Related papers: Optimal Discrimination Between Two Pure States and…
We derive the class of covariant measurements which are optimal according to the maximum likelihood criterion. The optimization problem is fully resolved in the case of pure input states, under the physically meaningful hypotheses of…
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…
In quantum theory general measurements are described by so-called Positive Operator-Valued Measures (POVMs). We show that in $d$-dimensional quantum systems an application of depolarizing noise with constant (independent of $d$) visibility…
We study the following metric distortion problem: there are two finite sets of points, $V$ and $C$, that lie in the same metric space, and our goal is to choose a point in $C$ whose total distance from the points in $V$ is as small as…
A direct derivation is given for the optimal mean fidelity of quantum state estimation of a d-dimensional unknown pure state with its N copies given as input, which was first obtained by M. Hayashi in terms of an infinite set of covariant…
We extend quantum state tomography with minimal cumulative disturbance, first investigated in [arXiv:2406.18370], to arbitrary finite-dimensional pure states. A learner sequentially receives fresh copies of an unknown pure state, chooses a…
We discuss the disturbance by measurements which unambiguously discriminate between given candidate states. We prove that such an optimal measurement necessarily changes distinguishable states indistinguishable when the inconclusive outcome…
We investigate the tradeoff between the quality of an approximate version of a given measurement and the disturbance it induces in the measured quantum system. We prove that if the target measurement is a non-degenerate von Neumann…
Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…
We consider a state discrimination problem which deals with settings of minimum-error and unambiguous discrimination systematically by introducing a margin for the probability of an incorrect guess. We analyze discrimination of three…
A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general…
The problem of unambiguously distinguishing among nonorthogonal but linearly independent quantum states can be solved by mapping the set of nonorthogonal quantum states onto a set of orthogonal ones, which can then be distinguished without…
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 show that given experimental data obtained from joint position and momentum measurements one can construct an optimal pure state approximating the observed quantum state. For that purpose we use a tool from multivariate statistical…
Various forms of optimality for quantum observables described as normalized positive operator valued measures (POVMs) are studied in this paper. We give characterizations for observables that determine the values of the measured quantity…
It is a crucial feature of quantum mechanics that not all measurements are compatible with each other. However, if measurements suffer from noise they may lose their incompatibility. Here, we consider the effect of white noise and determine…
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,…
Using tools from quantum information theory, we present a general theory of indistinguishability of identical bosons in experiments consisting of passive linear optics followed by particle number detection. Our results do neither rely on…
We propose and experimentally demonstrate non-destructive and noiseless removal (filtering) of vacuum states from an arbitrary set of coherent states of continuous variable systems. Errors i.e. vacuum states in the quantum information are…
Using quantum measurements to extract information from states is a matter of routine in quantum science and technologies. A recent work [Phys. Rev. Lett. 133, 040202 (2024)] reported the finding that the symmetric structures of a state can…