Quantum $k$-uniform states from quantum orthogonal arrays

Abstract

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform states whose every reductions to $k$ parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength 2 with levels of prime power, as well as some constructions of strength 3. As a consequence, we give infinite classes of 2-uniform states of $N$ systems with dimension of prime power $d\ge 2$ for arbitrary $N\ge 5$; 3-uniform states of $N$-qubit systems for arbitrary $N\ge 6$ and $N\ne 7,8,9,11$; 3-uniform states of $N$ systems with dimension of prime power $d\ge 7$ for arbitrary $N\ge 7$.

26 pages, 1 figures

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• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Maximally multipartite entangled states
• Genuinely multipartite entangled states and orthogonal arrays
• Quantum Teamwork for Unconditional Multiparty Communication with Gaussian States
• Holographic codes