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Quantum state tomography, which aims to find the best description of a quantum state -- the density matrix, is an essential building block in quantum computation and communication. Standard techniques for state tomography are incapable of…
Characterizing complex quantum systems is a vital task in quantum information science. Quantum tomography, the standard tool used for this purpose, uses a well-designed measurement record to reconstruct quantum states and processes. It is,…
In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state…
We apply the fidelity metric approach to analyze two recently introduced models that exhibit a quantum phase transition to a topologically ordered phase. These quantum models have a known connection to classical statistical mechanical…
Face recognition is one of the most ubiquitous examples of pattern recognition in machine learning, with numerous applications in security, access control, and law enforcement, among many others. Pattern recognition with classical…
Quantum noise constitutes a fundamental obstacle to realizing practical quantum technologies. To address the pivotal challenge of identifying quantum systems least affected by noise, we introduce the purest quantum state identification,…
We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate, namely produces states close to a target one within a prescribed threshold. We show that, when multiple measurements need…
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…
Quantum tomography is a process of quantum state reconstruction using data from multiple measurements. An essential goal for a quantum tomography algorithm is to find measurements that will maximize the useful information about an unknown…
Self-calibrating quantum state tomography aims at reconstructing the unknown quantum state and certain properties of the measurement devices from the same data. Since the estimates of the state and device parameters come from the same data,…
We describe a technique for self consistently characterizing both the quantum state of a single qubit system, and the positive-operator-valued measure (POVM) that describes measurements on the system. The method works with only ten…
In the current work we address the problem of quantum process tomography (QPT) in the case of imperfect preparation and measurement of the states which are used for QPT. The fuzzy measurements approach which helps us to efficiently take…
Several Bayesian estimation based heuristics have been developed to perform quantum state tomography (QST). Their ability to quantify uncertainties using region estimators and include a priori knowledge of the experimentalists makes this…
Estimating the fidelity with a target state is important in quantum information tasks. Many fidelity estimation techniques present a suitable measurement scheme to perform the estimation. In contrast, we present techniques that allow the…
We propose and investigate bounds on quantum process fidelity of quantum filters, i.e. probabilistic quantum operations represented by a single Kraus operator K. These bounds generalize the Hofmann bounds on quantum process fidelity of…
Quantum state tomography (QST) is one of the fundamental problems in quantum information. Among various metrics, sample complexity is widely used to evaluate QST algorithms. While multi-copy measurements are known to achieve optimal sample…
Measuring the distinguishability between quantum states is a basic problem in quantum information theory. In this paper, we develop optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure…
State of the art qubit systems are reaching the gate fidelities required for scalable quantum computation architectures. Further improvements in the fidelity of quantum gates demands characterization and benchmarking protocols that are…
In the framework of noisy quantum homodyne tomography with efficiency parameter $1/2 < \eta \leq 1$, we propose a novel estimator of a quantum state whose density matrix elements $\rho_{m,n}$ decrease like $Ce^{-B(m+n)^{r/ 2}}$, for fixed…
The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent…