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A prime goal of quantum tomography is to provide quantitatively rigorous characterisation of quantum systems, be they states, processes or measurements, particularly for the purposes of trouble-shooting and benchmarking experiments in…
The ability of fully reconstructing quantum maps is a fundamental task of quantum information, in particular when coupling with the environment and experimental imperfections of devices are taken into account. In this context we carry out a…
In the light of the progress in quantum technologies, the task of verifying the correct functioning of processes and obtaining accurate tomographic information about quantum states becomes increasingly important. Compressed sensing, a…
We address the problem of completely characterizing multi-particle states including loss of information to unobserved degrees of freedom. In systems where non-classical interference plays a role, such as linear-optics quantum gates, such…
Quantum learning (in metrology and machine learning) involves estimating unknown parameters from measurements of quantum states. The quantum Fisher information matrix can bound the average amount of information learnt about the unknown…
We show that given a quantum measurement, for an overwhelming majority of pure states, no meaningful information is produced. This is independent of the number of outcomes of the quantum measurement. Due to conservation inequalities, such…
Complete characterization of states and processes that occur within quantum devices is crucial for understanding and testing their potential to outperform classical technologies for communications and computing. However, solving this task…
Adaptive measurements were recently shown to significantly improve the performance of quantum state tomography. Utilizing information about the system for the on-line choice of optimal measurements allows to reach the ultimate bounds of…
The partial states of a multipartite quantum state may carry a lot of information: in some cases, they determine the global state uniquely. This result is known for tomographic information, that is for fully characterized measurements. We…
We provide a review of the experimental and theoretical research in the field of quantum tomography with an emphasis on recently developed adaptive protocols. Several statistical frameworks for adaptive experimental design are discussed. We…
Practical quantum state tomography is usually performed by carrying out repeated measurements on many copies of a given state. The accuracy of the reconstruction depends strongly on the dimensionality of the system and the number of copies…
Whenever we do not have an informationally complete set of measurements, the estimate of a quantum state can not be uniquely determined. In this case, among the density matrices compatible with the available data, it is commonly preferred…
In this paper, we consider the generalized measurement where one particular quantum signal is unambiguously extracted from a set of non-commutative quantum signals and the other signals are filtered out. Simple expressions for the maximum…
Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…
Proofs of the quantum advantage available in imaging or detecting objects under quantum illumination can rely on optimal measurements without specifying what they are. We use the continuous-variable Gaussian quantum information formalism to…
A framework for a quantum information theory is introduced that is based on the measure of quantum information associated with probability distribution predicted by quantum measuring of state. The entanglement between states of measured…
We show with explicit formulas that one can completely identify an unknown quantum process with only one weakly entangled state; and identify a quantum optical Gaussian process with either one two-mode squeezed state or a few different…
Quantum information refers to the distinctive information-processing properties of quantum systems, which arise when information is stored in or retrieved from nonorthogonal quantum states. More information is required to prepare an…
We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value. In this scenario, new notions of informationally complete POVMs emerge, which…