Local implementation of nonlocal operations of block forms

We investigate the local implementation of nonlocal operations with the block matrix form, and propose a protocol for any diagonal or offdiagonal block operation. This method can be directly generalized to the two-party multiqubit case and the multiparty case. Especially, in the multiparty cases, any diagonal block operation can be locally implemented using the same resources as the multiparty control-U operation discussed in Ref. [Eisert et al., Phys. Rev. A 62, 052317(2000)]. Although in the bipartite case, this kind of operations can be transformed to control-U operation using local operations, these transformations are impossible in the multiparty cases. We also compare the local implementation of nonlocal block operations with the remote implementation of local operations, and point out a relation between them.Comment: 7 pages, 3 figure

Toward Learning Societies for Digital Aging

The global aging population presents significant challenges for societies worldwide, particularly in an increasingly digitalized era. The Learning Society is crucial in preparing different societies and their people to address these challenges effectively. This paper extends this concept and proposes a new conceptual framework, Learning Societies for Digital Aging, empowering all members across various sectors from different ages to acquire and develop the necessary knowledge, skills, and competencies to navigate and thrive in an increasingly digital world. It presents seven guiding principles for developing this conceptual framework: 1) Centering Humanistic Values, 2) Embracing Digital, 3) Cultivating Learning Societies, 4) Advancing Inclusiveness, 5) Taking Holistic Approaches, 6) Encouraging Global Knowledge Sharing, and 7) Fostering Adaptability. By integrating these guiding principles into the design, implementation, and evaluation of formal, nonformal, and informal learning opportunities for people of all ages, stakeholders can contribute to creating and nurturing learning societies that cater to aging populations in the digital world. This paper aims to provide a foundation for further research and action toward building more inclusive, adaptive, and supportive learning environments that address the challenges of digital aging and foster more empathetic, informed, and prepared societies for the future of aging

Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping

In this paper we study blow-up and lifespan estimate for solutions to the Cauchy problem with small data for semilinear wave equations with scattering damping and negative mass term. We show that the negative mass term will play a dominant role when the decay of its coefficients is not so fast, thus the solutions will blow up in a finite time. What is more, we establish a lifespan estimate from above which is much shorter than the usual one.Comment: 14 pages. Accepted by a guest editor of a special volume on MSJ-SI 2018 in the journal of Advanced Studies in Pure Mathematic