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As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and…
We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a…
Quantum information has been drawing a wealth of research in recent years, shedding light on questions at the heart of quantum mechanics, as well as advancing fields such as complexity theory, cryptography, key distribution, and chemistry.…
We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify a quantum system which is constrained by prior information? We show that if the prior information restricts the system…
Quantum tomography is one of the major challenges of large-scale quantum information research due to the exponential time complexity. In this work, we develop and apply a Bayesian state estimation method to experimentally demonstrate…
In this work, we consider the fundamental task of quantum state certification: given copies of an unknown quantum state $\rho$, test whether it matches some target state $\sigma$ or is $\epsilon$-far from it. For certifying $d$-dimensional…
Matrix completion and quantum tomography are two unrelated research areas with great current interest in many modern scientific studies. This paper investigates the statistical relationship between trace regression in matrix completion and…
Random ensembles of pure states have proven to be extremely important in various aspects of quantum physics such as benchmarking the performance of quantum circuits, testing for quantum advantage, providing novel insights for many-body…
If the system is known to be in one of two non-orthogonal quantum states, $|\psi_1\rangle$ or $|\psi_2\rangle$, $\mathcal{PT}$-symmetric quantum mechanics can discriminate them, \textit{in principle}, by a single measurement. We extend this…
The exponential scaling of the wave function is a fundamental property of quantum systems with far reaching implications in our ability to process quantum information. A problem where these are particularly relevant is quantum state…
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…
With the advance of quantum information technology, the question of how to most efficiently test quantum circuits is becoming of increasing relevance. Here we introduce the statistics of lengths of measurement sequences that allows one to…
In a recent work [Phys. Rev. Lett. 120, 170502 (2018)], Pallister et al. proposed an optimal strategy to verify non-maximally entangled two-qubit pure states under the constraint that the accessible measurements being locally projective and…
Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and…
We study the discrimination of N mixed quantum states in an optimal measurement that maximizes the probability of correct results while the probability of inconclusive results is fixed at a given value. After considering the discrimination…
Partial tomography, which focuses on reconstructing reduced density matrices (RDMs), has emerged as a promising approach for characterizing complex quantum systems, particularly when full state tomography is impractical. Recently,…
We study the performance of efficient quantum state tomography methods based on neural network quantum states using measured data from a two-photon experiment. Machine learning inspired variational methods provide a promising route towards…
Quantum states and measurements exhibit wave-like --- continuous, or particle-like --- discrete, character. Hybrid discrete-continuous photonic systems are key to investigating fundamental quantum phenomena, generating superpositions of…
The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing…
Measurement-based quantum computing enables universal quantum computing with only adaptive single-qubit measurements on certain many-qubit states, such as the graph state, the Affleck-Kennedy-Lieb-Tasaki (AKLT) state, and several…