Separability and entanglement inC2⊗C2⊗CNcomposite quantum systems

2001/02/28 by S. Karnas, Siniša Karnas, Maciej Lewenstein +1
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physreva.64.042313

Finally corrected file submitted. Numerous misprints and small errors corrected, better versions of constructive separability checks included, updated and extended references

arxiv created 2001/03/13 · openalex publication_date 2001/09/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We investigate separability and entanglement of mixed states in C²\ensuremath\bigotimesC²\ensuremath\bigotimesC^N three party quantum systems. We show that all states with positive partial transposes that have rank<~N are separable. For the three-qubit case (N=2) we prove that all states \ensuremathρ that have positive partial transposes and rank three are separable. We also provide constructive separability checks for the states \ensuremathρ that have the sum of the rank of \ensuremathρ and the ranks of partial transposes with respect to all subsystems smaller than 15N\ensuremath-1.

Citations

• Three qubits can be entangled in two inequivalent ways
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Separability Criterion for Density Matrices
• Discussion of Probability Relations between Separated Systems
• Separability of mixed states: necessary and sufficient conditions
• Distributed Entanglement