Giacomo Mauro D’Ariano

Theoretical framework for quantum networks

We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination, estimation, and tomography. Our framework is based on the concepts of quantum comb---which describes all transformations achievable by a given quantum network---and link product---the operation of connecting two quantum networks. Quantum networks are treated both from a constructive point of view---based on connections of elementary circuits---and from an axiomatic one---based on a hierarchy of admissible quantum maps. In the axiomatic context a fundamental property is shown, which we call universality of quantum memory channels: any admissible transformation of quantum networks can be realized by a suitable sequence of memory channels. The open problem whether this property fails for some nonquantum theory, e.g., for no-signaling boxes, is posed.

Informationally complete measurements and group representation

Informationally complete measurements on a quantum system allow one to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kinds of measurement can be achieved through positive-operator valued measures (POVMs) related to unitary irreducible representations of a group on the Hilbert space of the system. With the help of frame theory we provide a constructive way to evaluate the data-processing function for arbitrary operators.

Clean positive operator valued measures

In quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure (POVM). A quantum channel transforms POVMs into POVMs, generally irreversibly, thus losing some of the information retrieved from the measurement. This poses the problem of which POVMs are “undisturbed,” i.e., they are not irreversibly connected to another POVM. We will call such POVMs clean. In a sense, the clean POVMs would be “perfect,” since they would not have any additional “extrinsical” noise. Quite unexpectedly, it turns out that such a “cleanness” property is largely unrelated to the convex structure of POVMs, and there are clean POVMs that are not extremal and vice versa. In this article we solve the cleannes classification problem for number n of outcomes n⩽d (d dimension of the Hilbert space), and we provide a set of either necessary or sufficient conditions for n>d, along with an iff condition for the case of informationally complete POVMs for n=d2.

Optimal phase-covariant cloning for qubits and qutrits

We consider cloning transformations of equatorial qubits

Operational Axioms for Quantum Mechanics

|{\ensuremath{\psi}}_{\ensuremath{\varphi}}〉=1/\sqrt{2}(|0〉{+e}^{i\ensuremath{\varphi}}|1〉)

Optical Fock-state synthesizer

and qutrits

Exploiting quantum parallelism of entanglement for a complete experimental quantum characterization of a single-qubit device

|{\ensuremath{\psi}}_{\ensuremath{\varphi},\ensuremath{\theta}}〉=1/\sqrt{3}(|0〉{+e}^{i\ensuremath{\varphi}}|1〉{+e}^{i\ensuremath{\theta}}|2〉),

Physics as Information Processing

with the transformation covariant for rotation of the phases

Approximate quantum cloning and the impossibility of superluminal information transfer

\ensuremath{\varphi}

Group theoretical quantum tomography

and