Seminars and Workshops

ABSTRACT

ABSTRACT
Entanglement is definitely one of the most peculiar features of quantum world; besides being the source of correlations which do not have any classical counterpart, nowadays it plays a key role in many quantum information protocols. In this talk I shall focus on single-particle entanglement (SPE), a particular kind of entanglement where quantum correlations are shared between different degrees of freedom of the same particle. Even if non-locality doesn’t play any role in this context, SPE can be certified via a test of quantum contextuality based on Bell inequalities violation. In addition, I shall describe how SPE can be efficiently applied to the entropy certification of a realistic Quantum Random Number Generator.

ABSTRACT

ABSTRACT
In the first part of the talk we show that on the C*-algebra of Canonical Anticommutation Relations spreadable, exchangeable and rotation invariant states states are the same. Interestingly, the analysis carried out to arrive at this result shows that the first equivalence holds true for all infinite tensor products (acted upon by permutations and monotone maps in the natural way). In particular, the set of spreadable states on such C*-algebras is a Choquet simplex whose extreme states are infinite products of a single state. Moreover, in Classical Probability, rotatable sequences of random variables are disciplined by a well-known theorem of Freedman, which says that their joint distribution is a mixture of independent identically distributed Gaussian variables. If time permits, in the second part of the talk I will discuss a recent generalization of this result that holds for states on the C*-algebra of Canonical Commutation Relations (CCR for short). Precisely, the CCR algebra is naturally acted upon the unitary group U(H) of all unitaries on a Hilbert space H. The set of all invariant states under this group action turns out to be a Bauer simplex whose extreme states are Gaussian with variance at least 1.

ABSTRACT

ABSTRACT
The talk will begin justifying why quantum channels are reasonable models for describing the evolution of the state of a quantum system and how they are related to unitary evolutions and measurement processes. Then, we will show how they can be considered as a generalisation of transition kernel in classical measure spaces. We will conclude presenting some relevant notions in the study of the qualitative analysis of (semigroups of) quantum channels and some applications.