RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

 TMF, 2009, Volume 160, Number 3, Pages 534–544 (Mi tmf6414)

Separability and entanglement in tripartite states

Shunlong Luoa, Wei Sunb

a Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People's Republic of China
b Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, Canada

Abstract: While classical correlations can be freely distributed among many systems, this is not true for entanglement and quantum correlations. If a quantum system $S^a$ is entangled with another quantum system $S^b$, then its entanglement with any third quantum system $S^c$ cannot be arbitrary. This is the celebrated monogamy of entanglement. Implicit in this general statement is the plausible belief that only entanglement between the systems $S^a$ and $S^b$ constrains the entanglement between $S^a$ and the third system $S^c$. We demonstrate that even classical correlations between $S^a$ and $S^b$ may impose surprisingly stringent restrictions on the possible entanglement between $S^a$ and $S^c$. In particular, perfect bipartite classical correlations and full entanglement cannot coexist in any tripartite state. An intuitive explanation of this monogamy of hybrid classical and quantum correlations might be that the system $S^a$ has a correlating capability, which cannot be used to establish any entanglement with a third system (but can still be used to establish classical correlations) if it is exhausted when correlated with $S^b$ (in either a classical or quantum fashion). This may be interpreted as an alternate version of monogamy.

Keywords: correlation, classical state, tripartite state, entanglement, separability

DOI: https://doi.org/10.4213/tmf6414

Full text: PDF file (379 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2009, 160:3, 1316–1323

Bibliographic databases:

Citation: Shunlong Luo, Wei Sun, “Separability and entanglement in tripartite states”, TMF, 160:3 (2009), 534–544; Theoret. and Math. Phys., 160:3 (2009), 1316–1323

Citation in format AMSBIB
\Bibitem{LuoSun09} \by Shunlong~Luo, Wei~Sun \paper Separability and entanglement in tripartite states \jour TMF \yr 2009 \vol 160 \issue 3 \pages 534--544 \mathnet{http://mi.mathnet.ru/tmf6414} \crossref{https://doi.org/10.4213/tmf6414} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2604588} \zmath{https://zbmath.org/?q=an:1184.81014} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2009TMP...160.1316L} \transl \jour Theoret. and Math. Phys. \yr 2009 \vol 160 \issue 3 \pages 1316--1323 \crossref{https://doi.org/10.1007/s11232-009-0118-z} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000271029500008} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350530390} 

• http://mi.mathnet.ru/eng/tmf6414
• https://doi.org/10.4213/tmf6414
• http://mi.mathnet.ru/eng/tmf/v160/i3/p534

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Luo Shun-Long, Li Nan, “Quantum Correlations Reduce Classical Correlations with Ancillary Systems”, Control Theory Appl., 27:12 (2010), 120304
2. Luo Shunlong, Sun Wei, “Decomposition of bipartite states with applications to quantum no-broadcasting theorems”, Phys. Rev. A, 82:1 (2010), 012338
3. Celeri L.C., Maziero J., Serra R.M., “Theoretical and Experimental Aspects of Quantum Discord and Related Measures”, International Journal of Quantum Information, 9:7–8 (2011), 1837–1873
4. Modi K., Brodutch A., Cable H., Paterek T., Vedral V., “The Classical-Quantum Boundary for Correlations: Discord and Related Measures”, Rev. Mod. Phys., 84:4 (2012), 1655–1707
•  Number of views: This page: 462 Full text: 88 References: 36 First page: 11