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

Exploring the Set of Quantum States

Åsa Ericsson

Published Jan 1, 2007• 4 citations
OpenAlex

Abstract

Quantum mechanical properties of finite dimensional quantum systems are used within the field of quantum information. In this thesis the set of states (density matrices) for such systems is studied ...

Related papers

Density Operator in Terms of Coherent States Representation with the Applications in the Quantum Information

Nicolina Pop, Dušan Popov, M. Davidovic

International Journal of Theoretical Physics•Feb 2, 2013•5 citations

SU(4) Euler Angle Parameterization and Bipartite Density Matrices

Todd Tilma, Mark Byrd, E. C. G. Sudarshan

In quantum mechanics, sets of density matrices are important for numerous reasons. For example, their compact notation make them useful for describing decoherence and entanglement properties of multi-particle quantum systems. In particular, two two-state density matrices, otherwise known as two qubit density matrices, are important for their role in explaining quantum teleportation, dense coding, and computation theorems. The aim of this paper is to show an explicit parameterization for the Hilbert space of all two qubit density matrices. Such a parameterization would be extremely useful for numerical calculations concerning entanglement and other quantum information parameters. We would also like to know the properties of such parameterized two qubit density matrices; in particular, the representation of their convex sets, their sub-sets, and their set boundaries in terms of our parameterization. Here we present a generalized Euler angle parameterization for SU(4) and all possible two qubit density matrices as well as the corrected Haar Measures for SU(3) and SU(4) from this parameterization. The role of the parameterization in the Peres-Horodecki criteria will also be introduced as well as its usefulness in calculating entangled two qubit states.

•Feb 3, 2002•0 citations

Structure and parametrization of stochastic maps of density matrices

E. C. G. Sudarshan, Anil Shaji

The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear convex set that may be viewed as supermatrices. The property of Hermiticity of density matrices renders an associated supermatrix Hermitian and hence diagonalizable. The positivity of the density matrix does not make the associated supermatrix positive though. If the map itself is positive, it is called completely positive and it has a simple parametrization. This is extended to all positive (not completely positive) maps. A general dynamical map that does not preserve the norm of the density matrices it acts on can be thought of as the contraction of a norm-preserving map of an extended system. The reconstruction of such extended dynamics is also given.

arXiv:quant-ph/0109158•Journal of Physics A Mathematical and General•Apr 24, 2003•18 citations

DENSITY MATRICES IN QUANTUM MECHANICS

WORLD SCIENTIFIC eBooks•Jul 1, 1995•1 citation

Measuring and Characterizing Quantum States and Processes

Daniel F. V. James

I will give an introductory overview of current experimental techniques used to characterize the density matrix of a system and the quantum process describing a device, with emphasis on applications in quantum optics.

Conference on Lasers and Electro-Optics•Jan 1, 2010•0 citations

Copying Quantum States

Hans Maassen, Burkhard Kümmerer

The no-broadcasting theorem in quantum information says that a set of states on a quantum system admits a common broadcasting (copying) operation if and only if their density matrices belong to a commuting family. We discuss and prove this theorem, as well as the closely related no-cloning theorem in the context of quantum probability theory, i.e. in the category of (finite dimensional) C-star-algebras with unital completely positive maps.

quant-pharXiv:2607.02408•Indian Journal of Pure and Applied Mathematics•Jul 3, 2026•0 citations
In quantum mechanics, sets of density matrices are important for numerous reasons. For example, their compact notation make them useful for describing decoherence and entanglement properties of multi-particle quantum systems. In particular, two two-state density matrices, otherwise known as two qubit density matrices, are important for their role in explaining quantum teleportation, dense coding, and computation theorems. The aim of this paper is to show an explicit parameterization for the Hilbert space of all two qubit density matrices. Such a parameterization would be extremely useful for numerical calculations concerning entanglement and other quantum information parameters. We would also like to know the properties of such parameterized two qubit density matrices; in particular, the representation of their convex sets, their sub-sets, and their set boundaries in terms of our parameterization. Here we present a generalized Euler angle parameterization for SU(4) and all possible two qubit density matrices as well as the corrected Haar Measures for SU(3) and SU(4) from this parameterization. The role of the parameterization in the Peres-Horodecki criteria will also be introduced as well as its usefulness in calculating entangled two qubit states.
The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear convex set that may be viewed as supermatrices. The property of Hermiticity of density matrices renders an associated supermatrix Hermitian and hence diagonalizable. The positivity of the density matrix does not make the associated supermatrix positive though. If the map itself is positive, it is called completely positive and it has a simple parametrization. This is extended to all positive (not completely positive) maps. A general dynamical map that does not preserve the norm of the density matrices it acts on can be thought of as the contraction of a norm-preserving map of an extended system. The reconstruction of such extended dynamics is also given.