Absolutely maximally entangled state: Difference between revisions

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The absolutely maximally entangled (AME) state is a concept in quantum information science, which has many applications in quantum error-correcting code,^[1] discrete AdS/CFT correspondence,^[2] AdS/CMT correspondenc e,^[2] and more. It is the multipartite generalization of the bipartite maximally entangled state.

Definition

The bipartite maximally entangled state $|\psi \rangle _{AB}$ is the one in which the reduced density operators are maximally mixed, i.e., $\rho _{A}=\rho _{B}=I/d$ . Typical examples are Bell states.

A multipartite state $|\psi \rangle$ of a system $S$ is called absolutely maximally entangled if for any bipartition $A|B$ of $S$ , the reduced density operator is maximally mixed $\rho _{A}=\rho _{B}=I/d$ , where $d=\min\{d_{A},d_{B}\}$ .

Property

The AME state does not always exist, in some given local dimension and number of parties. There is a table of AME states in low dimensions built by Huber and Wyderka^[3]^[4].

References

^ Goyeneche, Dardo; Alsina, Daniel; Latorre, José I.; Riera, Arnau; Życzkowski, Karol (2015-09-15). "Absolutely maximally entangled states, combinatorial designs, and multiunitary matrices". Physical Review A. 92 (3): 032316. doi:10.1103/PhysRevA.92.032316.
^ ^a ^b Pastawski, Fernando; Yoshida, Beni; Harlow, Daniel; Preskill, John (2015-06-23). "Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence". Journal of High Energy Physics. 2015 (6): 149. doi:10.1007/JHEP06(2015)149. ISSN 1029-8479.
^ Huber, F.; Wyderka, N. "Table of AME states".
^ Huber, Felix; Eltschka, Christopher; Siewert, Jens; Gühne, Otfried (2018-04-27). "Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity". Journal of Physics A: Mathematical and Theoretical. 51 (17): 175301. doi:10.1088/1751-8121/aaade5. ISSN 1751-8113.

[1] Goyeneche, Dardo; Alsina, Daniel; Latorre, José I.; Riera, Arnau; Życzkowski, Karol (2015-09-15). "Absolutely maximally entangled states, combinatorial designs, and multiunitary matrices". Physical Review A. 92 (3): 032316. doi:10.1103/PhysRevA.92.032316.

[:0-2] Pastawski, Fernando; Yoshida, Beni; Harlow, Daniel; Preskill, John (2015-06-23). "Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence". Journal of High Energy Physics. 2015 (6): 149. doi:10.1007/JHEP06(2015)149. ISSN 1029-8479.

[3] Huber, F.; Wyderka, N. "Table of AME states".

[4] Huber, Felix; Eltschka, Christopher; Siewert, Jens; Gühne, Otfried (2018-04-27). "Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity". Journal of Physics A: Mathematical and Theoretical. 51 (17): 175301. doi:10.1088/1751-8121/aaade5. ISSN 1751-8113.

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 == Property ==
-The AME state does not always exist, in some given local dimension and number of parties. For a table of AME states in low dimensions, see [https://www.tp.nt.uni-siegen.de/+fhuber/ame.html table of AME states].
+The AME state does not always exist, in some given local dimension and number of parties. There is a table of AME states in low dimensions built by Huber and Wyderka<ref>{{Cite web |last=Huber |first=F. |last2=Wyderka |first2=N. |title=Table of AME states |url=https://www.tp.nt.uni-siegen.de/+fhuber/ame.html}}</ref><ref>{{Cite journal |last=Huber |first=Felix |last2=Eltschka |first2=Christopher |last3=Siewert |first3=Jens |last4=Gühne |first4=Otfried |date=2018-04-27 |title=Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity |url=https://iopscience.iop.org/article/10.1088/1751-8121/aaade5 |journal=Journal of Physics A: Mathematical and Theoretical |volume=51 |issue=17 |pages=175301 |doi=10.1088/1751-8121/aaade5 |issn=1751-8113}}</ref>.
 ==References==