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Genuinely multipartite entangled states and orthogonal arrays
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Genuinely multipartite entangled states and orthogonal arrays
Bibliographic description
| title: | Genuinely multipartite entangled states and orthogonal arrays |
| author: | Goyeneche Dardo, Życzkowski Karol 
|
| journal title: | Physical Review. A, Atomic, Molecular, and Optical Physics |
| volume: | 90 |
| issue: | 2 |
| date of publication : | 2014 |
| article ID: | 022316 |
| ISSN: |
1050-2947 |
| eISSN: |
1094-1622 1538-4446 |
| DOI: | |
| language: | English |
| journal language: | English |
| abstract in English: | A pure quantum state of N subsystems with d levels each is called k-multipartite maximally entangled state, which we call a k-uniform state, if all its reductions to k qudits are maximally mixed. These states form a natural generalization of N-qudit Greenberger-Horne-Zeilinger states which belong to the class 1-uniform states. We establish a link between the combinatorial notion of orthogonal arrays and k-uniform states and prove the existence of several classes of such states for N-qudit systems. In particular, known Hadamard matrices allow us to explicitly construct 2-uniform states for an arbitrary number of N>5 qubits. We show that finding a different class of 2-uniform states would imply the Hadamard conjecture, so the full classification of 2-uniform states seems to be currently out of reach. Furthermore, we establish links between the existence of k-uniform states and classical and quantum error correction codes and provide a graph representation for such states. |
| keywords in English: | genuine multipartite entanglement, orthogonal arrays, Hadamard matrices |
| number of pulisher's sheets: | 2 |
| affiliation: | Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego |
| type: | journal article |
| subtype: | academic paper |
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