Bell-Type Inequalities for Partial Separability in $N$-Particle Systems and Quantum Mechanical Violations

Bell-Type Inequalities for Partial Separability in $N$ -Particle Systems and Quantum Mechanical Violations

Michael Seevinck and George Svetlichny

Phys. Rev. Lett. 89, 060401 – Published 18 July 2002

Abstract

We derive $N$ -particle Bell-type inequalities under the assumption of partial separability, i.e., that the $N$ -particle system is composed of subsystems which may be correlated in any way (e.g., entangled) but which are uncorrelated with respect to each other. These inequalities provide, upon violation, experimentally accessible sufficient conditions for full $N$ -particle entanglement, i.e., for $N$ -particle entanglement that cannot be reduced to mixtures of states in which a smaller number of particles are entangled. The inequalities are shown to be maximally violated by the $N$ -particle Greenberger-Horne-Zeilinger states.

Received 9 January 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.060401

Authors & Affiliations

Michael Seevinck^*

Subfaculty of Physics, University of Nijmegen, Nijmegen, The Netherlands and Institute for History and Foundations of Science, University of Utrecht, Utrecht, The Netherlands

George Svetlichny^†