Seminar on Positive Linear maps and Quantum Information

Seminar on Positive Linear maps and Quantum Information

Time:

Venue/Location: Phòng C102, VIASM

Abstract: Quantum entanglement is a key resource in quantum information theory, and detecting entangled states is a fundamental problem. Positive linear maps on matrix algebras provide an effective tool for this purpose, as they correspond to entanglement witnesses via the Choi–JamioĊ‚kowski isomorphism.

In this work, we study the construction and structural properties of positive (but not completely positive) linear maps, including decomposable and indecomposable cases, and analyze their role in detecting entangled states. Our results highlight the connection between operator theory and the geometry of quantum states.

Titles and Speakers:

  1. Talk 1: Detecting quantum entanglement witnesses by positive linear maps on matrix algebras I

Time: 2PM -3:30 Tuesday, March 11, 2026

Speaker: Hiroyuki Osaka (Ritsumeikan University, Japan)

  1. Talk 2: Detecting quantum entanglement witnesses by positive linear maps on matrix algebras II

Time: 2PM-3:30 Friday March 13, 2026

Speaker: Hiroyuki Osaka (Ritsumeikan University, Japan)

  1. Talk 3: Detecting quantum entanglement witnesses by positive linear maps on matrix algebras III

Time: 2PM-3:30 Monday, March 16, 2026

Speaker: Hiroyuki Osaka (Ritsumeikan University, Japan)

  1. Talk 4: The Spectral Geometric Mean and Trace Characterizations (this is a joint work with Drs. Anh Vu Le, A.M. Bikchentaev and M.S. Moslehian).

Time: 10 AM -11:30 Tuesday, March 17, 2026

Speaker: Dinh Trung Hoa (Troy University, USA)