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We analyze quantum state tomography in scenarios where measurements and states are both constrained. States are assumed to live in a semi-algebraic subset of state space and measurements are supposed to be rank-one POVMs, possibly with…

Quantum state tomography (QST) aiming at reconstructing the density matrix of a quantum state plays an important role in various emerging quantum technologies. Recognizing the challenges posed by imperfect measurement data, we develop a…

Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger…

The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…

Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness…

Quantum measurement is a physical process. What physical resources and constraints does quantum mechanics require for measurement to produce the classical world we observe? Treating measurement as a fully unitary quantum process, our goal…

We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice…

Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…

A software product line models the variability of highly configurable systems. Complete exploration of all valid configurations (the configuration space) is infeasible as it grows exponentially with the number of features in the worst case.…

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…

Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to reconstruct the density matrix of a physical system from measurement results. One strategy to deal with positivity and unit trace…

We consider a physical system in which the description of states and measurements follow the usual quantum mechanical rules. We also assume that the dynamics is linear, but may not be fully quantum (i.e unitary). We show that in such a…

Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed…

Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…

The reconstruction of quantum states from a sufficient set of experimental data can be achieved with arbitrarily weak measurement interactions. Since such weak measurements have negligible back-action, the quantum state reconstruction is…

Many experiments in quantum information aim at creating multi-partite entangled states. Quantifying the amount of entanglement that was actually generated can, in principle, be accomplished using full-state tomography. This method requires…

We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…

To improve the efficiency of the state tomography strategy via weak value, we have searched the optimal coupling strength between the system and measuring device. For an arbitrary d-dimensional quantum system, the optimal strengths being…

We discuss the concept of connection states (or connection matrices) that describe posterior ensembles, post-selected according to the outcomes of a quantum measurement. Connection matrices allow one to obtain results of any weak and some…

We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…