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

Journal of Nanchang University

The Calculation of Local Invariants For Bipartite Systems

Gong Ren-shan

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

By using the most general expression for the density matrix of bipartite systems,which has been given by virtue of the generatiors of su(N) algebra,and the matrix trace method for spectral resolution of density matrix,proposed by author before,it presents a complete set of successive iteration formulas for calculating all the local invariants for bipartite systems having a generic density matrix with full rank.Then,it shows that the complete set of local invariants proposed by S.Albeverio et al can be simplified.

Related papers

The Matrix Trace Method For Spectral Resolution of Bipartite Systems

Gong Ren-shan

By using the generators of su(N) algebra the most general expression for the density matrix of bipartite systems has been given.Furthermore,the successive iteration formulas for calculating any power of density matrix are derived.Then,we proposed the matrix trace method for spectral resolution of density matrix and all the correlative formulas are given.At the end,we forecast still possible applications in the theory of local invariants in quantum mechanics and quantum information.

Journal of Nanchang University•Jan 1, 2006•0 citations

Nonlocal properties and local invariants for bipartite systems

Sergio A Albeverio, Shao-Ming Fei, Preeti Parashar +1 more

The nonlocal properties for a kind of generic N-dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. It is shown that two generic density matrices are locally equivalent if and only if all these invariants have equal values in these density matrices.

arXiv:quant-ph/0307164•Physical Review A•Jul 21, 2003•49 citations

UNITARY LOCAL INVARIANCE

Matteo G. A. Paris

We address unitary local (UL) invariance of bipartite pure states. Given a bipartite state |Ψ〉〉 = ∑ij ψij |i〉1 ⊗ |j〉2 the complete characterization of the class of local unitaries U1 ⊗ U2 for which U1 ⊗ U2|Ψ〉〉 = |Ψ〉〉 is obtained. The two relevant parameters are the rank of the matrix Ψ, [Ψ]ij = ψij, and the number of its equal singular values, i.e. the degeneracy of the eigenvalues of the partial traces of |Ψ〉〉.

arXiv:quant-ph/0502025•International Journal of Quantum Information•Dec 1, 2005•7 citations

Local unitary equivalence of arbitrary dimensional bipartite quantum states

Chunqin Zhou, Ting-Gui Zhang, Shao-Ming Fei +2 more

The nonlocal properties of arbitrary dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. These invariants give rise to both sufficient and necessary conditions for the equivalence of quantum states under local unitary transformations: two density matrices are locally equivalent if and only if all these invariants have equal values.

arXiv:1207.2688•Physical Review A•Jul 11, 2012•32 citations

Local invariants for mixed qubit-qutrit states

Vladimir P. Gerdt, A. Khvedelidze, Dimitar M. Mladenov +1 more

In the present paper few steps are undertaken towards the description of the qubit-qutrit pair - quantum bipartite system composed of two and three level subsystems. The computational difficulties with the construction of the local unitary polynomial invariants are discussed. Calculations of the Molien functions and Poincare series for the qubit-qubit and qubit-qutrit local unitary invariants are outlined and compared with the known results. The requirement of positive semi-definiteness of the density operator is formulated explicitly as a set of inequalities in five Casimir invariants of the algebra su(6).

arXiv:1106.4905•Jun 24, 2011•1 citation

Density Matrix of Bipartite Fermi Systems in the Framework of Local CAR-Algebras

Аirat Sitdikov, A. S. Nikitin, D. V. Bushtets

An algebraic model for studying quantum Fermi systems has been formulated. An embedding of the algebra of canonical anticommutation relations ( $$CAR$$ ) into the Cuntz algebra $$\mathcal{O}_{2}$$ was used. Representing this embedding on an infinite-dimensional Hilbert space forms a Fock space, on which creation and annihilation operators act, expressed in terms of the generators of the Cuntz algebra. This approach, in some cases, simplifies the calculation of various physical quantities within the second quantization method. As an example, the calculation of a two-mode partial density matrix of a bipartite fermionic system within the proposed model is presented.

Lobachevskii Journal of Mathematics•Apr 1, 2026•0 citations
By using the most general expression for the density matrix of bipartite systems,which has been given by virtue of the generatiors of su(N) algebra,and the matrix trace method for spectral resolution of density matrix,proposed by author before,it presents a complete set of successive iteration formulas for calculating all the local invariants for bipartite systems having a generic density matrix with full rank.Then,it shows that the complete set of local invariants proposed by S.Albeverio et al can be simplified.
In the present paper few steps are undertaken towards the description of the qubit-qutrit pair - quantum bipartite system composed of two and three level subsystems. The computational difficulties with the construction of the local unitary polynomial invariants are discussed. Calculations of the Molien functions and Poincare series for the qubit-qubit and qubit-qutrit local unitary invariants are outlined and compared with the known results. The requirement of positive semi-definiteness of the density operator is formulated explicitly as a set of inequalities in five Casimir invariants of the algebra su(6).
An algebraic model for studying quantum Fermi systems has been formulated. An embedding of the algebra of canonical anticommutation relations ( CARCARCAR ) into the Cuntz algebra O2\mathcal{O}_{2}O2​ was used. Representing this embedding on an infinite-dimensional Hilbert space forms a Fock space, on which creation and annihilation operators act, expressed in terms of the generators of the Cuntz algebra. This approach, in some cases, simplifies the calculation of various physical quantities within the second quantization method. As an example, the calculation of a two-mode partial density matrix of a bipartite fermionic system within the proposed model is presented.