Related papers: Quantum state estimation when qubits are lost: A n…
Given a finite number of copies of an unknown qubit state that have already been measured optimally, can one still extract any information about the original unknown state? We give a positive answer to this question and quantify the…
Quantum resources, such as entanglement, can decrease the uncertainty of a parameter-estimation procedure beyond what is classically possible. This phenomenon is well described for noiseless systems with asymptotically many measurement…
The recently established resource theory of quantum coherence allows for a quantitative understanding of the superposition principle, with applications reaching from quantum computing to quantum biology. While different quantifiers of…
As commonly understood, the noise spectroscopy problem---characterizing the statistical properties of a noise process affecting a quantum system by measuring its response---is ill-posed. Ad-hoc solutions assume implicit structure which is…
The guesswork quantifies the minimum cost incurred in guessing the state of an ensemble, when only one state can be queried at a time. In the classical case, it is well known that the optimal strategy trivially consists of querying the…
We consider a two-mode bosonic state with fixed photon number $n \in \mathbb{N}$, whose upper and lower modes pick up a phase $\phi$ and $-\phi$ respectively. We compute the optimal Fock coefficients of the input state, such that the mean…
A model of quantum measurement, illustrated using the spin--boson model, is formulated in terms of a cascading pair of quantum phase transitions. The first produces the desired superposition of macroscopic responses to the microscopic state…
Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography…
Combining quantum and Bayesian principles leads to optimality in metrology, but the optimisation equations involved are often hard to solve. This work mitigates this problem with a novel class of measurement strategies for quantities…
Using quantum systems as sensors or probes has been shown to greatly improve the precision of parameter estimation by exploiting unique quantum features such as entanglement. A major task in quantum sensing is to design the optimal…
Optimal generalized measurements for state estimation are well understood. However, practical quantum state tomography is typically performed using a fixed set of projective measurements and the question of how to choose these measurements…
We study Haar-random bases and pretty good measurement for Bayesian state estimation. Given $N$ Haar-random bases we derive a bound on fidelity averaged over IID sequences of such random measurements for a uniform ensemble of pure states.…
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a…
We study the optimal way to estimate the quantum expectation value of a physical observable when a finite number of copies of a quantum pure state are presented. The optimal estimation is determined by minimizing the squared error averaged…
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…
Preparation of quantum states is of vital importance for performing quantum computations and quantum simulations. In this work, we propose a general framework for preparing ground states of many-body systems by combining the…
Quantum state tomography (QST) is typically performed from a frequentist viewpoint using maximum likelihood estimation (MLE) which seeks to find the best plausible state consistent with the data by maximizing a likelihood function /…
In the absence of experimental constraints, optimal measurement schemes for quantum state tomography are well understood. We consider the scenario where the experimenter doesn't have arbitrary freedom to construct their measurement set, and…
We report an experimental realization of an adaptive quantum state tomography protocol. Our method takes advantage of a Bayesian approach to statistical inference and is naturally tailored for adaptive strategies. For pure states we observe…
We discuss a procedure of measurement followed by the reproduction of the quantum state of a three-level optical system - a frequency- and spatially degenerate two-photon field. The method of statistical estimation of the quantum state…