ABSTRACT
Contextuality is a fundamental feature of quantum theory necessary for certain models of quantum computation and communication. Serious steps have therefore been taken towards a formal framework for contextuality as an operational resource. However, the main ingredient of a resource theory-a concrete, explicit form of free operations of contextuality-was still missing. Here we provide such a component by introducing noncontextual wirings: a class of contextuality-free operations with a clear operational interpretation and a friendly parametrization. We characterize them completely for general black-box measurement devices with arbitrarily many inputs and outputs. As applications, we show that the relative entropy of contextuality is a contextuality monotone and that maximally contextual boxes that serve as contextuality bits exist for a broad class of scenarios. Our results complete a unified resource-theoretic framework for contextuality and Bell nonlocality.
ABSTRACT
It has been argued that any test of quantum contextuality is nullified by the fact that perfect orthogonality and perfect compatibility cannot be achieved in finite precision experiments. We introduce experimentally testable two-qutrit violations of inequalities for noncontextual theories in which compatibility is guaranteed by the fact that measurements are performed on separated qutrits. The inequalities are inspired by the basic building block of the Kochen-Specker proof of quantum contextuality for a qutrit, despite the fact that their proof is completely independent of it.
ABSTRACT
We analyze the results of the most general measurement on two copies of a quantum state. We show that by using two copies of a quantum state it is possible to achieve an exponential improvement with respect to known methods for quantum state tomography. We demonstrate that mu can label a set of outcomes of a measurement on two copies if and only if there is a family of maps C_{micro} such that the probability Prob(micro) is the fidelity of each map, i.e., Prob(micro) = Tr[rhoC_{micro}(rho)]. Here, the map C_{micro} must be completely positive after being composed with the transposition (these are called completely copositive, or CCP, maps) and must add up to the fully depolarizing map. This implies that a positive operator valued measure on two copies induces a measure on the set of CCP maps (i.e., a CCP map valued measure).
