Next Article in Journal
A Note on Complexities by Means of Quantum Compound Systems
Next Article in Special Issue
A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises
Previous Article in Journal
Robust and Scalable Learning of Complex Intrinsic Dataset Geometry via ElPiGraph
Previous Article in Special Issue
Analytic Expression of Quantum Discords in Werner States under LQCC
Open AccessArticle

Symmetry-Like Relation of Relative Entropy Measure of Quantum Coherence

School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(3), 297; https://doi.org/10.3390/e22030297
Received: 18 January 2020 / Revised: 18 February 2020 / Accepted: 25 February 2020 / Published: 5 March 2020
(This article belongs to the Special Issue Quantum Information Processing)
Quantum coherence is an important physical resource in quantum information science, and also as one of the most fundamental and striking features in quantum physics. To quantify coherence, two proper measures were introduced in the literature, the one is the relative entropy of coherence C r ( ρ ) = S ( ρ diag ) S ( ρ ) and the other is the 1 -norm of coherence C 1 ( ρ ) = i j | ρ i j | . In this paper, we obtain a symmetry-like relation of relative entropy measure C r ( ρ A 1 A 2 A n ) of coherence for an n-partite quantum states ρ A 1 A 2 A n , which gives lower and upper bounds for C r ( ρ ) . As application of our inequalities, we conclude that when each reduced states ρ A i is pure, ρ A 1 A n is incoherent if and only if the reduced states ρ A i and tr A i ρ A 1 A n ( i = 1 , 2 , , n ) are all incoherent. Meanwhile, we discuss the conjecture that C r ( ρ ) C 1 ( ρ ) for any state ρ , which was proved to be valid for any mixed qubit state and any pure state, and open for a general state. We observe that every mixture η of a state ρ satisfying the conjecture with any incoherent state σ also satisfies the conjecture. We also observe that when the von Neumann entropy is defined by the natural logarithm ln instead of log 2 , the reduced relative entropy measure of coherence C ¯ r ( ρ ) = ρ diag ln ρ diag + ρ ln ρ satisfies the inequality C ¯ r ( ρ ) C 1 ( ρ ) for any state ρ . View Full-Text
Keywords: quantum coherence; measure; lower bound; upper bound quantum coherence; measure; lower bound; upper bound
MDPI and ACS Style

Zhang, C.; Guo, Z.; Cao, H. Symmetry-Like Relation of Relative Entropy Measure of Quantum Coherence. Entropy 2020, 22, 297.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop