Local description of quantum inseparability

1998/01/13 by Anna Sanpera, R. Tarrach, Rolf Tarrach +2 · 7 citations
Computer Science · Mathematics · Physics and Astronomy · #Arithmetic #Binary number #Geometry #Materials science #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Mixing (physics) #Physics #Product (mathematics) #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum mechanics #Separable space #Separable state #quant-ph

paper · pdf · doi:10.1103/physreva.58.826

published as Phys.Rev. A58 (1998) 826-830 · 5 pages latex

arxiv created 1998/01/13 · openalex publication_date 1998/08/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show how to decompose any density matrix of the simplest binary composite systems, whether separable or not, in terms of only product vectors. We determine for all cases the minimal number of product vectors needed for such a decomposition. Separable states correspond to mixing from one to four pure product states. Inseparable states can be described as pseudomixtures of four or five pure product states, and can be made separable by mixing them with one or two pure product states.

Citations

• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Codes for the quantum erasure channel
• Forces in Molecules
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Separability Criterion for Density Matrices
• Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
• Separability of mixed states: necessary and sufficient conditions
• Quantifying Entanglement

Cited by

• Entanglement detection with scrambled data
• Construction of bound entangled edge states with special ranks
• A parametrization of bipartite systems based onSU(4) Euler angles
• Inductive classification of multipartite entanglement under stochastic local operations and classical communication
• Separability conditions and limit temperatures for entanglement detection in two-qubit HeisenbergXYZmodels
• Representation of entanglement by negative quasiprobabilities
• Quantum correlations and distinguishability of quantum states