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Simulation of singlet correlation without any communication, but using a weaker resource: a "non-local machine"

Presented by: 
N Gisin [Geneva]
Thursday 26th August 2004 - 11:30 to 12:20
INI Seminar Room 1

The importance of quantum entanglement is by now widely appreciated as a resource for quantum information applications. A unit of entanglement has been identifies and named e-bit; it consists of a pair of maximally entangled qubits, e.g. of a singlet: the same singlet that Bohm used in his version of the EPR paradox. A few years ago connection with communication complexity started to be studied, with question like how much communication is required to simulate an e-bit? From Bell inequality we know that it is impossible to simulate a singlet without any communication even if one assumes that both parties share local hidden variables, or in modern terminology, share randomness. Recently, Tonner and Bacon proved that actually a single bit of communication suffice for perfect simulation. Independently from the above story, Popescu and Rochlich raised the following question: can there be correlation stronger than the quantum mechanical ones that do not allow one to signal? They answered by showing a hypothetical non-local machine that does not allow signaling, yet violates the CHSH-bell inequality by the absolute maximal value of 4 (while quantum correlation achieve at most $2\sqrt{2}$. They concluded asking why Nature is non-local, but not maximally non-local, where the maximum would be only limited by the no-signaling constraint? It is straightforward to simulate the PR machine with a single bit of communication. Consequently, the PR nonlocal machine is a strictly weaker resource than a bit of communication. We show that singlets can be simulated using only one instance of the PR non-local machine. Hence, assuming that Nature is sparing with resources, one is be tempted to conclude that she is using something like the non-local machine. Finally, we raise the question whether correlations arising from partially entangled qubits can be simulated using only an e-bit?

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons