Related papers: Quantum Tomography From Few Full-Rank Observables
The aim of sparse phase retrieval is to recover a $k$-sparse signal $\mathbf{x}_0\in \mathbb{C}^{d}$ from quadratic measurements $|\langle \mathbf{a}_i,\mathbf{x}_0\rangle|^2$ where $\mathbf{a}_i\in \mathbb{C}^d, i=1,\ldots,m$. Noting…
We consider a phase retrieval problem, where the goal is to reconstruct a $n$-dimensional complex vector from its phaseless scalar products with $m$ sensing vectors, independently sampled from complex normal distributions. We show that,…
The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum…
Phase retrieval refers to the problem of reconstructing an unknown vector $x_0 \in \mathbb{C}^n$ or $x_0 \in \mathbb{R}^n $ from $m$ measurements of the form $y_i = \big\vert \langle \xi^{\left(i\right)}, x_0 \rangle \big\vert^2 $, where $…
We present a simple and efficient Bayesian recursive algorithm for the data-pattern scheme for quantum state reconstruction, which is applicable to situations where measurement settings can be controllably varied efficiently. The algorithm…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
Quantum process tomography is an experimental technique to fully characterize an unknown quantum process. Standard quantum process tomography suffers from exponentially scaling of the number of measurements with the increasing system size.…
Estimating physical properties of quantum states from measurements is one of the most fundamental tasks in quantum science. In this work, we identify conditions on states under which it is possible to infer the expectation values of all…
The article establishes a framework for dynamic generation of informationally complete POVMs in quantum state tomography. Assuming that the evolution of a quantum system is given by a dynamical map in the Kraus representation, one can…
Quantum state tomography, a process that reconstructs a quantum state from measurements on an ensemble of identically prepared copies, plays a crucial role in benchmarking quantum devices. However, brute-force approaches to quantum state…
We propose a simple scheme for the quantum teleportation of both bipartite and multipartite entangled coherent states with the successful probability 1/2. The scheme is based on only linear optical devices such as beam splitters and phase…
Using a spontaneous parametric-downconversion source of photon pairs, we are working towards the creation of arbitrary 2-qubit quantum states with high fidelity. Currently, all physically allowable combinations of polarization entanglement…
Many prominent quantum computing algorithms with applications in fields such as chemistry and materials science require a large number of measurements, which represents an important roadblock for future real-world use cases. We introduce a…
The PhaseLift algorithm is an effective convex method for solving the phase retrieval problem from Fourier measurements with coded diffraction patterns (CDP). While exact reconstruction guarantees are well-established in the noiseless case,…
We prove that low-rank matrices can be recovered efficiently from a small number of measurements that are sampled from orbits of a certain matrix group. As a special case, our theory makes statements about the phase retrieval problem. Here,…
In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike…
We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the…
To obtain a complete description of a quantum system, one usually employs standard quantum state tomography, which however requires exponential number of measurements to perform and hence is impractical when the system's size grows large.…
We discuss the tomography of $N$-qubit states using collective measurements. The method is exact for symmetric states, whereas for not completely symmetric states the information accessible can be arranged as a mixture of irreducible SU(2)…
We construct a quantum algorithm that performs function-dependent phase transform and requires no initialization of an ancillary register. The algorithm recovers the initial state of an ancillary register regardless of whether its state is…