Nowadays, geometric tools are being used to treat a huge class of problems of quantum information science. By understanding the interplay between the geometry of the state space and information-theoretic quantities, it is possible to obtain less trivial and more robust physical constraints on quantum systems. Here we establish a geometric lower bound for the Wigner-Yanase skew information (WYSI), a well-known information-theoretic quantity recently recognized as a proper quantum coherence measure. In the case of a mixed state evolving under unitary dynamics generated by a given observable, the WYSI between the state and the observable is bounded from below by the rate of change of the state's statistical distinguishability from its initial value. Our result shows that, since WYSI fits in the class of Petz's metrics, this lower bound is the change rate of its respective geodesic distance on quantum state space. The geometric approach is advantageous because it raises several physical interpretations of this inequality under the same theoretical umbrella.Nowadays, geometric tools are being used to treat a huge class of problems of quantum information science. By understanding the interplay between the geometry of the state space and information-theoretic quantities, it is possible to obtain less trivial and more robust physical constraints on quantum systems. Here we establish a geometric lower bound for the Wigner-Yanase skew information (WYSI), a well-known information-theoretic quantity recently recognized as a proper quantum coherence measure. In the case of a mixed state evolving under unitary dynamics generated by a given observable, the WYSI between the state and the observable is bounded from below by the rate of change of the state's statistical distinguishability from its initial value. Our result shows that, since WYSI fits in the class of Petz's metrics, this lower bound is the change rate of its respective geodesic distance on quantum state space. The geometric approach is advantageous because it raises several physical interpretations of this inequality under the same theoretical umbrella.

arXiv:1501.05271Physical Review AApr 23, 2015106 citations

Resource Letter QIE-1: Research in quantum information education

Josephine C. Meyer, Simon Goorney, Tunde Kushimo +1 more

In celebration of the 2025 UN International Year of Quantum Science and Technology, this Resource Letter surveys the rapidly-growing field of scholarship in quantum information science and engineering (QISE) education. It is primarily written as a guide for educators wishing to get started teaching QISE using research-based teaching methods, as well as for discipline-based education research (DBER) practitioners looking to get started in this field. Topics covered include scoping the field of QISE education, research into student reasoning in QISE, research-based and research-inspired curricular materials from the high school to graduate level, research-based assessments, simulation and gamification tools, and tools for incorporating discussion of the societal and ethical implications of quantum technologies into the classroom.In celebration of the 2025 UN International Year of Quantum Science and Technology, this Resource Letter surveys the rapidly-growing field of scholarship in quantum information science and engineering (QISE) education. It is primarily written as a guide for educators wishing to get started teaching QISE using research-based teaching methods, as well as for discipline-based education research (DBER) practitioners looking to get started in this field. Topics covered include scoping the field of QISE education, research into student reasoning in QISE, research-based and research-inspired curricular materials from the high school to graduate level, research-based assessments, simulation and gamification tools, and tools for incorporating discussion of the societal and ethical implications of quantum technologies into the classroom.

physics.ed-phCross-listedarXiv:2606.06445Jun 5, 2026

Quantum information processing with a geometric scenario

Qinghua Zhang

Jan 1, 20070 citations

Quantifying subspace entanglement with geometric measures

Xuanran Zhu, Chao Zhang, Bei Zeng

Determining whether a subspace spanned by certain quantum states is entangled and its entanglement dimensionality remains a fundamental challenge in quantum information science. This paper introduces a geometric measure of $r$ -bounded rank, ${E}_{r}(\mathcal{S})$ , for a given subspace $\mathcal{S}$ . Derived from the established geometric measure of entanglement, this measure is specifically designed to assess the entanglement within $\mathcal{S}$ . It not only serves as a tool for determining the entanglement dimensionality but also illuminates the subspace's capacity to preserve such entanglement. By employing developed nonconvex optimization techniques utilized in machine learning area, we can accurately calculate ${E}_{r}(\mathcal{S})$ within the manifold optimization framework. Our approach demonstrates notable advantages over existing hierarchical methods, PPT relaxation techniques, and the seesaw strategy, particularly by combining computational efficiency with broad applicability. More importantly, it paves the way for high-dimensional entanglement certification, which is crucial for numerous quantum information tasks. We showcase its effectiveness in validating high-dimensional entangled subspaces in bipartite systems, determining the border rank of multipartite pure states, and identifying genuinely or completely entangled subspaces.Determining whether a subspace spanned by certain quantum states is entangled and its entanglement dimensionality remains a fundamental challenge in quantum information science. This paper introduces a geometric measure of $r$-bounded rank, ${E}_{r}(\mathcal{S})$, for a given subspace $\mathcal{S}$. Derived from the established geometric measure of entanglement, this measure is specifically designed to assess the entanglement within $\mathcal{S}$. It not only serves as a tool for determining the entanglement dimensionality but also illuminates the subspace's capacity to preserve such entanglement. By employing developed nonconvex optimization techniques utilized in machine learning area, we can accurately calculate ${E}_{r}(\mathcal{S})$ within the manifold optimization framework. Our approach demonstrates notable advantages over existing hierarchical methods, PPT relaxation techniques, and the seesaw strategy, particularly by combining computational efficiency with broad applicability. More importantly, it paves the way for high-dimensional entanglement certification, which is crucial for numerous quantum information tasks. We showcase its effectiveness in validating high-dimensional entangled subspaces in bipartite systems, determining the border rank of multipartite pure states, and identifying genuinely or completely entangled subspaces.

arXiv:2311.10353Physical Review AJul 22, 20244 citations

A geometrical study in quantum information systems

彰夫藤原

Jan 1, 199512 citations

r

-bounded rank,

{E}_{r}(\mathcal{S})

, for a given subspace

\mathcal{S}

. Derived from the established geometric measure of entanglement, this measure is specifically designed to assess the entanglement within

\mathcal{S}

. It not only serves as a tool for determining the entanglement dimensionality but also illuminates the subspace's capacity to preserve such entanglement. By employing developed nonconvex optimization techniques utilized in machine learning area, we can accurately calculate

{E}_{r}(\mathcal{S})

within the manifold optimization framework. Our approach demonstrates notable advantages over existing hierarchical methods, PPT relaxation techniques, and the seesaw strategy, particularly by combining computational efficiency with broad applicability. More importantly, it paves the way for high-dimensional entanglement certification, which is crucial for numerous quantum information tasks. We showcase its effectiveness in validating high-dimensional entangled subspaces in bipartite systems, determining the border rank of multipartite pure states, and identifying genuinely or completely entangled subspaces.