Bell’s theorem for N qubits
No local realistic theory agrees with all predictions of quantum mechanics as quantitatively expressed by violation of Bell's inequalities. Local Realism is one of the major principles in our understanding of Nature, which is based on everyday experience and classical physics. Realism supposes that measurement results are predetermined by the properties the particles carry prior to and independent of observations. Locality supposes that these results are independent of any action at space-like separations.
What are the most general constraints on correlations imposed by local realism? Which quantum states violate these constraints? Despite considerable research efforts these questions could be answered only for the case of two particles in pure states and for two-qubit mixed states.
In 2001 we derived a single general Bell inequality that summarizes all possible inequalities for the case in which each observer has a choice between two arbitrary dichotomic observables. This inequality is shown to be tight, i.e. it is a sufficient and necessary condition for the correlation function for N particles to be describable in a local and realistic picture. We also derive a necessary and sufficient condition for an arbitrary N-qubit mixed state to violate this inequality.
Marek Zukowski & Caslav Brukner
Bell's theorem for general N-qubit states
