Related papers: Optimal weak value measurements: Pure states
We derive the optimal measurement for quantum state discrimination without a priori probabilities, i.e. in a minimax strategy instead of the usually considered Bayesian one. We consider both minimal-error and unambiguous discrimination…
We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared quantum systems. The state is represented through the Wigner function, a generalized probability density on…
Not all entangled states can exhibit quantum steering, and determining whether a given entangled state is steerable is a crucial problem in quantum information theory. The main challenge lies in verifying the existence of a local…
We explore the possibility of using "weak" measurements to carry out quantum state tomography. Given a certain fixed number of copies of identically prepared states of a qubit, we simulate state tomography using weak as well as projective…
Tomography of a quantum state is usually based on positive operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose…
A model is proposed for the statistical analysis of arbitrary-strength quantum measurements, based on a picture of "sampling weak values" from different configurations of the system. The model is comprised of two elements: a "local weak…
The time-symmetric formalism endows the weak measurement and its outcome, the weak value,many unique features. In particular, it allows a direct tomography of quantum states without resort to complicated reconstruction algorithms and…
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…
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting…
The efficiency of quantum state tomography is discussed from the point of view of quantum parameter estimation theory, in which the trace of the weighted covariance is to be minimized. It is shown that tomography is optimal only when a…
In this work, we consider the systematic error of quantum metrology by weak measurements under decoherence. We derive the systematic error of maximum likelihood estimation in general to the first-order approximation of a small deviation in…
Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the…
We investigate the optimal measurement strategy for state discrimination of the trine ensemble of qubit states prepared with arbitrary prior probabilities. Our approach generates the minimum achievable probability of error and also the…
The weak measurement proposed by Aharonov and his colleagues extracts information of a physical quantity of the system by the post selection as the shifts of the argument of the probe wavefunction. The shift is called the weak value and is…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
For continuous weak measurement of qubits, we obtain exact expressions for weak values (WVs) from the post-selection restricted average of measurement outputs, by using both the quantumtrajectory- equation (QTE) and quantum Bayesian…
Maximum likelihood estimation (MLE) is the most common approach to quantum state tomography. In this letter, we investigate whether it is also optimal in any sense. We show that MLE is an inadmissible estimator for most of the commonly used…
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…
Quantum state tomography aims to determine the quantum state of a system from measured data and is an essential tool for quantum information science. When dealing with continuous variable quantum states of light, tomography is often done by…
It is known that mutually unbiased bases, whenever they exist, are optimal in an information theoretic sense for the determination of unknown state of a quantum ensemble. These bases may not exist in most dimensions and some suboptimal…