Related papers: Estimation of pure qubit states with collective an…
We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…
We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: Hilbert-Schmidt measure, Bures (statistical) measure, the measures induced by…
When estimating an unknown single pure qubit state, the optimum fidelity is 2/3. As it is well known, the value 2/3 can be achieved in one step, by a single ideal measurement of the polarization along a random direction. I analyze the…
We extend quantum state tomography with minimal cumulative disturbance, first investigated in [arXiv:2406.18370], to arbitrary finite-dimensional pure states. A learner sequentially receives fresh copies of an unknown pure state, chooses a…
We propose an adaptive, two steps strategy, for the estimation of mixed qubit states. We show that the strategy is optimal in a local minimax sense for the trace norm distance as well as other locally quadratic figures of merit. Local…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
We analyze quantum state estimation for finite samples based on symmetry information. The used measurement concept compares an unknown qubit to a reference state. We describe explicitly an adaptive strategy, that enhances the estimation…
We consider unambiguous discrimination of two separable bipartite states, one being pure and the other being a rank-2 mixed state. There is a gap between the optimal success probability under global measurements and the one achieved by…
We consider the evolution of a spin 1/2 (qubit) under the simultaneous continuous measurement of three non-commuting qubit operators sigma_x, sigma_y, sigma_z. For identical ideal detectors the qubit state evolves by approaching a pure…
Fidelity is the standard measure for quantifying the similarity between two quantum states. It is equal to the square of the minimum Bhattacharyya coefficient between the probability distributions induced by quantum measurements on the two…
This letter generalizes the expression for the average fidelity of single qubits, as found by Bowdrey et al., to the case of n qubits. We use a simple algebraic approach with basis elements for the density-matrix expansion expressed as…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
Quantum state tomography and other measures of the global properties of a quantum state are indispensable tools in understanding many body physics through quantum simulators. Unfortunately, the number of experimental measurements of the…
We consider n identically prepared qubits and study the asymptotic properties of the joint state \rho^{\otimes n}. We show that for all individual states \rho situated in a local neighborhood of size 1/\sqrt{n} of a fixed state \rho^0, the…
The article undertakes the problem of pure state estimation from projective measurements based on photon counting. Two generic frames for qubit tomography are considered -- one composed of the elements of the SIC-POVM and the other defined…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
We address the problem of estimating pure qubit states with non-ideal (noisy) measurements in the multiple-copy scenario, where the data consists of a number N of identically prepared qubits. We show that the average fidelity of the…
Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterise the output state by quantum state tomography; or…
We study quantum tomography based on a stochastic continuous-time measurement record obtained from a probe field collectively interacting with an ensemble of identically prepared systems. In comparison to previous studies, we consider here…
The size of the Hilbert space for a multiqubit state scales exponentially with the number of constituent qubits. Often this leads to a similar exponential scaling of the experimental resources required to characterize the state. Contrary to…