# The number of terms in the superpositions upper bounds the amount of the coherence change

The number of terms in the superpositions upper bounds the amount of the coherence change For the \$\$l_{1}\$\$ l 1 norm of coherence, what is the relation between the coherence of a state and the individual terms that by superposition yield the state? We find upper bounds on the coherence change before and after the superposition. When every term comes from one Hilbert subspace, the upper bound is the number of terms in the superpositions minus one. However, when the terms have support on orthogonal subspaces, the coherence of the superposition cannot be more the double of the above upper bound than the average of the coherence of the all terms being superposed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# The number of terms in the superpositions upper bounds the amount of the coherence change

, Volume 15 (10) – Jul 28, 2016
7 pages

/lp/springer_journal/the-number-of-terms-in-the-superpositions-upper-bounds-the-amount-of-xkv0DiaBXf
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/s11128-016-1399-4
Publisher site
See Article on Publisher Site

### Abstract

For the \$\$l_{1}\$\$ l 1 norm of coherence, what is the relation between the coherence of a state and the individual terms that by superposition yield the state? We find upper bounds on the coherence change before and after the superposition. When every term comes from one Hilbert subspace, the upper bound is the number of terms in the superpositions minus one. However, when the terms have support on orthogonal subspaces, the coherence of the superposition cannot be more the double of the above upper bound than the average of the coherence of the all terms being superposed.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 28, 2016

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