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Quantum state tomography (QST) remains the prevailing method for benchmarking and verifying quantum devices; however, its application to large quantum systems is rendered impractical due to the exponential growth in both the required number…
Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases…
Likelihood-based methods are widely considered the best approaches for reconstructing ancestral states. Although much effort has been made to study properties of these methods, previous works often assume that both the tree topology and…
In maximum-likelihood quantum state tomography, both the sample size and dimension grow exponentially with the number of qubits. It is therefore desirable to develop a stochastic first-order method, just like stochastic gradient descent for…
Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices.…
The initialization of a quantum system into a certain state is a crucial aspect of quantum information science. While a variety of measurement strategies have been developed to characterize how well the system is initialized, for a given…
We investigate the optimal quantum state reconstruction from cloud to many spatially separated users by measure-broadcast-prepare scheme without the availability of quantum channel. The quantum state equally distributed from cloud to…
Reconstructing quantum states from measurement data represents a formidable challenge in quantum information science, especially as system sizes grow beyond the reach of traditional tomography methods. While recent studies have explored…
In 3-D reconstruction problems, the image data obtained from cryo electron microscopy is the projection of many heterogeneous instances of the object under study (e.g., a virus). When the object is heterogeneous but has an overall symmetry,…
Crystallization is a key step in macromolecular structure determination by crystallography. While a robust theoretical treatment of the process is available, due to the complexity of the system, the experimental process is still largely one…
This work introduces a rigorous notion of localization probability of a quantum state within a given subspace of its Hilbert space. A non-negative operator A is uniquely decomposed as A=B+C, where B is the maximal positive operator…
Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of $2$-outcome POVMs. However, these shadow tomography…
We analyze the problem of reconstructing an unknown quantum state of a multipartite system from repeated measurements of local observables. In particular, via a system-theoretic observability analysis, we show that, even when the initial…
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…
To improve the efficiency of the state tomography strategy via weak value, we have searched the optimal coupling strength between the system and measuring device. For an arbitrary d-dimensional quantum system, the optimal strengths being…
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…
Entanglement detection is one of the most conventional tasks in quantum information processing. While most experimental demonstrations of high-dimensional entanglement rely on fidelity-based witnesses, these are powerless to detect…
We report on the first experimental reconstruction of an entanglement quasiprobability. In contrast to related techniques, the negativities in our distributions are a necessary and sufficient identifier of separability and entanglement and…
Quantum tomography is an essential method of the photonic technology toolbox and is routinely used for evaluation of experimentally prepared states of light and characterization of devices transforming such states. The tomography procedure…
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…