Quantum coherence in mutually unbiased bases

Abstract

We investigate the l1 norm of coherence of quantum states in mutually unbiased bases. We find that the sum of squared l1 norm of coherence of the mixed state single qubit is less than two. We derive the l1 norm of coherence of three classes of X states in nontrivial mutually unbiased bases for 4-dimensional Hilbert space is equal. We proposed "autotensor of mutually unbiased basis(AMUB)" by the tensor of mutually unbiased bases, and depict the level surface of constant the sum of the l1 norm of coherence of Bell-diagonal states in AMUB. We find the l1 norm of coherence of Werner states and isotropic states in AMUB is equal respectively.

Geometry of skew information-based quantum coherence

“…for ¹ k l. The following set is an AMUBs derived from two-dimensional MUBs [61]: In general, a two qubit X states can be represented as…”

“…The level surfaces of entanglement and quantum discord for Bell-diagonal states [57], the level surfaces of quantum discord for a class of twoqubit states [58], the geometry of one-way information deficit for a class of two-qubit states [59], the surfaces of constant quantum discord and super-quantum discord for Bell-diagonal states [60] have been depicted. Recently, the l 1 norm of coherence of quantum states in MUBs has been discussed [61], and the geometry with respect to relative entropy of coherence and l 1 norm of coherence for Bell-diagonal states has been investigated [62,63].…”

Mutually unbiased coherence of Bell Diagonal States*

“…The dependence of coherence value on the reference basis underscores the importance of exploring the relationship between quantum coherence and MUBs. Hu [20] demonstrated that MUBs are optimal for various coherence measures, Alexey et al [21] introduced a novel coherence quantifier based on uncertainty relations within a set of MUBs, Wang [22] calculated the l 1 norm coherence for Bell-diagonal states using the autotensor of MUBs (AMUBs), while Cheng [23] proposed complementary relations between the l 1 norm coherence and the relative entropy of coherence across all complete sets of MUBs. Furthermore, Wu [24] analyzed the skew information of coherence for Bell-diagonal states under AMUBs, elucidating its geometric structure.…”

Complementary relations between l p norm coherence and mixedness of quantum states

“…It is shown that any two-qubit states can be transformed into the Bell-diagonal state under irreversible stochastic local operation and classical communication [21]. The theoretical and experimental study on Bell-diagonal states has attracted much attention as it can paves the way for the study of other complex problems, for example, the geometries of the quantum correlation [22][23][24][25][26][27][28], the level surfaces of quantum coherence [29][30][31][32][33], and the surfaces of the complementary relations between coherence and mixedness [34][35][36][37][38].…”