We establish methods for quantum state tomography based on compressed sensing. These
methods are specialized for quantum states that are fairly pure, and they offer a significant …

Intuitively, if a density operator has small rank, then it should be easier to estimate from
experimental data, since in this case only a few eigenvectors need to be learned. We prove …

We provide a detailed analysis of the question: how many measurement settings or
outcomes are needed in order to identify an unknown quantum state which is constrained by …

We consider measurements, described by a positive-operator-valued measure (POVM),
whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum …

This paper introduces a novel and efficient technique for quantum state estimation, coined
as low-rank matrix-completion quantum state tomography for characterizing pure quantum …

In the framework of quantum information geometry, we derive, from quantum relative Tsallis
entropy, a family of quantum metrics on the space of full rank, N level quantum states, by …

We discuss the uniqueness of quantum states compatible with given measurement results
for a set of observables. For a given pure state, we consider two different types of …

Reconstruction of density matrices is important in NMR quantum computing. An analysis is
made for a 2-qubit system using the error matrix method. It is found that the state tomography …

We examine the problem of finding the minimum number of Pauli measurements needed to
uniquely determine an arbitrary n-qubit pure state among all quantum states. We show that …

In view of the probabilistic quantizer–dequantizer operators introduced, the qubit states (spin-
1/2 particle states, two-level atom states) realizing the irreducible representation of the SU …