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

This article is cited in 4 scientific papers (total in 4 papers)

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

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

Bibliographic databases:

Received: 26.11.2008

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
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    Citing articles on Google Scholar: Russian citations, English citations
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    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  crossref  isi  scopus  scopus
    2. Luo Shunlong, Sun Wei, “Decomposition of bipartite states with applications to quantum no-broadcasting theorems”, Phys. Rev. A, 82:1 (2010), 012338  crossref  mathscinet  adsnasa  isi  scopus  scopus
    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  crossref  mathscinet  zmath  isi  scopus  scopus
    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  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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