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Achieving quantum-enhanced performances when measuring unknown quantities requires developing suitable methodologies for practical scenarios, that include noise and the availability of a limited amount of resources. Here, we report on the…
Quantum state smoothing is a technique to construct an estimate of the quantum state at a particular time, conditioned on a measurement record from both before and after that time. The technique assumes that an observer, Alice, monitors…
Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…
Measures of quantum properties are essential to understanding the fundamental differences between quantum and classical systems as well as quantifying resources for quantum technologies. Here two broad classes of bosonic phase-space…
We study the time evolution of mean values of quantum operators in a regime plagued by two difficulties: The smallness of $\hbar$ and the presence of strong and ubiquitous classical chaos. While numerics become too computationally expensive…
Analyzing the impact of noise is of fundamental importance to understand the advantages provided by quantum systems. While the classical simulability of noisy discrete-variable systems is increasingly well understood, noisy bosonic circuits…
We generalize the operational quasiprobability involving sequential measurements proposed by Ryu {\em et al.} [Phys. Rev. A {\bf 88}, 052123] to a continuous-variable system. The quasiprobabilities in quantum optics are incommensurate,…
In this comment on the paper by F. Kaneda, S.-Y. Baek, M. Ozawa and K. Edamatsu [Phys. Rev. Lett. 112, 020402, 2014, arXiv:1308.5868], we point out that the claim of having refuted Heisenberg's error-disturbance relation is unfounded since…
Leveraging quantum effects in metrology such as entanglement and coherence allows one to measure parameters with enhanced sensitivity. However, time-dependent noise can disrupt such Heisenberg-limited amplification. We propose a…
I show that the application of the quantum-mechanical (QM) which-way weak measurement scheme of Vaidman may lead to logical inconsistencies. To this end, I study weak values of projection operators. Weak values are (normalized) amplitudes,…
We address the experimental determination of entanglement for systems made of a pair of polarization qubits. We exploit quantum estimation theory to derive optimal estimators, which are then implemented to achieve ultimate bound to…
We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement schemes. Detection probability has…
Quantum mechanics predicts the joint probability distributions of the outcomes of simultaneous measurements of commuting observables, but the current formulation lacks the operational definition of simultaneous measurements. In order to…
The sum-of-squares method can give rigorous lower bounds on the energy of quantum Hamiltonians. Unfortunately, typically using this method requires solving a semidefinite program, which can be computationally expensive. Further, the…
The sampling, quantization, and estimation of a bounded dynamic-range bandlimited signal affected by additive independent Gaussian noise is studied in this work. For bandlimited signals, the distortion due to additive independent Gaussian…
Obtaining the expectation value of an observable on a quantum computer is a crucial step in the variational quantum algorithms. For complicated observables such as molecular electronic Hamiltonians, a common strategy is to present the…
Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic…
This paper focuses on random projection operators when the subspace of projection is estimated. We derive non-asymptotic upper bounds on the error between the projection onto the estimated subspace and the projection onto the underlying…
Noisy, intermediate-scale quantum computers come with intrinsic limitations in terms of the number of qubits (circuit "width") and decoherence time (circuit "depth") they can have. Here, for the first time, we demonstrate a recently…
Successful implementations of quantum technologies require protocols and algorithms that use as few quantum resources as possible. However, many important quantum operations, such as continuous rotation gates in quantum computing or…