A. Volta

Maximum-likelihood estimation of the density matrix

We present a universal technique for quantum-state estimation based on the maximum-likelihood method. This approach provides a positive-definite estimate for the density matrix from a sequence of measurements performed on identically prepared copies of the system. The method is versatile and can be applied to multimode radiation fields as well as to spin systems. The incorporation of physical constraints, which is natural in the maximum-likelihood strategy, leads to a substantial reduction of statistical errors. Numerical implementation of the method is based on a particular form of the Gauss decomposition for positive-definite Hermitian matrices. PACS number~s!: 03.67.2a, 03.65.Bz In quantum mechanics, the achievable information on a physical system is encoded into the density matrix % ˆ , which allows one to evaluate all possible expectation values through the Born statistical rule ^O ˆ &5Tr(% ˆO ˆ). In order to obtain full information on a quantum system we need to estimate its density matrix. In principle, this can be accomplished by successive measurements on repeated identical preparations of the same system. With a proper choice of the measurements, and after collecting a suitably large number of data, we can arrive at a reliable knowledge of the quantum state of the system.

Generating qudits with d=3,4 encoded on two-photon states

We present an experimental method to engineer arbitrary pure states of qudits with d=3,4 using linear optics and a single nonlinear crystal.

Information-disturbance trade-off in quantum-state discrimination

(Dated: February 1, 2008)When discriminating between two pure quantum states, there exists a quantitative tradeoff be-tween the information retrieved by the measurement and the disturbance caused on the unknownstate. We derive the optimal tradeoff and provide the corresponding quantum measurement. Such anoptimal measurement smoothly interpolates between the two limiting cases of maximal informationextraction and no measurement at all.

Informationally complete measurements on bipartite quantum systems: comparing local with global measurements

Informationally complete measurements allow the estimation of expectation values of any operator on a quantum system, by changing only the data processing of the measurement outcomes. In particular, an informationally complete measurement can be used to perform quantum tomography, namely to estimate the density matrix of the quantum state. The data processing is generally nonunique, and can be optimized according to a given criterion. In this paper we provide the solution of the optimization problem which minimizes the variance in the estimation. We then consider informationally complete measurements performed over bipartite quantum systems focusing attention on universally covariant measurements, and compare their statistical efficiency when performed either locally or globally on the two systems. Among global measurements we consider the special case of Bell measurements, which allow us to estimate the expectation of a restricted class of operators. We compare the variance in the three cases: local, Bell, and unrestricted global—and derive conditions for the operators to be estimated such that one type of measurement is more efficient than the other. In particular, we find that for factorized operators and Bell projectors the Bell measurement always performs better than the unrestricted global measurement, which in turn outperforms the local one. For estimation of the matrix elements of the density operator, the relative performances depend on the basis on which the state is represented, and on the matrix element being diagonal or off-diagonal, however, with the global unrestricted measurement generally performing better than the local one.

MAXIMUM LIKELIHOOD ESTIMATION FOR A GROUP OF PHYSICAL TRANSFORMATIONS

The maximum likelihood strategy for the estimation of group parameters allows one to derive in a general fashion optimal measurements, optimal signal states, and their relations with other information theoretical quantities. These results provide deep insight into the general structure underlying optimal quantum estimation strategies. The entanglement between representation spaces and multiplicity spaces of the group action appears to be the unique kind of entanglement which is really useful for the optimal estimation of group parameters.

Phase-covariant cloning of coherent states

We consider the problem of phase-covariant cloning for coherent states. We show that an experimental scheme based on ideal phase measurement and feedforward outperforms the semiclassical procedure of ideal phase measurement and preparation in terms of fidelity. A realistic scheme where the ideal phase measurement is replaced with double-homodyne detection is shown to be unable to overcome the semiclassical cloning strategy. On the other hand, such a realistic scheme is better than semiclassical cloning based on doublehomodyne phase measurement and preparation.

Interferometric tunability of absorption

We propose an interferometric setup that permits to tune the quantity of radiation absorbed by an object illuminated by a fixed light source. The method can be used to selectively irradiate portions of an object based on their transmissivities or to accurately estimate the transmissivities from rough absorption measurements.

MINIMUM OUTPUT ENTROPY OF A GAUSSIAN BOSONIC CHANNEL

The entropy at the output of a Bosonic channel is analyzed when coherent fields are randomly added to the signal. Coherent-state inputs are conjectured to provide the minimum output entropy. Supporting physical and mathematical evidence is provided.

To take a (binary) decision you'd better use entanglement

We address two-mode quantum interferometry as binary measurements aimed at determining whether or not a phase perturbation has occurred. We show that optimized measurements achieve the best sensitivity when the input state is entangled. A concrete set-up based on parametric sources of entanglement and photodetection is also suggested and shown to approach ideal sensitivity.