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Qiang Lei

Publications and source records attributed to Qiang Lei.

9 recordsLinked to original sources
arXiv2026

Quantifying and detecting quantum-state texture

Quantum-state texture is a recently proposed quantum resource that characterizes the inhomogeneity of a quantum state's matrix element distribution in the computational basis, enriching our understanding of quantum state structure. To expand its quantification toolkit and establish detection methods, in this article, we investigate the resource theory of texture from both quantitative and detection perspectives. First, we construct a texture measure $\mathcal{T}^{\text{GR}}_{\alpha,z}(\rho)$ based on the $\alpha$-$z$ R\'enyi relative entropy and present some of its inherent properties. Second, we analyze the mathematical relationships between several existing texture measures, revealing connections among different quantifiers. Finally, drawing on the witness concept from other resource theories, we systematically introduce texture witnesses into the texture theory and provide examples of texture witnesses with special properties.

quant-ph↗
arXiv2026

Construction and characterization of measures in block coherence resource theory

Quantum coherence, as a direct manifestation of the quantum superposition principle, is a crucial resource in quantum information processing. Block coherence resource theory generalizes the traditional coherence framework by defining coherence via a set of orthogonal projectors. Within this framework, we investigates the construction and comparison of block coherence measures. First, we propose two universal methods for constructing coherence measures and introduce a two-parameter family of measures based on the $\alpha$-$z$ R\'enyi relative entropy and a family of measures based on the Tsallis relative operator entropy. Second, through theoretical proofs and numerical counterexamples, we compares the ordering relations and numerical magnitudes among different block coherence measures and establishes a series of universal numerical inequalities to constrain their values. Besides, we also use $C_{\alpha,1}$ to show the role of coherence in complex dynamic evolution of the Kominis master equation that includes recombination reactions.

quant-ph↗
arXiv2024

Imaginarity of quantum channels: Refinement and Alternative

In this paper, we introduce the framework for quantifying the imaginarity of quantum channels. Besides, an alternative framework is given together to simplify the process of verifying the condition. We present three imaginarity measures of quantum channels based on the robustness, the trace norm, and the entropy, respectively. Some properties are also given.

quant-ph↗
arXiv2024

Imaginarity measures induced by relative entropy

In this paper, we introduce two measures for the resource theory of imaginarity. One is induced by $\alpha$--$z$--R\'enyi relative entropy and the other, defined for positive definite density matrices, is induced by Tsallis relative operator entropy. The relationships between different imaginarity measures and their properties are also discussed.

quant-ph↗
arXiv2023

Dilation, Discrimination and Uhlmann's Theorem of Link Products of Quantum Channels

The study of quantum channels is the most fundamental theoretical problem in quantum information and quantum communication theory. The link product theory of quantum channels is an important tool for studying quantum networks. In this paper, we establish the Stinespring dilation theorem of the link product of quantum channels in two different ways, discuss the discrimination of quantum channels and show that the distinguishability can be improved by self-linking each quantum channel n times as n grows. We also find that the maximum value of Uhlmann's theorem can be achieved for diagonal channels.

quant-ph↗
arXiv2018

Quantum Observable Generalized Orthoalgebras

Let ${\cal S}(\mathcal{H})$ denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space $\mathcal{H}$, which is the set of all physical quantities on a quantum system $\mathcal{H}$. We introduce a binary relation $\bot$ on ${\cal S}(\mathcal{H})$. We show that if $A\bot B$, then $A$ and $B$ are affiliated with some abelian von Neumann algebra. The relation $\bot$ induces a partial algebraic operation $\oplus$ on ${\cal S}(\mathcal{H})$. We prove that $({\cal S}({\mathcal{H}}), \bot, \oplus, 0)$ is a generalized orthoalgebra. This algebra is a generalization of the famous Birkhoff\,--\,von Neumann quantum logic model. It establishes a mathematical structure on all physical quantities on $\mathcal{H}$. In particular, we note that $({\cal S}({\mathcal{H}}), \bot, \oplus, 0)$ has a partial order $\preceq$, and prove that $A\preceq B$ if and only if $A$ has a value in $Δ$ implies that $B$ has a value in $Δ$ for every Borel set $Δ$ not containing $0$. Moreover, the existence of the infimum $A\wedge B$ and supremum $A\vee B$ for $A,B\in \mathcal{S}(\mathcal{H})$ (with respect to $\preceq$) is studied, and it is shown at the end that the position operator $Q$ and momentum operator $P$ in the Heisenberg commutation relation satisfy $Q\wedge P=0$.

math-ph↗
arXiv2015

The Continuity of Sequential Product of Sequential Quantum Effect Algebras

In order to study quantum measurement theory, sequential product defined for any two quantum effects is introduced. Physically motivated conditions ask the sequential product to be continuous with respect to the strong operator topology. In this paper, we study the continuity problems of the sequential product with respect to the other important topologies, as norm topology, weak operator topology, order topology, interval topology, etc.

math-ph↗