A bird's eye view of quantum computers

Quantum computers are discussed in the general framework of computation, the laws of physics and the foundations of quantum mechanics.Comment: 6 pages, 1 figur

Computing the distance between quantum channels: Usefulness of the Fano representation

The diamond norm measures the distance between two quantum channels. From an operational vewpoint, this norm measures how well we can distinguish between two channels by applying them to input states of arbitrarily large dimensions. In this paper, we show that the diamond norm can be conveniently and in a physically transparent way computed by means of a Monte-Carlo algorithm based on the Fano representation of quantum states and quantum operations. The effectiveness of this algorithm is illustrated for several single-qubit quantum channels.Comment: 8 pages, 7 figure

Non-perturbative interpretation of the Bloch vector's path beyond rotating wave approximation

The Bloch vector's path of a two-level system exposed to a monochromatic field exhibits, in the regime of strong coupling, complex corkscrew trajectories. By considering the infinitesimal evolution of the two-level system when the field is treated as a classical object, we show that the Bloch vector's rotation speed oscillates between zero and twice the rotation speed predicted by the rotating wave approximation. Cusps appear when the rotation speed vanishes. We prove analytically that in correspondence to cusps the curvature of the Bloch vector's path diverges. On the other hand, numerical data show that the curvature is very large even for a quantum field in the deep quantum regime with mean number of photons $\bar{n}\lesssim 1$. We finally compute numerically the typical error size in a quantum gate when the terms beyond rotating wave approximation are neglected.Comment: 9 pages, 8 figure

Exotic States in the Dynamical Casimir Effect

We consider the interaction of a qubit with a single mode of the quantized electromagnetic field and show that, in the ultrastrong coupling regime and when the qubit-field interaction is switched on abruptly, the dynamical Casimir effect leads to the generation of a variety of exotic states of the field, which cannot be simply described as squeezed states. Such effect also appears when initially both the qubit and the field are in their ground state. The non-classicality of the obtained exotic states is characterized by means of a parameter based on the volume of the negative part of the Wigner function. A transition to non-classical states is observed by changing either the interaction strength or the interaction time. The observed phenomena appear as a general feature of nonadiabatic quantum gates, so that the dynamical Casimir effect can be the origin of a fundamental upper limit to the maximum speed of quantum computation and communication protocols.Comment: 5 pages, 4 figure

Dynamical Casimir Effect in Quantum Information Processing

We demonstrate, in the regime of ultrastrong matter-field coupling, the strong connection between the dynamical Casimir effect (DCE) and the performance of quantum information protocols. Our results are illustrated by means of a realistic quantum communication channel and show that the DCE is a fundamental limit for quantum computation and communication and that novel schemes are required to implement ultrafast and reliable quantum gates. Strategies to partially counteract the DCE are also discussed.Comment: 7 pages, 5 figure

Competition Between National Economies and Competition Between Businesses--A Response to Judge Pescatore

This Article challenges the validity of Judge Pescatore’s theory [that Member States of the ECC are prevented by Community law from intervening in the marketplace by legislation]

Fixed point theorems for metric spaces with a conical geodesic bicombing

We derive two fixed point theorems for a class of metric spaces that includes all Banach spaces and all complete Busemann spaces. We obtain our results by the use of a 1-Lipschitz barycenter construction and an existence result for invariant Radon probability measures. Furthermore, we construct a bounded complete Busemann space that admits an isometry without fixed points.Comment: 19 page

Entanglement, randomness and chaos

Entanglement is not only the most intriguing feature of quantum mechanics, but also a key resource in quantum information science. The entanglement content of random pure quantum states is almost maximal; such states find applications in various quantum information protocols. The preparation of a random state or, equivalently, the implementation of a random unitary operator, requires a number of elementary one- and two-qubit gates that is exponential in the number n_q of qubits, thus becoming rapidly unfeasible when increasing n_q. On the other hand, pseudo-random states approximating to the desired accuracy the entanglement properties of true random states may be generated efficiently, that is, polynomially in n_q. In particular, quantum chaotic maps are efficient generators of multipartite entanglement among the qubits, close to that expected for random states. This review discusses several aspects of the relationship between entanglement, randomness and chaos. In particular, I will focus on the following items: (i) the robustness of the entanglement generated by quantum chaotic maps when taking into account the unavoidable noise sources affecting a quantum computer; (ii) the detection of the entanglement of high-dimensional (mixtures of) random states, an issue also related to the question of the emergence of classicality in coarse grained quantum chaotic dynamics; (iii) the decoherence induced by the coupling of a system to a chaotic environment, that is, by the entanglement established between the system and the environment.Comment: Review paper, 40 pages, 7 figures, added reference

For a history of effects: Hume and German anti-rationalism

L'articolo analizza la ricezione del pensiero di Hume da parte di quello che I. Berlin ha definito l'anti-razionalismo tedesco, in pensatori come Hamann e, in particolare, H.F. Jacobi. E' anche attraverso tale ricezione infatti che si è annunciato lo spirito del grande movimento romantico. Di qui l'importanza di questi autori che sono stati protagonisti di una vera svolta d'epoca