相关论文: Quantum State Tomography with Joint SIC POMs and P…
We present a new method for quantum process tomography. The method enables us to efficiently estimate, with fixed precision, any of the parameters characterizing a quantum channel. It is selective since one can choose to estimate the value…
We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…
Matrix product state has become the algorithm of choice when studying one-dimensional interacting quantum many-body systems, which demonstrates to be able to explore the most relevant portion of the exponentially large quantum Hilbert space…
Recently, the statistical restricted isometry property (RIP) has been formulated to analyze the performance of deterministic sampling matrices for compressed sensing. In this paper, we propose the usage of orthogonal symmetric Toeplitz…
Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the integrability of many probabilistic systems,…
In this paper, the distinguishability of multipartite geometrically uniform quantum states obtained from a single reference state is studied in the symmetric subspace. We specially focus our attention on the unitary transformation in a way…
In the present work, we suggest an approach for describing dynamics of finite-dimensional quantum systems in terms of pseudostochastic maps acting on probability distributions, which are obtained via minimal informationally complete quantum…
Given the state of a quantum system, one can calculate the expectation value of any observable of the system. However, the inverse problem of determining the state by performing different measurements is not a trivial task. In various…
Quantum tomography is an important tool for obtaining information about the quantum state from experimental data. In this study, we conduct a comparative analysis of various quantum tomography protocols, including protocols based on highly…
We consider a quantum version of the famous low-rank approximation problem. Specifically, we consider the distance $D(\rho,\sigma)$ between two normalized quantum states, $\rho$ and $\sigma$, where the rank of $\sigma$ is constrained to be…
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…
Quantum state estimation is an important task of many quantum information protocols. We consider two families of unitary evolution operators, one with a one-parameter and the other with a two-parameter, which enable the estimation of a…
In the four-dimensional Hilbert space, there exist 16 Heisenberg--Weyl (HW) covariant symmetric informationally complete positive operator valued measures (SIC~POVMs) consisting of 256 fiducial states on a single orbit of the Clifford…
The generalized $Q$-function of a spin system can be considered the outcome probability distribution of a state subjected to a measurement represented by the spin-coherent-state (SCS) positive-operator-valued measure (POVM). As fundamental…
The Schmidt number characterizes the quantum entanglement of a bipartite mixed state and plays a significant role in certifying entanglement of quantum states. We derive a Schmidt number criterion based on the trace norm of the correlation…
The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it allows to derive the ultimate bounds of the achievable precision. We show a relation between the statistical distance…
The need to perform quantum state tomography on ever larger systems has spurred a search for methods that yield good estimates from incomplete data. We study the performance of compressed sensing (CS) and least squares (LS) estimators in a…
Quantum probability provides a novel framework for formulating machine-learning (ML) problems in Hilbert space. We introduce a prototype-based learning scheme where class representatives are encoded as generative matrix product states…
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…
Gauging a global symmetry of a system amounts to introducing new degrees of freedom whose transformation rule makes the overall system observe a local symmetry. In quantum systems there can be obstructions to gauging a global symmetry. When…