Zurück zum Zitat Walgate, J., Short, A.J., Hardy, L., Vedral, V.: Local distinguishability of multipartite orthogonal quantum states. Phys. Rev. Lett. 85, 4972 (2000)ADSCrossRef Walgate, J., Short, A.J., Hardy, L., Vedral, V.: Local distinguishability of multipartite orthogonal quantum states. Phys. Rev. Lett. 85, 4972 (2000)ADSCrossRef
3.
Zurück zum Zitat Duan, R.Y., Feng, Y., Xin, Y., Ying, M.S.: Distinguishability of quantum states by separable operations. IEEE Trans. Inf. Theory 55, 1320 (2009)MathSciNetCrossRef Duan, R.Y., Feng, Y., Xin, Y., Ying, M.S.: Distinguishability of quantum states by separable operations. IEEE Trans. Inf. Theory 55, 1320 (2009)MathSciNetCrossRef
4.
Zurück zum Zitat Duan, R.Y., Xin, Y., Ying, M.S.: Locally indistinguishable subspaces spanned by three-qubit unextendible product bases. Phys. Rev. A 81, 032329 (2010)ADSCrossRef Duan, R.Y., Xin, Y., Ying, M.S.: Locally indistinguishable subspaces spanned by three-qubit unextendible product bases. Phys. Rev. A 81, 032329 (2010)ADSCrossRef
5.
Zurück zum Zitat Yu, N.K., Duan, R.Y., Ying, M.S.: Any \(2\otimes n\) subspace is locally distinguishable. Phys. Rev. A 84, 012304 (2011)ADSCrossRef Yu, N.K., Duan, R.Y., Ying, M.S.: Any \(2\otimes n\) subspace is locally distinguishable. Phys. Rev. A 84, 012304 (2011)ADSCrossRef
6.
Zurück zum Zitat Yu, N.K., Duan, R.Y., Ying, M.S.: Four locally indistinguishable ququad–ququad orthogonal maximally entangled states. Phys. Rev. Lett. 109, 020506 (2012)ADSCrossRef Yu, N.K., Duan, R.Y., Ying, M.S.: Four locally indistinguishable ququad–ququad orthogonal maximally entangled states. Phys. Rev. Lett. 109, 020506 (2012)ADSCrossRef
7.
Zurück zum Zitat Nathanson, M.: Three maximally entangled states can require two-way local operations and classical communication for local discrimination. Phys. Rev. A 88, 062316 (2013)ADSCrossRef Nathanson, M.: Three maximally entangled states can require two-way local operations and classical communication for local discrimination. Phys. Rev. A 88, 062316 (2013)ADSCrossRef
8.
Zurück zum Zitat Tian, G.-J., Yu, S.-X., Gao, F., Wen, Q.-Y., Oh, C.H.: Local discrimination of four or more maximally entangled states. Phys. Rev. A 91, 052314 (2015)ADSCrossRef Tian, G.-J., Yu, S.-X., Gao, F., Wen, Q.-Y., Oh, C.H.: Local discrimination of four or more maximally entangled states. Phys. Rev. A 91, 052314 (2015)ADSCrossRef
9.
Zurück zum Zitat Tian, G.-J., Wu, X., Cao, Y., Gao, F., Wen, Q.-Y.: General existence of locally distinguishable maximally entangled states only with two-way classical communication. Sci. Rep. 6, 30181 (2016)ADSCrossRef Tian, G.-J., Wu, X., Cao, Y., Gao, F., Wen, Q.-Y.: General existence of locally distinguishable maximally entangled states only with two-way classical communication. Sci. Rep. 6, 30181 (2016)ADSCrossRef
10.
Zurück zum Zitat Yang, Y.-H., Yuan, J.-T., Wang, C.-H., Geng, S.-J., Zuo, H.-J.: Locally indistinguishable generalized Bell states with one-way local operations and classical communication. Phys. Rev. A 98, 042333 (2018)ADSCrossRef Yang, Y.-H., Yuan, J.-T., Wang, C.-H., Geng, S.-J., Zuo, H.-J.: Locally indistinguishable generalized Bell states with one-way local operations and classical communication. Phys. Rev. A 98, 042333 (2018)ADSCrossRef
11.
Zurück zum Zitat Zhang, Z.-C., Wen, Q.-Y., Gao, F., Tian, G.-J., Cao, T.-Q.: One-way LOCC indistinguishability of maximally entangled states. Quant. Inf. Process. 13, 795 (2014)ADSMathSciNetCrossRef Zhang, Z.-C., Wen, Q.-Y., Gao, F., Tian, G.-J., Cao, T.-Q.: One-way LOCC indistinguishability of maximally entangled states. Quant. Inf. Process. 13, 795 (2014)ADSMathSciNetCrossRef
12.
Zurück zum Zitat Zhang, Z.-C., Feng, K.-Q., Gao, F., Wen, Q.-Y.: Distinguishing maximally entangled states by one-way local operations and classical communication. Phys. Rev. A 91, 012329 (2015)ADSMathSciNetCrossRef Zhang, Z.-C., Feng, K.-Q., Gao, F., Wen, Q.-Y.: Distinguishing maximally entangled states by one-way local operations and classical communication. Phys. Rev. A 91, 012329 (2015)ADSMathSciNetCrossRef
13.
Zurück zum Zitat Wang, Y.-L., Li, M.-S., Zheng, Z.-J., Fei, S.-M.: On small set of one-way LOCC indistinguishability of maximally entangled states. Quant. Inf. Process. 15, 1661 (2016)ADSMathSciNetCrossRef Wang, Y.-L., Li, M.-S., Zheng, Z.-J., Fei, S.-M.: On small set of one-way LOCC indistinguishability of maximally entangled states. Quant. Inf. Process. 15, 1661 (2016)ADSMathSciNetCrossRef
