Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Quantum Information Processing
Published in: Quantum Information Processing 10/2019

01-10-2019

Role of maximally entangled states in the context of linear steering inequalities

Authors: Debarshi Das, Souradeep Sasmal, Arup Roy

Published in: Quantum Information Processing | Issue 10/2019

Log in

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

search-config
loading …

Abstract

Linear steering inequalities are useful to check whether a bipartite state is steerable when both the parties are allowed to perform n dichotomic measurements on their parts. In the present study, we propose the necessary and sufficient condition under which two-setting linear steering inequality will be violated for any given set of spin-\(\frac{1}{2}\) observables at trusted and untrusted parties’ sides. The important result revealed by the present paper is that maximally entangled two-qubit states give the largest quantum violations of two-setting as well as three-setting linear steering inequalities attainable for any given set of spin-\(\frac{1}{2}\) observables at trusted and untrusted parties’ sides (if any violation exists for that given set of spin-\(\frac{1}{2}\) observables).
previous article Weak quantum correlation quantifiers with generalized entropies
next article A formulation of Rényi entropy on -algebras

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!

inform now

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!

inform now

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!

inform now
Literature
1.
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)ADSCrossRef
2.
Schrodinger, E.: Discussion of probability relations between separated systems. Proc. Cambridge Philos. Soc. 31, 555 (1935)ADSCrossRef
3.
Schrodinger, E.: Probability relations between separated systems. Proc. Cambridge Philos. Soc. 32, 446 (1936)ADSCrossRef
4.
Wiseman, H.M., Jones, S.J., Doherty, A.C.: Steering, entanglement, nonlocality, and the Einstein–Podolsky–Rosen paradox. Phys. Rev. Lett. 98, 140402 (2007)ADSMathSciNetCrossRef
5.
Jones, S.J., Wiseman, H.M., Doherty, A.C.: Entanglement, Einstein–Podolsky–Rosen correlations, Bell nonlocality, and steering. Phys. Rev. A 76, 052116 (2007)ADSMathSciNetCrossRef
6.
Wittmann, B., Ramelow, S., Steinlechner, F., Langford, N.K., Brunner, N., Wiseman, H., Ursin, R., Zeilinger, A.: Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering. New. J. Phys. 14, 053030 (2012)ADSCrossRef
7.
He, Q.Y., Reid, M.D.: Genuine multipartite Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 111, 250403 (2013)ADSCrossRef
8.
Milne, A., Jevtic, S., Jennings, D., Wiseman, H., Rudolph, T.: Quantum steering ellipsoids, extremal physical states and monogamy. New J. Phys. 16, 083017 (2014)ADSCrossRef
9.
Jevtic, S., Pusey, M., Jennings, D., Rudolph, T.: Quantum steering ellipsoids. Phys. Rev. Lett. 113, 020402 (2014)ADSCrossRef
10.
Evans, D.A., Wiseman, H.M.: Optimal measurements for tests of Einstein–Podolsky–Rosen steering with no detection loophole using two-qubit Werner states. Phys. Rev. A 90, 012114 (2014)ADSCrossRef
11.
Skrzypczyk, P., Navascues, M., Cavalcanti, D.: Quantifying Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 112, 180404 (2014)ADSCrossRef
12.
Jevtic, S., Hall, M.J.W., Anderson, M.R., Zwierz, M., Wiseman, H.M.: Einstein–Podolsky–Rosen steering and the steering ellipsoid. JOSA B 32, A40 (2015)ADSCrossRef
13.
Piani, M., Watrous, J.: Necessary and sufficient quantum information characterization of Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 114, 060404 (2015)ADSMathSciNetCrossRef
14.
Hsieh, C.-Y., Liang, Y.-C., Lee, R.-K.: Quantum steerability: characterization, quantification, superactivation, and unbounded amplification. Phys. Rev. A 94, 062120 (2016)ADSCrossRef
15.
Gallego, R., Aolita, L.: Resource theory of steering. Phys. Rev. X 5, 041008 (2015)MATH
16.
Cavalcanti, D., Skrzypczyk, P.: Quantum steering: a review with focus on semidefinite programming. Rep. Prog. Phys. 80, 024001 (2017)ADSMathSciNetCrossRef
17.
Das, D., Datta, S., Jebaratnam, C., Majumdar, A.S.: Cost of Einstein–Podolsky–Rosen steering in the context of extremal boxes. Phys. Rev. A 97, 022110 (2018)ADSCrossRef
18.
Ku, H.-Y., Chen, S.-L., Budroni, C., Miranowicz, A., Chen, Y.-N., Nori, F.: Einstein–Podolsky–Rosen steering: its geometric quantification and witness. Phys. Rev. A 97, 022338 (2018)ADSCrossRef
19.
Quintino, M.T., Vertesi, T., Cavalcanti, D., Augusiak, R., Demianowicz, M., Acin, A., Brunner, N.: Inequivalence of entanglement, steering, and Bell nonlocality for general measurements. Phys. Rev. A 92, 032107 (2015)ADSCrossRef
20.
Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)ADSCrossRef
21.
22.
Bowles, J., Vertesi, T., Quintino, M.T., Brunner, N.: One-way Einstein–Podolsky–Rosen steering. Phys. Rev. Lett. 112, 200402 (2014)ADSCrossRef
23.
