Related papers: Estimating the eigenstates of an unknown density o…
The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…
Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a…
Any observable with finite eigenvalue spectrum can be measured using a multiport apparatus realizing an appropriate unitary transformation and an array of detector instruments, where each detector operates as an indicator of one possible…
The goal of self-testing is to characterize an a priori unknown quantum system based solely on measurement statistics, i.e. using an uncharacterized measurement device. Here we develop self-testing methods for quantum prepare-and-measure…
Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on…
We present three different matrix bases that can be used to decompose density matrices of d--dimensional quantum systems, so-called qudits: the generalized Gell-Mann matrix basis, the polarization operator basis, and the Weyl operator…
We prove the existence of extensive many-body Hamiltonians with few-body interactions and a many-body mobility edge: all eigenstates below a nonzero energy density are localized in an exponentially small fraction of "energetically allowed…
We study the dynamics of electrons in crystalline solids in the presence of inhomogeneous external electric and magnetic fields. We present a manifestly gauge-invariant operator-based approach without relying on a semiclassical wavepacket…
We propose to quantify the complexity of non-equilibrium steady state density operators, as well as of long-lived Liouvillian decay modes, in terms of level spacing distribution of their spectra. Based on extensive numerical studies in a…
In a qubit system, the measurement operator does not necessarily commute with the qubit Hamiltonian, so that the readout process demolishes (mixes) the qubit energy eigenstates. The readout time is therefore limited by such a mixing time…
We propose and analyze a method to detect and characterize the drift of a nonstationary quantum source. It generalizes a standard measurement for detecting phase diffusion of laser fields to quantum systems of arbitrary Hilbert space…
We show that every density matrix of an n-particle system prepared by a quantum network of constant depth is asymptotically commuting with the mean-field observables. We introduce certain pairs of hypersurfaces in the space of density…
We use polarization operators known from quantum theory of angular momentum to expand the $N \times N$ dimensional density operators. Thereby, we construct generalized Bloch vectors representing density matrices. We study their properties…
We propose a high efficiency tomographic scheme to reconstruct an unknown quantum state of the qubits by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the…
A method to establish a qubit decomposition of a general qudit state is presented. This new representation allows a geometrical depiction of any qudit state in the Bloch sphere. Additionally, we show that the nonnegativity conditions of the…
Adopting quantum resources for parameter estimation discloses the possibility to realize quantum sensors operating at a sensitivity beyond the standard quantum limit. Such approach promises to reach the fundamental Heisenberg scaling as a…
The usual scenario in fault tolerant quantum computation involves certain amount of qubits encoded in each code block, transversal operations between them and destructive measurements of ancillary code blocks. We introduce a new approach in…
We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and…
Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave…
We experimentally test the recently predicted anisotropic invariance properties of pure three-qubit states, via generation and measurement of polarisation-path entangled three-qubit states. These properties do not require aligned reference…