15.
Zurück zum Zitat Jiang, D.-H., Xu, G.-B.: Nonlocal sets of orthogonal product states in an arbitrary multipartite quantum system. Phys. Rev. A 102, 032211 (2020)ADSMathSciNetCrossRef Jiang, D.-H., Xu, G.-B.: Nonlocal sets of orthogonal product states in an arbitrary multipartite quantum system. Phys. Rev. A 102, 032211 (2020)ADSMathSciNetCrossRef
16.
17.
Zurück zum Zitat Ghosh, S., Kar, G., Roy, A., Sarkar, D.: Distinguishability of maximally entangled states. Phys. Rev. A 70, 022304 (2004)ADSMathSciNetCrossRef Ghosh, S., Kar, G., Roy, A., Sarkar, D.: Distinguishability of maximally entangled states. Phys. Rev. A 70, 022304 (2004)ADSMathSciNetCrossRef
18.
Zurück zum Zitat Nathanson, M.: Distinguishing bipartitite orthogonal states using LOCC: best and worst cases. J. Math. Phys. 46, 062103 (2005)ADSMathSciNetCrossRef Nathanson, M.: Distinguishing bipartitite orthogonal states using LOCC: best and worst cases. J. Math. Phys. 46, 062103 (2005)ADSMathSciNetCrossRef
19.
Zurück zum Zitat Bandyopadhyay, S., Ghosh, S., Kar, G.: LOCC distinguishability of unilaterally transformable quantum states. New J. Phys. 13, 123013 (2011)ADSCrossRef Bandyopadhyay, S., Ghosh, S., Kar, G.: LOCC distinguishability of unilaterally transformable quantum states. New J. Phys. 13, 123013 (2011)ADSCrossRef
20.
Zurück zum Zitat Wang, Y.-L., Li, M.-S., Fei, S.-M., Zheng, Z.-J.: The local distinguishability of any three generalized Bell states. Quant. Inf. Process. 16, 126 (2017)ADSMathSciNetCrossRef Wang, Y.-L., Li, M.-S., Fei, S.-M., Zheng, Z.-J.: The local distinguishability of any three generalized Bell states. Quant. Inf. Process. 16, 126 (2017)ADSMathSciNetCrossRef
21.
Zurück zum Zitat Fan, H.: Distinguishability and indistinguishability by local operations and classical communication. Phys. Rev. Lett. 92, 177905 (2004)ADSCrossRef Fan, H.: Distinguishability and indistinguishability by local operations and classical communication. Phys. Rev. Lett. 92, 177905 (2004)ADSCrossRef
22.
Zurück zum Zitat Tian, G.-J., Yu, S.-X., Gao, F., Wen, Q.-Y., Oh, C.H.: Local discrimination of qudit lattice states via commutativity. Phys. Rev. A 92, 042320 (2015)ADSCrossRef Tian, G.-J., Yu, S.-X., Gao, F., Wen, Q.-Y., Oh, C.H.: Local discrimination of qudit lattice states via commutativity. Phys. Rev. A 92, 042320 (2015)ADSCrossRef
23.
Zurück zum Zitat Tian, G.-J., Yu, S.-X., Gao, F., Wen, Q.-Y., Oh, C.H.: Classification of locally distinguishable and indistinguishable sets of maximally entangled states. Phys. Rev. A 94, 052315 (2016)ADSCrossRef Tian, G.-J., Yu, S.-X., Gao, F., Wen, Q.-Y., Oh, C.H.: Classification of locally distinguishable and indistinguishable sets of maximally entangled states. Phys. Rev. A 94, 052315 (2016)ADSCrossRef
24.
Zurück zum Zitat Singal, T., Rahaman, R., Ghosh, S., Kar, G.: Necessary condition for local distinguishability of maximally entangled states: beyond orthogonality preservation. Phys. Rev. A 96, 042314 (2017)ADSCrossRef Singal, T., Rahaman, R., Ghosh, S., Kar, G.: Necessary condition for local distinguishability of maximally entangled states: beyond orthogonality preservation. Phys. Rev. A 96, 042314 (2017)ADSCrossRef
25.
Zurück zum Zitat Yang, Y.-H., Wang, C.-H., Yuan, J.-T., Wu, X., Zuo, H.-J.: Local distinguishability of generalized Bell states. Quant. Inf. Process. 17, 29 (2018)ADSMathSciNetCrossRef Yang, Y.-H., Wang, C.-H., Yuan, J.-T., Wu, X., Zuo, H.-J.: Local distinguishability of generalized Bell states. Quant. Inf. Process. 17, 29 (2018)ADSMathSciNetCrossRef
26.
Zurück zum Zitat Wang, Y.-L., Li, M.-S., Xiong, Z.-X.: One-way local distinguishability of generalized Bell states in arbitrary dimension. Phys. Rev. A 99, 022307 (2019)ADSCrossRef Wang, Y.-L., Li, M.-S., Xiong, Z.-X.: One-way local distinguishability of generalized Bell states in arbitrary dimension. Phys. Rev. A 99, 022307 (2019)ADSCrossRef
27.
Metadaten
Titel
Distinguishability of generalized Bell states in arbitrary dimension system via one-way local operations and classical communication
verfasst von
Ying-Hui Yang
Gao-Feng Mu
Jiang-Tao Yuan
Cai-Hong Wang
Publikationsdatum
01.02.2021
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 2/2021
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-021-02990-9

Weitere Artikel der Ausgabe 2/2021

Quantum Information Processing 2/2021 Zur Ausgabe

Neuer Inhalt