Marco G. Genoni

Quantifying the non-Gaussian character of a quantum state by quantum relative entropy

We introduce a measure to quantify the non-Gaussian character of a quantum state: the quantum relative entropy between the state under examination and a reference Gaussian state. We analyze in detail the properties of our measure and illustrate its relationships with relevant quantities in quantum information such as the Holevo bound and the conditional entropy; in particular, a necessary condition for the Gaussian character of a quantum channel is also derived. The evolution of non-Gaussianity is analyzed for quantum states undergoing conditional Gaussification toward twin beams and de-Gaussification driven by Kerr interaction. Our analysis allows us to assess non-Gaussianity as a resource for quantum information and, in turn, to evaluate the performance of Gaussification and de-Gaussification protocols.

Optical phase estimation in the presence of phase diffusion.

The measurement problem for the optical phase has been traditionally attacked for noiseless schemes or in the presence of amplitude or detection noise. Here we address the estimation of phase in the presence of phase diffusion and evaluate the ultimate quantum limits to precision for phase-shifted Gaussian states. We look for the optimal detection scheme and derive approximate scaling laws for the quantum Fisher information and the optimal squeezing fraction in terms of the total energy and the amount of noise. We also find that homodyne detection is a nearly optimal detection scheme in the limit of very small and large noise.

Quantifying non-Gaussianity for quantum information

We address the quantification of non-Gaussianity (nG) of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in detail the properties and the relationships of two recentlyproposedmeasuresofnGbasedontheHilbert-Schmidtdistanceandthequantumrelativeentropy(QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behavior in most of the examples taken into account. However, we also show that they introduce a different relation of order; that is, they are not strictly monotone to each other. We exploit the nG measures for states in order to introduce a measure of nG for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in detail the role played by nG in entanglement-distillation protocols. Besides, we exploit the QRE-based nG measure to provide different insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information, and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE nG to the quantum Fisher information. Finally, since evaluation of the QRE nG measure requires the knowledge of the full density matrix, we derive some experimentally friendly lower bounds to nG for some classes of states and by considering the possibility of performing on the states only certain efficient or inefficient measurements.

Homodyne Estimation of Gaussian Quantum Discord

We address the experimental estimation of Gaussian quantum discord for a two-mode squeezed thermal state, and demonstrate a measurement scheme based on a pair of homodyne detectors assisted by Bayesian analysis, which provides nearly optimal estimation for small value of discord. In addition, though homodyne detection is not optimal for Gaussian discord, the noise ratio to the ultimate quantum limit, as dictated by the quantum Cramer-Rao bound, is limited to about 10 dB.

Non-Gaussianity of quantum states: An experimental test on single-photon-added coherent states

(Received 18 October 2010; published 28 December 2010)Non-Gaussian states and processes are useful resources in quantum information with continuous variables.An experimentally accessible criterion has been proposed to measure the degree of non-Gaussianity of quantumstates based on the conditional entropy of the state with a Gaussian reference. Here we adopt such a criterionto characterize an important class of nonclassical states: single-photon-added coherent states. Our studiesdemonstrate the reliability and sensitivity of this measure and use it to quantify how detrimental is the roleof experimental imperfections in our implementation.DOI: 10.1103/PhysRevA.82.063833 PACS number(s): 42

Experimental estimation of one-parameter qubit gates in the presence of phase diffusion

We address estimation of one-parameter qubit gates in the presence of phase diffusion. We evaluate the ultimate quantum limits to precision, seek optimal probes and measurements, and demonstrate an optimal estimation scheme for polarization encoded optical qubits. An adaptive method to achieve optimal estimation in any working regime is also analyzed in detail and experimentally implemented.

Conditional measurements on multimode pairwise entangled states from spontaneous parametric downconversion

We address the intrinsic multimode nature of the quantum state of light obtained by pulsed spontaneous parametric downconversion and develop a theoretical model based only on experimentally accessible quantities. We exploit the pairwise entanglement as a resource for conditional multimode measurements and derive closed formulas for the detection probability and the density matrix of the conditional states. We present a set of experiments performed to validate our model in different conditions that are in excellent agreement with experimental data. Finally, we evaluate the non-Gaussianity of the conditional states obtained from our source with the aim of discussing the effects of the different experimental parameters on the effectiveness of this type of conditional state preparation.

Detecting quantum non-Gaussianity via the Wigner function

We introduce a family of criteria to detect quantum non-Gaussian states of a harmonic oscillator, that is, quantum states that can not be expressed as a convex mixture of Gaussian states. In particular we prove that, for convex mixtures of Gaussian states, the value of the Wigner function at the origin of phase space is bounded from below by a non-zero positive quantity, which is a function only of the average number of excitations (photons) of the state. As a consequence, if this bound is violated then the quantum state must be quantum non-Gaussian. We show that this criterion can be further generalized by considering additional Gaussian operations on the state under examination. We then apply these criteria to various non-Gaussian states evolving in a noisy Gaussian channel, proving that the bounds are violated for high values of losses, and thus also for states characterized by a positive Wigner function.

Optical interferometry in the presence of large phase diffusion

Phase diffusion represents a crucial obstacle towards the implementation of high precision interferometric measurements and phase shift based communication channels. Here we present a nearly optimal interferometric scheme based on homodyne detection and coherent signals for the detection of a phase shift in the presence of large phase diffusion. In our scheme the ultimate bound to interferometric sensitivity is achieved already for a small number of measurements, of the order of hundreds, without using nonclassical light.

Reliable source of conditional states from single-mode pulsed thermal fields by multiple-photon subtraction

We address both theoretically and experimentally the gener ation of pulsed non-Gaussian states from classical Gaussian ones by means of conditional measurements. The set up relies on a beam splitter and a pair of linear photodetectors able to resolve up to tens of photons in the tw o outputs. We show the reliability of the setup and the good agreement with the theory for a single-mode ther mal field entering the beam splitter and present a thorough characterization of the photon statistics of the c onditional states.