Pawel Horodecki

A mixed state is called entangled (non-separable) if it is not a mixture of product states. It called bound entangled if it is entangled, but cannot be distilled i.e. brought to the maximally entangled form by means of local quantum operations and classical communication. A characterization of bound entangled states is given.

We consider quantum statistics from the perspective of post-quantum no-signaling theories in which either none or only a certain number of systems are trusted. These scenarios can be fully described by so-called no-signaling boxes or no-signaling assemblages respectively. It has been shown so far that in the usual Bell non-locality scenario with a single measurement run, quantum correlations can never reproduce an extremal non-local point within the set of no-signaling boxes. We provide here a general no-go rule showing that the latter stays true even if arbitrary sequential measurements are allowed. On the other hand, we prove a positive result showing that already a single trusted qubit is enough for quantum theory to produce a self-testable extremal point within the corresponding set of no-signaling assemblages. This result provides a tool that opens up possibilities for security proofs of cryptographic protocols against general no-signaling adversaries in semi-device-independent scenarios.

A direct analysis of the protocol of randomness amplification using Bell inequality violation is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. The probability distributions of bits generated by a Santha-Vazirani source are shown to be mixtures of permutations of Bernoulli distributions with parameter defined by the source. An intuitive proof is provided for the range of partial randomness from which perfect randomness can be extracted using quantum correlations violating the chain inequalities. Exact values are derived in the asymptotic limit of a large number of measurement settings.