# Construction of mutually unbiased bases in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}$$ C d ⊗ C 2 l d ′

Construction of mutually unbiased bases in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}$$... We study mutually unbiased bases in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}$$ C d ⊗ C 2 l d ′ . A systematic way of constructing mutually unbiased maximally entangled bases (MUMEBs) in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'} (l\in {\mathbb {Z}}^{+})$$ C d ⊗ C 2 l d ′ ( l ∈ Z + ) from MUMEBs in $${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd, k\in {\mathbb {Z}}^+)$$ C d ⊗ C d ′ ( d ′ = k d , k ∈ Z + ) and a general approach to construct mutually unbiased unextendible maximally entangled bases (MUUMEBs) in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^ld'} (l \in {\mathbb {Z}}^{+})$$ C d ⊗ C 2 l d ′ ( l ∈ Z + ) from MUUMEBs in $${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd+r, 0<r<d)$$ C d ⊗ C d ′ ( d ′ = k d + r , 0 < r < d ) have been presented. Detailed examples are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Construction of mutually unbiased bases in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}$$ C d ⊗ C 2 l d ′

, Volume 14 (7) – Apr 19, 2015
10 pages

/lp/springer_journal/construction-of-mutually-unbiased-bases-in-mathbb-c-d-otimes-mathbb-c-ME70yoewWS
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-0961-9
Publisher site
See Article on Publisher Site

### Abstract

We study mutually unbiased bases in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}$$ C d ⊗ C 2 l d ′ . A systematic way of constructing mutually unbiased maximally entangled bases (MUMEBs) in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'} (l\in {\mathbb {Z}}^{+})$$ C d ⊗ C 2 l d ′ ( l ∈ Z + ) from MUMEBs in $${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd, k\in {\mathbb {Z}}^+)$$ C d ⊗ C d ′ ( d ′ = k d , k ∈ Z + ) and a general approach to construct mutually unbiased unextendible maximally entangled bases (MUUMEBs) in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^ld'} (l \in {\mathbb {Z}}^{+})$$ C d ⊗ C 2 l d ′ ( l ∈ Z + ) from MUUMEBs in $${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd+r, 0<r<d)$$ C d ⊗ C d ′ ( d ′ = k d + r , 0 < r < d ) have been presented. Detailed examples are given.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Apr 19, 2015

### References

• Quantum systems with finite Hilbert space
Vourdas, A
• Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases
Mafu, M; Dudley, A; Goyal, S; Giovannini, D; McLaren, M; Padgett, MJ; Konrad, T; Petruccione, F; Lutkenhaus, N; Forbes, A
• Increasing the security of the ping-pong protocol by using many mutually unbiased bases
Zawadzki, P; Puchala, Z; Miszczak, JA
• Unextendible maximally entangled bases and mutually unbiased bases
Chen, B; Fei, SM

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