Skip to main content
Erschienen in: Soft Computing 19/2017

20.02.2017 | Focus

Extrapolated quantum states, void states and a huge novel class of distillable entangled states

verfasst von: Michel Boyer, Aharon Brodutch, Tal Mor

Erschienen in: Soft Computing | Ausgabe 19/2017

Einloggen

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

search-config
loading …

Abstract

A nice and interesting property of any pure tensor product state is that each such state has distillable entangled states at an arbitrarily small distance \(\epsilon \) in its neighborhood. We say that such nearby states are \(\epsilon \)-entangled, and we call the tensor product state in that case, a “boundary separable state,” as there is entanglement at any distance from this “boundary.” Here we find a huge class of separable states that also share the property mentioned above—they all have \(\epsilon \)-entangled states at any small distance in their neighborhood. Furthermore, the entanglement they have is proved to be distillable. We then extend this result to the discordant/classical cut and show that all classical states (correlated and uncorrelated) have discordant states at distance \(\epsilon \), and provide a constructive method for finding \(\epsilon \)-discordant states.

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 "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!

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!

Anhänge
Nur mit Berechtigung zugänglich
Fußnoten
1
A preliminary version of this work (without discordant states) appeared in TPNC-2014 (Boyer and Mor 2014).
 
2
The term product basis should not be confused with the classical basis of Groisman et al. (2007) which is a product of local bases, rather than a basis of product states.
 
3
Note that a separable \(N-1\)-void state is a tensor product state.
 
4
The term classical is used in a variety of ways in the literature; here, we use it in the sense of correlations as in Modi et al. (2012).
 
5
Although the Peres criterion is well known, it is provided for completeness of the exposition in Appendix 8.
 
Literatur
Zurück zum Zitat Acín A, Augusiak R, Cavalcanti D, Hadley C, Korbicz JK, Lewenstein M, Masanes L, Piani M (2010) Unified framework for correlations in terms of local quantum observables. Phys Rev Lett 104(140):404. doi:10.1103/PhysRevLett.104.140404 Acín A, Augusiak R, Cavalcanti D, Hadley C, Korbicz JK, Lewenstein M, Masanes L, Piani M (2010) Unified framework for correlations in terms of local quantum observables. Phys Rev Lett 104(140):404. doi:10.​1103/​PhysRevLett.​104.​140404
Zurück zum Zitat Bengtsson I, Życzkowski K (2006) Geometry of quantum states: an introduction to quantum entanglement. Cambridge University Press, CambridgeCrossRefMATH Bengtsson I, Życzkowski K (2006) Geometry of quantum states: an introduction to quantum entanglement. Cambridge University Press, CambridgeCrossRefMATH
Zurück zum Zitat Boyer M, Brodutch A, Mor T (2017) Entanglement and deterministic quantum computing with one qubit. Phys Rev A (2017, to appear). arXiv:1606.05283 Boyer M, Brodutch A, Mor T (2017) Entanglement and deterministic quantum computing with one qubit. Phys Rev A (2017, to appear). arXiv:​1606.​05283
Zurück zum Zitat Boyer M, Mor T (2014) Extrapolated states, void states, and a huge novel class of distillable entangled states. In: Dediu AH, Lozano M, Martín-Vide C (eds) Theory and practice of natural computing. Lecture notes in computer science, vol 8890. Springer, Berlin, pp 107–118. doi:10.1007/978-3-319-13749-0_10 Boyer M, Mor T (2014) Extrapolated states, void states, and a huge novel class of distillable entangled states. In: Dediu AH, Lozano M, Martín-Vide C (eds) Theory and practice of natural computing. Lecture notes in computer science, vol 8890. Springer, Berlin, pp 107–118. doi:10.​1007/​978-3-319-13749-0_​10
Zurück zum Zitat Gurvits L (2003) Classical deterministic complexity of Edmonds’ problem and quantum entanglement. In: Proceedings of the thirty-fifth annual ACM symposium on theory of computing, ACM, New York, NY, USA, STOC ’03, pp 10–19. doi:10.1145/780542.780545 Gurvits L (2003) Classical deterministic complexity of Edmonds’ problem and quantum entanglement. In: Proceedings of the thirty-fifth annual ACM symposium on theory of computing, ACM, New York, NY, USA, STOC ’03, pp 10–19. doi:10.​1145/​780542.​780545
Metadaten
Titel
Extrapolated quantum states, void states and a huge novel class of distillable entangled states
verfasst von
Michel Boyer
Aharon Brodutch
Tal Mor
Publikationsdatum
20.02.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 19/2017
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-017-2518-6

Weitere Artikel der Ausgabe 19/2017

Soft Computing 19/2017 Zur Ausgabe