Related papers: Designing Optimal Quantum Detectors Via Semidefini…
We prove that for a programmable measurement device that approximates every POVM with an error $\le \delta$, the dimension of the program space has to grow at least polynomially with $\frac{1}{\delta}$. In the case of qubits we can improve…
Quantum measurements of physical quantities are usually described as ideal measurements. However, only a few measurements fulfil the conditions of ideal measurements. The aim of the present work is to describe real position measurements…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of…
Quantum bits, or qubits, are the fundamental building blocks of present quantum computers. Hence, it is important to be able to characterize the state of a qubit as accurately as possible. By evaluating the qubit characterization problem…
While algebraic derivations establish theoretical limits for quantum cloning, practical implementations require explicit operator representations that are often unavailable analytically. We present a computational framework that…
Implementing fast and high-fidelity quantum operations using open-loop quantum optimal control relies on having an accurate model of the quantum dynamics. Any deviations between this model and the complete dynamics of the device, such as…
Quantum state tomography (QST) represents an essential tool for the characterization, verification, and validation (QCVV) of quantum processors. Only for a few idealized scenarios, there are analytic results for the optimal measurement set…
Quantum state estimation aims at determining the quantum state from observed data. Estimating the full state can require considerable efforts, but one is often only interested in a few properties of the state, such as the fidelity with a…
For any pair of quantum states (the hypotheses), the task of binary quantum hypotheses testing is to derive the tradeoff relation between the probability $p_{01}$ of rejecting the null hypothesis and $p_{10}$ of accepting the alternative…
A computational problem fed into a gate-model quantum computer identifies an objective function with a particular computational pathway (objective function connectivity). The solution of the computational problem involves identifying a…
We construct a device that can unambiguously discriminate between two unknown quantum states. The unknown states are provided as inputs, or programs, for the program registers and a third system, which is guaranteed to be prepared in one of…
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg…
A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor…
Leveraging quantum computers for optimization problems holds promise across various application domains. Nevertheless, utilizing respective quantum computing solvers requires describing the optimization problem according to the Quadratic…
This paper introduces the Quantum Covariance Embedding, which embeds Positive Operator-Valued Measures into a tensor product of a Reproducing Kernel Hilbert Space and the quantum state space via a tensorized Bochner integral. This…
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…
We provide a rate distortion interpretation of the problem of quantum data compression of ensembles of mixed states with commuting density operators. There are two versions of this problem. In the visible case the sequence of states is…
We study the measurement for the unambiguous discrimination of two mixed quantum states that are described by density operators $\rho_1$ and $\rho_2$ of rank d, the supports of which jointly span a 2d-dimensional Hilbert space. Based on two…
Atomic norm minimization is a convex optimization framework to recover point sources from a subset of their low-pass observations, or equivalently the underlying frequencies of a spectrally-sparse signal. When the amplitudes of the sources…