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:quant-ph/0305080 · International Journal of Quantum Information

SEPARABILITY OF RANK TWO QUANTUM STATES ON MULTIPLE QUANTUM SPACES WITH DIFFERENT DIMENSIONS

Shao-Ming Fei, Xiu-Hong Gao, Xiaohong Wang, Zhi‐Xi Wang, Ke Wu

Published Mar 1, 2003• 5 citations
arXivHTMLPDF

Abstract

We consider the separability of rank two quantum states on multiple quantum spaces with different dimensions. The sufficient and necessary conditions for separability of these multiparty quantum states are explicitly presented. A nonseparability inequality is also given for the case where one of the eigenvectors corresponding to nonzero eigenvalues of the density matrix is maximally entangled.

DOI
10.1142/s0219749903000048

Related papers

Separability of Rank—Two Quantum States in C^M ×CN Composite Quantum Systems

FEIShao-Ming, GAOXiu-Hong, WANGXiao-Hong +2 more

We consider rank-two density matrices ρ supported on an M × N Hilbert space for arbitrary dimensions M and N. Explicit sufficient and necessary conditions for separability of ρ are presented.

理论物理通讯：英文版•Jan 1, 2003•0 citations

Separability of Rank-Two Quantum States in $C^M \otimes C^N$ Composite Quantum Systems

Shao-Ming Fei, Xiu-Hong Gao, Xiaohong Wang +2 more

We consider rank-two density matrices ρ supported on an M × N Hilbert space for arbitrary dimensions M and N . Explicit sufficient and necessary conditions for separability of ρ are presented.

Communications in Theoretical Physics•May 15, 2003•2 citations

CANONICAL FORM AND SEPARABILITY OF PPT STATES ON MULTIPLE QUANTUM SPACES

Xiaohong Wang, Shao-Ming Fei

By using the "subtracting projectors" method in proving the separability of PPT states on multiple quantum spaces, we derive a canonical form of PPT states in [Formula: see text] composite quantum systems with rank N, from which a sufficient separability condition for these states is presented.

arXiv:quant-ph/0504145•International Journal of Quantum Information•Dec 17, 2004•2 citations

Multiparticle entanglement and ranks of density matrices

Joachim Stolze, Bo Chong, Hellmut Keiter

Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we obtain necessary conditions for the separability of a given mixed state with respect to partitions of all particles of the system into subsets. The special case of pure states is discussed separately.

arXiv:quant-ph/0512199•Jan 1, 2005•1 citation

SEPARABILITY OF PURE N-QUBIT STATES: TWO CHARACTERIZATIONS

Philippe Jorrand, Mehdi Mhalla

Given a pure state |ψN>∈ℋN of a quantum system composed of n qubits, where ℋN is the Hilbert space of dimension N=2n, this paper answers two questions: what conditions should the amplitudes in |ψN> satisfy for this state to be separable (i) into a tensor product of n qubit states |ψ2>0⊗ |ψ2>1 ⊗⋯⊗ |ψ2>n-1, and (ii), into a tensor product of two subsystems states |ψP> ⊗ |ψQ> with P=2p and Q=2q such that p+q=n? For both questions, necessary and sufficient conditions are proved, thus characterizing at the same time families of separable and entangled states of n qubit systems. A number of more refined questions about separability in n qubit systems can be studied on the basis of these results.

arXiv:quant-ph/0209125•International Journal of Foundations of Computer Science•Oct 1, 2003•10 citations

Separable States Are More Disordered Globally than Locally

Michael A. Nielsen, Julia Kempe

A remarkable feature of quantum entanglement is that an entangled state of two parties, Alice ( A) and Bob ( B), may be more disordered locally than globally. That is, S(A)>S(A,B), where S(*) is the von Neumann entropy. It is known that satisfaction of this inequality implies that a state is nonseparable. In this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system AB is majorized by the vector of eigenvalues of the density matrix of system A alone. This gives a strong sense in which a separable state is more disordered globally than locally and a new necessary condition for separability of bipartite states in arbitrary dimensions.

arXiv:quant-ph/0011117•Physical Review Letters•May 28, 2001•299 citations
We consider the separability of rank two quantum states on multiple quantum spaces with different dimensions. The sufficient and necessary conditions for separability of these multiparty quantum states are explicitly presented. A nonseparability inequality is also given for the case where one of the eigenvectors corresponding to nonzero eigenvalues of the density matrix is maximally entangled.
Separability of Rank-Two Quantum States in CM⊗CNC^M \otimes C^NCM⊗CN Composite Quantum Systems
Given a pure state |ψN>∈ℋN of a quantum system composed of n qubits, where ℋN is the Hilbert space of dimension N=2n, this paper answers two questions: what conditions should the amplitudes in |ψN> satisfy for this state to be separable (i) into a tensor product of n qubit states |ψ2>0⊗ |ψ2>1 ⊗⋯⊗ |ψ2>n-1, and (ii), into a tensor product of two subsystems states |ψP> ⊗ |ψQ> with P=2p and Q=2q such that p+q=n? For both questions, necessary and sufficient conditions are proved, thus characterizing at the same time families of separable and entangled states of n qubit systems. A number of more refined questions about separability in n qubit systems can be studied on the basis of these results.
A remarkable feature of quantum entanglement is that an entangled state of two parties, Alice ( A) and Bob ( B), may be more disordered locally than globally. That is, S(A)>S(A,B), where S(*) is the von Neumann entropy. It is known that satisfaction of this inequality implies that a state is nonseparable. In this paper we prove the stronger result that for separable states the vector of eigenvalues of the density matrix of system AB is majorized by the vector of eigenvalues of the density matrix of system A alone. This gives a strong sense in which a separable state is more disordered globally than locally and a new necessary condition for separability of bipartite states in arbitrary dimensions.