Quantum Computation and Information Seminar 

26/09/2007, 15:00 — 16:00 — Room P4.35, Mathematics Building
Adán Cabello, U Seville

Nonlocality for graph states

The possibility of preparing two-photon hyper-entangled states encoding three or more qubits in each photon leads to the following problem: If we distribute N qubits between two parties, what quantum pure states and distributions of qubits allow all-versus-nothing (or Greenberger-Horne-Zeilinger-like) proofs of Bell's theorem using only single-qubit measurements? We show a necessary and sufficient condition for the existence of these proofs, and provide all possible proofs up to N=7 qubits. On the other hand, the possibility of preparing N-photon N-qubit graph states leads to the following problems: Which are the best Bell inequalities for graph states? How nonlocality grows with the number of qubits for different graph states? We provide all optimal Mermin-like Bell inequalities for all graph states up to N=5 qubits, and some interesting Bell inequalities for certain relevant classes of graph states of any number of qubits.