Related papers: Optimal weak value measurements: Pure states
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…
We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a…
We discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same…
We characterize minimal measurement setups for validating the quantum coherence of an unknown quantum state. We show that for a $d$-level system, the optimal strategy consists of measuring $d$ orthonormal bases such that each measured basis…
We give an algorithm for pure state tomography with near-optimal copy and time complexity using only single-qubit measurements. Specifically, given $\widetilde{O}(2^n/\epsilon)$ copies of an unknown $n$-qubit pure state $|\psi\rangle$, the…
In quantum estimation for a $d$-parameter family of density operators on a finite-dimensional Hilbert space $\mathcal{H}$, an estimator is specified by a pair $\left(M,\hat{\theta}\right)$, where $M$ is a POVM with a finite outcome set…
Conventional quantum mechanics describes a pre- and post-selected system in terms of virtual (Feynman) paths via which the final state can be reached. In the absence of probabilities, a weak measurement (WM) determines the probability…
Quantum measurements, alongside quantum states and processes, form a cornerstone of quantum information processing. However, unlike states and processes, their efficient characterisation remains relatively unexplored. We resolve this…
In hypothesis testing with quantum states, given a black box containing one of the two possible states, measurement is performed to detect in favor of one of the hypotheses. In postselected hypothesis testing, a third outcome is added,…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
Deterministic discrimination of nonorthogonal states is forbidden by quantum measurement theory. However, if we do not want to succeed all the time, i.e. allow for inconclusive outcomes to occur, then unambiguous discrimination becomes…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing…
We study the problem of discriminating between non-orthogonal quantum states with least probability of error. We demonstrate that this problem can be simplified if we solve for the error itself rather than solving directly for the optimal…
We give a review of the most important results on optimal tomography as mathematical wave-pattern recognition theory emerged in the 70's in connection with the problems of optimal estimation and hypothesis testing in quantum theory. In…
A quantum state contains the maximal amount of information available for a given quantum system. In this paper we use weak-value expressions to reconstruct quantum states of continuous-variable systems in the quantum optical domain. The…
Rather than point estimators, states of a quantum system that represent one's best guess for the given data, we consider optimal regions of estimators. As the natural counterpart of the popular maximum-likelihood point estimator, we…
We define a positive operator valued measure $E$ on $[0,2\pi]\times R$ describing the measurement of randomly sampled quadratures in quantum homodyne tomography, and we study its probabilistic properties. Moreover, we give a mathematical…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
The Wigner quasiprobability distribution of a narrowband single-photon state was reconstructed by quantum state tomography using photon-number-resolving measurements with transition-edge sensors (TES) at system efficiency 58(2)%. This…