Related papers: Minimal orthonormal bases for pure quantum state e…
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…
In this paper we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can…
An optimal estimator of quantum states based on a modified Kalman Filter is presented in this work. Such estimator acts after state measurement, allowing to obtain an optimal estimation of quantum state resulting in the output of any…
We revisit the problem of estimating an unknown parameter of a pure quantum state, and investigate `null-measurement' strategies in which the experimenter aims to measure in a basis that contains a vector close to the true system state.…
We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, "as close as possible" to orthonormal bases for the space of quantum states. These measures are distinguished by an…
Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify…
We present, and analyze thoroughly, a highly symmetric and efficient scheme for the determination of a single-qubit state, such as the polarization properties of photons emitted by a single-photon source. In our scheme there are only four…
We study the optimal way to estimate the quantum expectation value of a physical observable when a finite number of copies of a quantum pure state are presented. The optimal estimation is determined by minimizing the squared error averaged…
We introduce a reliable compressive procedure to uniquely characterize any given low-rank quantum measurement using a minimal set of probe states that is based solely on data collected from the unknown measurement itself. The procedure is…
Quantum tomography is a critically important tool to evaluate quantum hardware, making it essential to develop optimized measurement strategies that are both accurate and efficient. We compare a variety of strategies using nearly pure test…
It is known that mutually unbiased bases, whenever they exist, are optimal in an information theoretic sense for the determination of unknown state of a quantum ensemble. These bases may not exist in most dimensions and some suboptimal…
In quantum-state tomography on sources with quantum degrees of freedom of large Hilbert spaces, inference of quantum states of light for instance, a complete characterization of the quantum states for these sources is often not feasible…
Quantum state tomography is the standard tool in current experiments for verifying that a state prepared in the lab is close to an ideal target state, but up to now there were no rigorous methods for evaluating the precision of the state…
The reconstruction of quantum states from experimental measurements, often achieved using quantum state tomography (QST), is crucial for the verification and benchmarking of quantum devices. However, performing QST for a generic…
We present the optimal measurement strategy for distinguishing between three quantum states exhibiting a mirror symmetry. The three states live in a two-dimensional Hilbert space, and are thus overcomplete. By mirror symmetry we understand…
A central task in quantum information science is state certification: testing whether an unknown state is $\epsilon_1$-close to a fixed target state, or $\epsilon_2$-far. Recent work has shown that surprisingly simple measurement…
Quantum state tomography is an indispensable but costly part of many quantum experiments. Typically, it requires measurements to be carried in a number of different settings on a fixed experimental setup. The collected data is often…
Quantum phase estimation is an important routine in many quantum algorithms, particularly for estimating the ground state energy in quantum chemistry simulations. This estimation involves applying powers of a unitary to the ground state,…
We present a tomographic method which requires only $4d-3$ measurement outcomes to reconstruct \emph{any} pure quantum state of arbitrary dimension $d$. Using the proposed scheme we have experimentally reconstructed a large number of pure…
We present a three-qubit quantum state tomography scheme requiring a set of 17 measurement settings, significantly reducing the experimental overhead compared to the conventional 63 Pauli measurement settings. Using IBM's 127-qubit…