题目：Gaussian quantum information over general quantum kinematical systems
报告人：Hun Hee LEE（首尔国立大学）
摘要：In quantum information theory (QIT) focusing on the realizations through optical devices the right mathematical formulation comes from the n-modes Bosonic quantum systems. The corresponding Hilbert space is L2(R2n), which is infinite dimensional. Since the set of quantum states are too large for analysis the researchers usually focus on the particular choices called the Gaussian state, thus the terminology Gaussian QIT is justified.
In this talk we develop a theory of Gaussian states over general quantum kinematical systems with finitely many degrees of freedom. The abstraction begins with replacing the phase space R2n with a locally compact abelian (LCA) group G with a symplectic structure determined by a 2-cocycle on G. We use the concept of Gaussian distributions on LCA groups in the sense of Bernstein to define Gaussian states and completely characterize Gaussian states over 2-regular LCA groups of the form G= F×∧F endowed with a canonical normalized 2-cocycle. This covers the case of n-qudit systems with odd d≥3, and p-adic quantum systems, angle-number systems with phase space Tn×Zn and fermionic/hard-core bosonic systems with phase space Z22n.