Seminars and Workshops

ABSTRACT

ABSTRACT
The statistics of the (finite alphabet) outcomes of repeated quantum measurements is studied by methods of thermodynamic formalism. Viewed as one-dimensional spin systems with long range interactions, repeated quantum measurements exhibit very rich (and sometimes very singular) thermodynamic behaviour. We will describe general thermodynamical formalism of these systems and illustrate its unexpected features on a number of examples.

ABSTRACT

ABSTRACT
We develop a notion of dephasing under the action of a quantum? Markov semigroup in terms of convergence of operators to a block-diagonal? form determined by irreducible invariant subspaces. If the latter are all ?one-dimensional, we say the dephasing is maximal. We study characterization ?of a maximally dephasing evolution in terms of unitary dilations ?with only classical noise. In particular, we introduce an intrinsic? quantity constructed from the generator which quantities the? degree of obstruction to having a classical diffusive noise model.? (Joint work with J.E. Gough, H.I. Nurdin and L. Viola)?

ABSTRACT

ABSTRACT
This is a joint work with Uwe Franz. We describe the construction of the quantum Levy process on Lorentz-Lie algebra.

ABSTRACT

ABSTRACT
We discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later time. Two different scenarios then arise: either Bob is allowed to arrange his measurement set-up after Alice has announced him the chosen ensemble (pre-measurement scenario), or he is forced to perform the measurement before of Alice’s announcement (post-measurement scenario). In the latter case, he can only post-process his measurement outcome when Alice’s extra information becomes available. We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task within the pre-measurement scenario. This is done by showing that only incompatible measurements allow for an efficient use of pre-measurement information in order to improve Bob’s probability of guessing the correct state. The gap between the guessing probabilities with pre- and post-measurement information is thus a witness of the incompatibility of a given collection of measurements. We prove that all linear incompatibility witnesses can be implemented as some state discrimination protocol according to this scheme.