Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Buchtitelbild

2023 | OriginalPaper | Buchkapitel

Quantification of Correlations in Quantum States

verfasst von : Cristian E. Susa-Quintero

Erschienen in: Quantum Computing: A Shift from Bits to Qubits

Verlag: Springer Nature Singapore

Einloggen

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

search-config
loading …

Abstract

Non-classical correlations such as entanglement and quantum discord are essential concepts in the context of quantum technologies nowadays. A plethora of both theoretical and experimental advances on this sort of correlation can be found in the literature. However, it is worth pointing out that new insights on their quantification, detection and application, to name a few, continue to be very welcome. In this chapter, we present a discussion on the quantification of correlations in quantum states. For doing so, we discuss how to quantify the so-called quantum discord in the light of a recently proposed measure inspired by the resource theory for coherence and operationally well-defined in the context of parameter estimation. On the other hand, we also comment on the problem of identifying genuine multipartite correlations in many-body systems. In this case, we discuss a proposal to quantify genuine total (classical plus quantum) correlations at different order \(2\le k\le N\).

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!

Jetzt informieren

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!

Jetzt informieren

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!

Jetzt informieren
Nächstes Kapitel From Quantum Mechanics to Quantum Computing
Fußnoten
1
A system with two parts (subsystems) is usually referred to as a bipartite system. Along the chapter, we make use of the term multipartite to refer to many-body systems (generally with more than two parts).
 
2
The SIO is assumed to have the Kraus representation \(\mathcal {E}(\rho )=\sum _kK_k\rho K_k^{\dagger }\) with \(K_k^{\dagger }=\sum _ic_{k,i}^*\left| i \rangle \langle f_k(i) \right| \), and \(f_k(i)\) any permutation of the set \(\{0,1,\dots ,d-1\}\). It turns out that \(\left\langle l \right| K_k\rho K_k^{\dagger }\left| l \right\rangle =\sum _{j,i}c_{k,j}c_{k,i}^*\left\langle j \right| \rho \left| i \right\rangle \) with vanishing off-diagonal elements as \(K_k^{\dagger }\left| j \right\rangle =\sum _ic_{k,i}^*\left| i \right\rangle \langle f_k(i) | j \rangle \) has only one nonzero term for a given k.
 
3
In the context of quantum resource theories, the free operations for quantum discord is still subject to debate. The accepted set so far is the set of commutativity-preserving operations (CPO) [5]; \([\mathcal {E}(\rho ),\mathcal {E}(\sigma )]=0\), for any CPO \(\mathcal {E}\) and any density operators such that \([\rho ,\sigma ]=0\). In [6], we introduced the extension ECPO as operations defined as follows: for any extension \(\rho _{SA}\) of \(\rho _S\) throughout an ancillary system A; there exists an operation \(\mathcal {F}_{SA}(\rho _{SA})\) such that \(\mathcal {E}_{S}=\text {Tr}_{A}[\mathcal {F}_{SA}]\). We say that \(\mathcal {F}_{SA}(\rho _{SA})\) is free for any free \(\mathcal {E}_{S}(\rho _S)\).
 
4
A genuine multipartite correlation is understood as a joint correlation that cannot be reduced to properties of the composing parts. For instance, a genuine tripartite correlation cannot be described in terms of either two-partite correlations or single-part properties.
 
Literatur
1.
A. Einstein, B. Podolsky, N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)CrossRefMATH
2.
H. Ollivier, W.H. Zurek, Quantum discord: A measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)CrossRefMATH
3.
4.
K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655–1707 (2012)CrossRef
5.
G. Adesso, T.R. Bromley, M. Cianciaruso, Measures and applications of quantum correlations. J. Phys. A: Math. Theoret. 49(47), 473001 (2016)
6.
B. Yadin, P. Bogaert, C.E. Susa, D. Girolami, Coherence and quantum correlations measure sensitivity to dephasing channels. Phys. Rev. A 99, 012329 (2019). (Jan)CrossRef
7.
D. Girolami, T. Tufarelli, C.E. Susa, Quantifying genuine multipartite correlations and their pattern complexity. Phys. Rev. Lett. 119, 140505 (2017). (Oct)CrossRef
8.
9.
S. Haddadi, M. Bohloul, A brief overview of bipartite and multipartite entanglement measures. Int. J. Theor. Phys. 57, 3912–3916 (2018). (Dec)MathSciNetCrossRefMATH
10.
M. Navascués, E. Wolfe, D. Rosset, A. Pozas-Kerstjens, Genuine network multipartite entanglement. Phys. Rev. Lett. 125, 240505 (2020). (Dec)MathSciNetCrossRef
11.
12.
A. Bera, T. Das, D. Sadhukhan, S.S. Roy, A. Sen(De), U. Sen, Quantum Discord Its allies: Rev. Recent Progr. 81(2), 024001 (2017)
13.
A. Streltsov, G. Adesso, M.B. Plenio, Colloquium: quantum coherence as a resource. Rev. Mod. Phys. 89, 041003 (2017). (Oct)MathSciNetCrossRef
14.
G.A. Matteo, Paris. Quantum estimation for quantum technology. Int. J. Quantum Inform. 07(supp01), 125–137 (2009)
15.
T. Baumgratz, M. Cramer, M.B. Plenio, Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014). (Sep)CrossRef
16.
C.H. Bennett, A. Grudka, M. Horodecki, P. Horodecki, R. Horodecki, Postulates for measures of genuine multipartite correlations. Phys. Rev. A 83, 012312 (2011). (Jan)CrossRef
17.
D.M. Greenberger, M.A. Horne, A. Zeilinger, Going Beyond Bell’s Theorem (Springer, Netherlands, 1989), pp. 69–72
Metadaten
Titel
Quantification of Correlations in Quantum States
verfasst von
Cristian E. Susa-Quintero
Copyright-Jahr
2023
Verlag
Springer Nature Singapore
Buch
Quantum Computing: A Shift from Bits to Qubits

Print ISBN: 978-981-19-9529-3

Electronic ISBN: 978-981-19-9530-9

Copyright-Jahr: 2023

DOI
https://doi.org/10.1007/978-981-19-9530-9_1

Premium Partner

    Bildnachweise