Related papers: Discrete Wigner Function Reconstruction and Compre…
We review the problem of state reconstruction in classical and in quantum physics, which is rarely considered at the textbook level. We review a method for retrieving a classical state in phase space, similar to that used in medical imaging…
We present a filtered backprojection algorithm for reconstructing the Wigner function of a system of large angular momentum j from Stern-Gerlach-type measurements. Our method is advantageous over the full determination of the density matrix…
The possible state space dimension increases exponentially with respect to the number of qubits. This feature makes the quantum state tomography expensive and impractical for identifying the state of merely several qubits. The recent…
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…
Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy…
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…
The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms…
Numerous applications in signal processing have benefited from the theory of compressed sensing which shows that it is possible to reconstruct signals sampled below the Nyquist rate when certain conditions are satisfied. One of these…
Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…
Quantum process tomography is the task of reconstructing unknown quantum channels from measured data. In this work, we introduce compressed sensing-based methods that facilitate the reconstruction of quantum channels of low Kraus rank. Our…
We present the reconstruction of the Wigner function of a classical phase-sensitive state, a pulsed coherent state, by measurements of the distributions of detected-photons of the state displaced by a coherent probe field. By using a hybrid…
Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Quantum state tomography is a crucial technique for characterizing the state of a quantum system, which is essential for many applications in quantum technologies. In recent years, there has been growing interest in leveraging neural…
We present an experimental scanning-based tomography approach for near-term quantum devices. The underlying method has previously been introduced in an ensemble-based NMR setting. Here we provide a tutorial-style explanation along with…
Using tomographic reconstruction we determine the complete internuclear quantum state, represented by the Wigner function, of a dissociating I2 molecule based on femtosecond time resolved position and momentum distributions of the atomic…
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.…
We describe an advanced image reconstruction algorithm for pseudothermal ghost imaging, reducing the number of measurements required for image recovery by an order of magnitude. The algorithm is based on compressed sensing, a technique that…
Quantum network is an emerging type of network structure that leverages the principles of quantum mechanics to transmit and process information. Compared with classical data reconstruction algorithms, quantum networks make image…
We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…