Related papers: Quantum homodyne tomography with a priori constrai…
Optical homodyne tomography is discussed in the context of classical image processing. Analogies between these two fields are traced and used to formulate an iterative numerical algorithm for reconstructing the Wigner function from homodyne…
We present a method for reconstructing the photon number distribution from the homodyne statistics based on maximization of the likelihood function derived from the exact statistical description of a homodyne experiment. This method…
I propose an iterative expectation maximization algorithm for reconstructing a quantum optical ensemble from a set of balanced homodyne measurements performed on an optical state. The algorithm applies directly to the acquired data,…
An iterative algorithm for reconstructing the photon distribution from the random phase homodyne statistics is discussed. This method, derived from the maximum-likelihood approach, yields a positive definite estimate for the photon…
We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared pulses. The state is represented through the Wigner function, a ``quasi-probability density'' on $\mathbb{R}^{2}$…
Pulsed homodyne quantum tomography usually requires a high detection efficiency limiting its applicability in quantum optics. Here, it is shown that the presence of low detection efficiency ($<50\%$) does not prevent the tomographic…
We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum systems. The state is represented through the Wigner function, a generalized probability density on…
We investigate the capabilities of loss-tolerant quantum state characterization using a photon-number resolving, time-multiplexed detector (TMD). We employ the idea of probing the Wigner function point-by-point in phase space via photon…
A new reconstruction method for Wigner function is reported for quantum tomography based on compressed sensing. By analogy with computed tomography, Wigner functions for some quantum states can be reconstructed with less measurements…
We propose a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements. The algorithm is characterized by a very high convergence rate and features a simple adaptive…
We propose a method for characterizing a photodetector by directly reconstructing the Wigner functions of the detector's Positive-Operator-Value-Measure (POVM) elements. This method extends the works of S. Wallentowitz and Vogel [Phys. Rev.…
Wigner function tomography is indispensable for characterizing quantum states, but its commonly used version, balanced homodyne detection, suffers from several weaknesses. First, it requires efficient detection, which is critical for…
We introduce an efficient method to reconstruct the Wigner function of many-mode continuous variable systems. It is based on convex optimization with semidefinite programs, and also includes a version of the maximum entropy principle, in…
We demonstrate the reconstruction of the Wigner function from marginal distributions of the motion of a single trapped particle using homodyne detection. We show that it is possible to generate quantum states of levitated optomechanical…
The characterization of quantum features in large Hilbert spaces is a crucial requirement for testing quantum protocols. In the continuous variables encoding, quantum homodyne tomography requires an amount of measurements that increases…
We provide optimized recursion relations for homodyne tomography. We improve previous methods by mitigating the divergences intrinsic in the calculation of the pattern functions used previously, and detail how to implement the data analysis…
We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner…
New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not…
I present a simple and robust method of quantum state reconstruction using non-ideal detectors able to distinguish only between presence and absence of photons. Using the scheme, one is able to determine a value of Wigner function in any…
We present a continuous variable tomography scheme that reconstructs the Husimi Q-function (Wigner function) by Lagrange interpolation, using measurements of the Q-function (Wigner function) at the Padua points, the optimal sampling points…