Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1612.01092 · International Journal of Theoretical Physics

Constructing Separable States in Infinite-Dimensional Systems by Operator Matrices

Jinchuan Hou, Jinfei Chai

Published Mar 25, 2017• 2 citations
arXivHTMLPDF
DOI
10.1007/s10773-017-3346-2

Related papers

Realignment Operation and CCNR Criterion of Separability for States in Infinite-Dimensional Quantum Systems

Yu Jing Guo, Jinchuan Hou

Reports on Mathematical Physics•Aug 1, 2013•10 citations

The canonical forms of matrix product states in infinite-dimensional Hilbert spaces

Niilo Heikkinen

Abstract In this work, we prove that any element in the tensor product of separable infinite-dimensional Hilbert spaces can be expressed as a matrix product state (MPS) of possibly infinite bond dimension. The proof is based on the singular value decomposition of compact operators and the connection between tensor products and Hilbert–Schmidt operators via the Schmidt decomposition in infinite-dimensional separable Hilbert spaces. The construction of infinite-dimensional MPS (idMPS) is analogous to the well-known finite-dimensional construction in terms of singular value decompositions of matrices. The infinite matrices in idMPS give rise to operators acting on (possibly infinite-dimensional) auxiliary Hilbert spaces. As an example we explicitly construct an MPS representation for certain eigenstates of a chain of three coupled harmonic oscillators.

arXiv:2502.12934•Journal of Physics A Mathematical and Theoretical•Jul 28, 2025•0 citations

Quantum Systems in Finite-Dimensional Hilbert Spaces

Gianluca Stefanucci

Springer eBooks•Jan 1, 2024•0 citations

Fidelity of states in infinite-dimensional quantum systems

Jinchuan Hou, Xiaofei Qi

arXiv:1107.0354•Science China Physics Mechanics and Astronomy•Aug 9, 2012•16 citations

Violation of the area law and long-range correlations in infinite-dimensional-matrix product states

Anne E. B. Nielsen, Germán Sierra, J. I. Cirac

We propose to construct a family of states of one-dimensional spin chains by replacing the finite-dimensional matrices in matrix product states by infinite-dimensional operators constructed from bosonic annihilation and creation operators. The resulting states are demonstrated to violate the area law and to exhibit long-range correlations. In addition, we propose an efficient way to prepare the states experimentally, in which the spins interact sequentially with an ancilla system.

arXiv:1103.2205•Physical Review A•May 6, 2011•15 citations

Separability of Quantum Systems: A Density Matrix Approach

Roy Mcweeny

Advances in quantum chemistry•Jan 1, 1998•17 citations
Abstract In this work, we prove that any element in the tensor product of separable infinite-dimensional Hilbert spaces can be expressed as a matrix product state (MPS) of possibly infinite bond dimension. The proof is based on the singular value decomposition of compact operators and the connection between tensor products and Hilbert–Schmidt operators via the Schmidt decomposition in infinite-dimensional separable Hilbert spaces. The construction of infinite-dimensional MPS (idMPS) is analogous to the well-known finite-dimensional construction in terms of singular value decompositions of matrices. The infinite matrices in idMPS give rise to operators acting on (possibly infinite-dimensional) auxiliary Hilbert spaces. As an example we explicitly construct an MPS representation for certain eigenstates of a chain of three coupled harmonic oscillators.