 
Summary: Commuting multiparty quantum observables and local compatibility
Claudio Altafini
SISSAISAS
International School for Advanced Studies
via Beirut 24, 34014 Trieste, Italy
A formula for the commutator of tensor product matrices is used to shows that, for qubits,
compatibility of quantum multiparty observables almost never implies local compatibility at each
site and to predict when this happens/does not happen in a concise manner. In particular, it is
shown that two "fully nontrivial" nqubit observables are compatible locally and globally if and
only if they are equal up to sign. In addition, the formula gives insight into the construction of
new paradoxes of the type of the KochenSpecker Theorem, which can then be easily rephrased
into proposals for new no hidden variable experiments of the type of the "Bell Theorem without
inequalities".
PACS numbers: 03.65.Ta, 03.65.Ud, 03.67.a
I. INTRODUCTION
In the literature that deals with Bell theorem and its
consequences for quantum mechanics of multiparty sys
tems, see [18] for an overview, a common aspect of the
tests aiming at proving/disproving the notion of local re
alism is the use of two or more measurements along suit