Chen, J.L., Ye, X.J., Wu, C.F., Su, H.Y., Cabello, A., Kwek, L.C., Oh, C.H.: All-versus-nothing proof of Einstein–Podolsky–Rosen steering. Sci. Rep. 3, 2143 (2013)CrossRef
24.
Branciard, C., Cavalcanti, E.G., Walborn, S.P., Scarani, V., Wiseman, H.M.: One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering. Phys. Rev. A 85, 010301(R) (2012)ADSCrossRef
25.
Cavalcanti, E.G., Jones, S.J., Wiseman, H.M., Reid, M.D.: Experimental criteria for steering and the Einstein–Podolsky–Rosen paradox. Phys. Rev. A 80, 032112 (2009)ADSCrossRef
26.
Reid, M.D.: Demonstration of the Einstein–Podolsky–Rosen paradox using nondegenerate parametric amplification. Phys. Rev. A 40, 913 (1989)ADSCrossRef
27.
Ou, Z.Y., Pereira, S.F., Kimble, H.J., Peng, K.C.: Realization of the Einstein–Podolsky–Rosen paradox for continuous variables. Phys. Rev. Lett. 68, 3663 (1992)ADSCrossRef
28.
Walborn, S.P., Salles, A., Gomes, R.M., Toscano, F., Souto Ribeiro, P.H.: Revealing hidden Einstein–Podolsky–Rosen nonlocality. Phys. Rev. Lett. 106, 130402 (2011)ADSCrossRef
29.
Schneeloch, J., Broadbent, C.J., Walborn, S.P., Cavalcanti, E.G., Howell, J.C.: Einstein–Podolsky–Rosen steering inequalities from entropic uncertainty relations. Phys. Rev. A 87, 062103 (2013)ADSCrossRef
30.
Pramanik, T., Kaplan, M., Majumdar, A.S.: Fine-grained Einstein–Podolsky–Rosen steering inequalities. Phys. Rev. A 90, 050305(R) (2014)ADSCrossRef
31.
Chowdhury, P., Pramanik, T., Majumdar, A.S., Agarwal, G.S.: Einstein–Podolsky–Rosen steering using quantum correlations in non-Gaussian entangled states. Phys. Rev. A 89, 012104 (2014)ADSCrossRef
32.
Chowdhury, P., Pramanik, T., Majumdar, A.S.: Stronger steerability criterion for more uncertain continuous-variable systems. Phys. Rev. A 92, 042317 (2015)ADSCrossRef
33.
Cavalcanti, E.G., Foster, C.J., Fuwa, M., Wiseman, H.M.: Analog of the Clauser–Horne–Shimony–Holt inequality for steering. J. Opt. Soc. Am. B 32, A74 (2015)ADSCrossRef
34.
Girdhar, P., Cavalcanti, E.G.: All two-qubit states that are steerable via Clauser–Horne–Shimony–Holt-type correlations are Bell nonlocal. Phys. Rev. A 94, 032317 (2016)ADSCrossRef
35.
Sasmal, S., Pramanik, T., Home, D., Majumdar, A.S.: A tighter steering criterion using the Robertson–Schrodinger uncertainty relation. Phys. Lett. A 382, 27 (2018)ADSMathSciNetCrossRef
36.
Costa, A.C.S., Uola, R., Guhne, O.: Steering criteria from general entropic uncertainty relations. Phys. Rev. A 98, 050104(R) (2018)ADSCrossRef
37.
Costa, A.C.S., Uola, R., Guhne, O.: Entropic steering criteria: applications to bipartite and tripartite systems. Entropy 20(10), 763 (2018)ADSMathSciNetCrossRef
38.
39.
Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969)ADSCrossRef
40.
Horodecki, R., Horordecki, P., Horodecki, M.: Violating Bell inequality by mixed spin-\(\frac{1}{2}\) states: necessary and sufficient condition. Phys. Lett. A 200, 340 (1995)ADSMathSciNetCrossRef
41.
Costa, A.C.S., Angelo, R.M.: Quantification of Einstein–Podolsky–Rosen steering for two-qubit states. Phys. Rev. A 93, 020103(R) (2016)ADSCrossRef
42.
Mal, S., Das, D., Sasmal, S., Majumdar, A. S.: Necessary and sufficient state condition for two-qubit steering using two measurement settings per party and monogamy of steering. arXiv:​1711.​00872 [quant-ph] (2017)
43.
44.
45.
Peres, A.: Quantum Theory: Concepts and Methods. Kluwer, Dordrecht (1993)MATH
46.
Hughston, L.P., Jozsa, R., Wootters, W.K.: A complete classification of quantum ensembles having a given density matrix. Phys. Lett. A 183, 14 (1993)ADSMathSciNetCrossRef
47.
Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S.: Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88, 040404 (2002)ADSMathSciNetCrossRef
48.
Acin, A., Massar, S., Pironio, S.: Randomness versus nonlocality and entanglement. Phys. Rev. Lett. 108, 100402 (2012)ADSCrossRef
Metadata
Title
Role of maximally entangled states in the context of linear steering inequalities
Authors
Debarshi Das
Souradeep Sasmal
Arup Roy
Publication date
01-10-2019
Publisher
Springer US
Published in
Quantum Information Processing / Issue 10/2019
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-019-2427-y

Other articles of this Issue 10/2019

Quantum Information Processing 10/2019 Go to the issue

OriginalPaper

The performance of reference-frame-independent measurement-device-independent quantum key distribution

OriginalPaper

Intercept-and-resend attack and improvement of semiquantum secure direct communication using EPR pairs

OriginalPaper

Multipartite quantum coherence and monogamy for Dirac fields subject to Hawking radiation

OriginalPaper

Measurement-induced geometric measures of correlations based on the Hellinger distance and their local decoherence

OriginalPaper

Non-Gaussian bosonic channels in the Tavis–Cummings model

OriginalPaper

Orbital angular momentum-encoded measurement device independent quantum key distribution under atmospheric turbulence