To find the criterion of a set of positive-definite matrices which can be written as reduced density matrices of a multipartite matrix is a hard and important problem. When the problem is concerned with multiparty density matrices, it is much more significant for computational many-body physics and many-body quantum entanglement which is one of the focuses of current quantum information theory. We give several results on the necessary compatibility relations between a set of two-party reduced density matrices and a global state in Hilbert space ${N}_{A}\ifmmode\times\else\texttimes\fi{}{N}_{B}\ifmmode\times\else\texttimes\fi{}{N}_{C}$ where ${N}_{A}$ , ${N}_{B}$ , and ${N}_{C}$ are arbitrary.To find the criterion of a set of positive-definite matrices which can be written as reduced density matrices of a multipartite matrix is a hard and important problem. When the problem is concerned with multiparty density matrices, it is much more significant for computational many-body physics and many-body quantum entanglement which is one of the focuses of current quantum information theory. We give several results on the necessary compatibility relations between a set of two-party reduced density matrices and a global state in Hilbert space ${N}_{A}\ifmmode\times\else\texttimes\fi{}{N}_{B}\ifmmode\times\else\texttimes\fi{}{N}_{C}$ where ${N}_{A}$, ${N}_{B}$, and ${N}_{C}$ are arbitrary.

arXiv:quant-ph/0403151Physical Review ANov 29, 20056 citations

Quantum entanglement and its applications

Shengjun Wu

Jan 1, 20030 citations

Compatibility relations between the reduced and global density matrices

Yong‐Jian Han, Y.-S. Zhang, Guang‐Can Guo

It is a hard and important problem to find the criterion of a set of positive-definite matrices which can be written as reduced density operators of a multipartite global quantum state. This problem is closely related to the study of many-body quantum entanglement, which is one of the focuses of current quantum-information theory. We give several results on the necessary compatibility relations between a set of reduced and global density matrices, including (i) compatibility conditions for the one-party reduced density matrices of any $({N}_{A}\ifmmode\times\else\texttimes\fi{}{N}_{B})$-dimensional bipartite mixed quantum state, (ii) compatibility conditions for the one-party reduced matrices of any $M$ -partite quantum states with the dimension ${N}^{\ensuremath{\bigotimes}M}$, and (iii) compatibility conditions for the two-party reduced density matrixes of $(2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2)$-dimensional tripartite mixed quantum state.It is a hard and important problem to find the criterion of a set of positive-definite matrices which can be written as reduced density operators of a multipartite global quantum state. This problem is closely related to the study of many-body quantum entanglement, which is one of the focuses of current quantum-information theory. We give several results on the necessary compatibility relations between a set of reduced and global density matrices, including (i) compatibility conditions for the one-party reduced density matrices of any $({N}_{A}\ifmmode\times\else\texttimes\fi{}{N}_{B})$-dimensional bipartite mixed quantum state, (ii) compatibility conditions for the one-party reduced matrices of any $M$-partite quantum states with the dimension ${N}^{\ensuremath{\bigotimes}M}$, and (iii) compatibility conditions for the two-party reduced density matrixes of $(2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2)$-dimensional tripartite mixed quantum state.

Physical Review AMay 5, 200513 citations

Quantum entanglement and the Bell matrix

Anna Chiara Lai, Marco Pedicini, Silvia Rognone

Quantum Information ProcessingApr 13, 20161 citation

Quantum Entanglement Theory

Michigan State University Press eBooksJan 1, 20260 citations

Entangling power of quantized chaotic systems

Arul Lakshminarayan

We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied through the von Neumann entropy of the reduced density matrices. We demonstrate that classical chaos can lead to substantially enhanced entanglement. Conversely, entanglement provides a useful characterization of quantum states in higher-dimensional chaotic or complex systems. Information about eigenfunction localization is stored in a graded manner in the Schmidt vectors, and the principal Schmidt vectors can be scarred by the projections of classical periodic orbits onto subspaces. The eigenvalues of the reduced density matrices is sensitive to the degree of wave-function localization, and is roughly exponentially arranged. We also point out the analogy with decoherence, as reduced density matrices corresponding to subsystems of fully chaotic systems, are diagonally dominant.We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied through the von Neumann entropy of the reduced density matrices. We demonstrate that classical chaos can lead to substantially enhanced entanglement. Conversely, entanglement provides a useful characterization of quantum states in higher-dimensional chaotic or complex systems. Information about eigenfunction localization is stored in a graded manner in the Schmidt vectors, and the principal Schmidt vectors can be scarred by the projections of classical periodic orbits onto subspaces. The eigenvalues of the reduced density matrices is sensitive to the degree of wave-function localization, and is roughly exponentially arranged. We also point out the analogy with decoherence, as reduced density matrices corresponding to subsystems of fully chaotic systems, are diagonally dominant.

arXiv:nlin/0012010Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsAug 20, 2001146 citations

{N}_{A}

{N}_{B}

, and

{N}_{C}

are arbitrary.

M

-partite quantum states with the dimension ${N}^{\ensuremath{\bigotimes}M}$, and (iii) compatibility conditions for the two-party reduced density matrixes of $(2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2)$-dimensional tripartite mixed quantum state.