Related papers: Optimal weak value measurements: Pure states
We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy…
We study the problem of mapping an unknown mixed quantum state onto a known pure state without the use of unitary transformations. This is achieved with the help of sequential measurements of two non-commuting observables only. We show that…
Using the convex structure of positive operator value measurements and of several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to…
We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
The weak-value-amplification (WVA) technique has been extensively considered and debated in the field of quantum precision measurement, largely owing to the reduced Fisher information caused by the low probability of successful…
We explore precision in a measurement process incorporating pure probe states, unitary dynamics and complete measurements via a simple formalism. The concept of `information complement' is introduced. It undermines measurement precision and…
Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to reconstruct the density matrix of a physical system from measurement results. One strategy to deal with positivity and unit trace…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
The existence of \emph{weak conical K\"ahler-Einstein} metrics along smooth hypersurfaces with angle between $0$ and $2\pi$ is obtained by studying a smooth continuity method and a \emph{local Moser's iteration} technique. In the case of…
Quantum nonlocality offers a secure way to produce random numbers: their unpredictability is intrinsic and can be certified just by observing the statistic of the measurement outcomes, without assumptions on how they are produced. To do…
Maximum likelihood quantum state tomography yields estimators that are consistent, provided that the likelihood model is correct, but the maximum likelihood estimators may have bias for any finite data set. The bias of an estimator is the…
We consider weak measurements (WM) of a spin observable in quantum mechanics beyond the usual asymptotic regime. This is done by obtaining the exact time-dependent wave functions of the measuring apparatus for general non-ideal…
We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a…
It is a well-known fact that the optimal POVM for quantum state tomography is the symmetric, informationally complete, positive operator valued measure (SIC-POVM). We investigate the same problem only in the case when there are some a…
We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the…
We study quantum metrology for unitary dynamics. Analytic solutions are given for both the optimal unitary state preparation starting from an arbitrary mixed state and the corresponding optimal measurement precision. This represents a…
The indeterminism of quantum mechanics generally permits the independent specification of both an initial and a final condition on the state. Quantum pre-and-post-selection of states opens up a new, experimentally testable, sector of…
Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases…
The optimization conditions for minimum error discrimination of linearly independent pure states comprise of two kinds: stationary conditions over the space of rank one projective measurements and the global maximization conditions. A…