Vittorio Giovannetti

Advances in quantum metrology

The statistical error in any estimation can be reduced by repeating the measurement and averaging the results. The central limit theorem implies that the reduction is proportional to the square root of the number of repetitions. Quantum metrology is the use of quantum techniques such as entanglement to yield higher statistical precision than purely classical approaches. In this Review, we analyse some of the most promising recent developments of this research field and point out some of the new experiments. We then look at one of the major new trends of the field: analyses of the effects of noise and experimental imperfections.

Entangling macroscopic oscillators exploiting radiation pressure

It is shown that radiation pressure can be profitably used to entangle macroscopic oscillators like movable mirrors, using present technology. We prove a new sufficient criterion for entanglement and show that the achievable entanglement is robust against thermal noise. Its signature can be revealed using common optomechanical readout apparatus.

Classical Capacity of the Lossy Bosonic Channel: The Exact Solution

The classical capacity of the lossy bosonic channel is calculated exactly. It is shown that its Holevo information is not superadditive, and that a coherent-state encoding achieves capacity. The capacity of far-field, free-space optical communications is given as an example.

Quantum-enhanced positioning and clock synchronization

A wide variety of positioning and ranging procedures are based on repeatedly sending electromagnetic pulses through space and measuring their time of arrival. The accuracy of such procedures is classically limited by the available power and bandwidth. Quantum entanglement and squeezing have been exploited in the context of interferometry, frequency measurements, lithography and algorithms. Here we report that quantum entanglement and squeezing can also be employed to overcome the classical limits in procedures such as positioning systems, clock synchronization and ranging. Our use of frequency-entangled pulses to construct quantum versions of these protocols results in enhanced accuracy compared with their classical analogues. We describe in detail the problem of establishing a position with respect to a fixed array of reference points.

Quantum limits to dynamical evolution

We establish the minimum time it takes for an initial state of mean energy E and energy spread {delta}E to move from its initial configuration by a predetermined amount. Distances in Hilbert space are estimated by the fidelity between the initial and final states. In this context, we study the role of entanglement among subsystems in speeding up the dynamics of a composite system.

Characterizing the entanglement of bipartite quantum systems

We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.

Positioning and clock synchronization through entanglement

A method is proposed to em- ploy entangled and squeezed light for de- termining the position of a party and for synchronizing distant clocks. An accuracy gain over analogous protocols that employ classical resources is demonstrated and a quantum-cryptographic positioning applica- tion is given, which allows only trusted par- ties to learn the position of whatever must be localized. The presence of a lossy channel and imperfect photodetection is considered. The advantages in using partially entangled states is discussed.

Additivity properties of a Gaussian channel

The Amosov-Holevo-Werner conjecture implies the additivity of the minimum Renyi entropies at the output of a channel. The conjecture is proven true for all Renyi entropies of integer order greater than two in a class of Gaussian bosonic channel where the input signal is randomly displaced or where it is coupled linearly to an external environment.

Generating Entangled Two-Photon States with Coincident Frequencies

It is shown that parametric down-conversion, with a short-duration pump pulse and a long nonlinear crystal that is appropriately phase matched, can produce a frequency-entangled biphoton state whose individual photons are coincident in frequency. Quantum interference experiments which distinguish this state from the familiar time-coincident biphoton state are described.

Minimum Rényi and Wehrl entropies at the output of bosonic channels

The minimum Renyi and Wehrl output entropies are found for bosonic channels in which the signal photons are either randomly displaced by a Gaussian distribution (classical-noise channel), or coupled to a thermal environment through lossy propagation (thermal-noise channel). It is shown that the Renyi output entropies of integer orders z{>=}2 and the Wehrl output entropy are minimized when the channel input is a coherent state.