# Ordering states with Tsallis relative $$\alpha$$ α -entropies of coherence

Ordering states with Tsallis relative $$\alpha$$ α -entropies of coherence In this paper, we study the ordering states with Tsallis relative $$\alpha$$ α -entropies of coherence and $$l_{1}$$ l 1 norm of coherence for single-qubit states. Firstly, we show that any Tsallis relative $$\alpha$$ α -entropies of coherence and $$l_{1}$$ l 1 norm of coherence give the same ordering for single-qubit pure states. However, they do not generate the same ordering for some high-dimensional states, even though these states are pure. Secondly, we also consider three special Tsallis relative $$\alpha$$ α -entropies of coherence for $$\alpha =2, 1, \frac{1}{2}$$ α = 2 , 1 , 1 2 and show these three measures and $$l_{1}$$ l 1 norm of coherence will not generate the same ordering for some single-qubit mixed states. Nevertheless, they may generate the same ordering if we only consider a special subset of single-qubit mixed states. Furthermore, we find that any two of these three special measures generate different ordering for single-qubit mixed states. Finally, we discuss the degree of violation of between $$l_{1}$$ l 1 norm of coherence and Tsallis relative $$\alpha$$ α -entropies of coherence. In a sense, this degree can measure the difference between these two coherence measures in ordering states. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Ordering states with Tsallis relative $$\alpha$$ α -entropies of coherence

, Volume 16 (1) – Dec 22, 2016
17 pages

/lp/springer_journal/ordering-states-with-tsallis-relative-alpha-entropies-of-coherence-2bJYic5CSn
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/s11128-016-1488-4
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we study the ordering states with Tsallis relative $$\alpha$$ α -entropies of coherence and $$l_{1}$$ l 1 norm of coherence for single-qubit states. Firstly, we show that any Tsallis relative $$\alpha$$ α -entropies of coherence and $$l_{1}$$ l 1 norm of coherence give the same ordering for single-qubit pure states. However, they do not generate the same ordering for some high-dimensional states, even though these states are pure. Secondly, we also consider three special Tsallis relative $$\alpha$$ α -entropies of coherence for $$\alpha =2, 1, \frac{1}{2}$$ α = 2 , 1 , 1 2 and show these three measures and $$l_{1}$$ l 1 norm of coherence will not generate the same ordering for some single-qubit mixed states. Nevertheless, they may generate the same ordering if we only consider a special subset of single-qubit mixed states. Furthermore, we find that any two of these three special measures generate different ordering for single-qubit mixed states. Finally, we discuss the degree of violation of between $$l_{1}$$ l 1 norm of coherence and Tsallis relative $$\alpha$$ α -entropies of coherence. In a sense, this degree can measure the difference between these two coherence measures in ordering states.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 22, 2016

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