Related papers: Beating full state tomography for unentangled spec…
In this paper, we examine a variety of strategies for numerical quantum-state estimation from data of the sort commonly measured in experiments involving quantum state tomography. We find that, in some important circumstances, an elaborate…
There exists, in general, a convex set of quantum state estimators that maximize the likelihood for informationally incomplete data. We propose an estimation scheme, catered to measurement data of this kind, to search for the exact…
We consider online strategies for discriminating between symmetric pure states with zero error when $n$ copies of the states are provided. Optimized online strategies involve local, possibly adaptive measurements on each copy and are…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
A long-standing problem in quantum physics is to determine the minimal number of measurement bases required for the complete characterization of unknown quantum states, a question of particular relevance to high-dimensional quantum…
In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that…
Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such…
We propose an iterative algorithm that computes the maximum-likelihood estimate in quantum state tomography. The optimization error of the algorithm converges to zero at an $O ( ( 1 / k ) \log D )$ rate, where $k$ denotes the number of…
Inferring nonlinear features of quantum states is fundamentally important across quantum information science, but remains challenging due to the intrinsic linearity of quantum mechanics. It is widely recognized that quantum memory and…
Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect…
We introduce the concept of selective quantum state tomography or SQST, a tomographic scheme that enables a user to estimate arbitrary elements of an unknown quantum state using a fixed measurement record. We demonstrate how this may be…
In quantum purity amplification, one is given $n$ copies of a noisy quantum state $\rho \in \mathbb{C}^{d \times d}$ and asked to prepare $k$ copies of its principal eigenstate $|v_d\rangle$. Several prior works have derived…
Given a source of iid samples of edges of an input graph $G$ with $n$ vertices and $m$ edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in $G$? Moreover, is it possible to obtain…
Characterising large-scale quantum systems is central to fundamental physics and essential for applications of quantum technologies. While a full characterisation requires exponentially increasing resources, focusing on application-relevant…
Determining an unknown quantum state from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in quantum science. Here we study the number of measurement bases needed to fully characterize an arbitrary…
We revisit the problem of Pauli shadow tomography: given copies of an unknown $n$-qubit quantum state $\rho$, estimate $\text{tr}(P\rho)$ for some set of Pauli operators $P$ to within additive error $\epsilon$. This has been a popular…
A recently identified class of receivers which demultiplex an optical field into a set of orthogonal spatial modes prior to detection can surpass canonical diffraction limits on spatial resolution for simple incoherent imaging tasks.…
We prove that given the ability to make entangled measurements on at most $k$ replicas of an $n$-qubit state $\rho$ simultaneously, there is a property of $\rho$ which requires at least order $2^n$ measurements to learn. However, the same…
A fundamental task in quantum information science is to measure nonlinear functionals of quantum states, such as $\mathrm{Tr}(\rho^k O)$. Intuitively, one expects that computing a $k$-th order quantity generally requires $O(k)$ copies of…
In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its…