Huber, Felix and Eltschka, Christopher and Siewert, Jens and Guehne, Otfried (2018) Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 51 (17): 175301. ISSN 1751-8113, 1751-8121
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A pure multipartite quantum state is called absolutely maximally entangled (AME), if all reductions obtained by tracing out at least half of its parties are maximally mixed. Maximal entanglement is then present across every bipartition. The existence of such states is in many cases unclear. With the help of the weight enumerator machinery known from quantum error correction and the shadow inequalities, we obtain new bounds on the existence of AME states in dimensions larger than two. To complete the treatment on the weight enumerator machinery, the quantum MacWilliams identity is derived in the Bloch representation. Finally, we consider AME states whose subsystems have different local dimensions, and present an example for a 2 x 3 x 3 x 3 system that shows maximal entanglement across every bipartition.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DUAL ADDITIVE CODES; CLASSIFICATION; multipartite entanglement; quantum error correcting codes; absolutely maximally entangled states; quantum weight enumerators |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 19 Mar 2020 15:34 |
| Last Modified: | 19 Mar 2020 15:34 |
| URI: | https://pred.uni-regensburg.de/id/eprint/14704 |
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