Related papers: Optimal covariant quantum measurements
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…
We characterize the asymptotic performance of a class of positive operator valued measurements (POVMs) where the only task is to make measurements on independent and identically distributed quantum states on finite-dimensional systems. The…
We study extreme points of the set of finite-outcome positive-operator-valued measures (POVMs) on finite-dimensional Hilbert spaces and particularly the possible ranks of the effects of an extreme POVM. We give results discussing ways of…
Joint approximate measurement schemes of position and momentum provide us with a means of inferring pieces of complementary information if we allow for the irreducible noise required by quantum theory. One such scheme is given by the…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…
The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on…
Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The…
It is well known that a quantum correlated probe can yield better precision in estimating an unknown parameter than classically possible. However, how such a quantum probe should be measured remains somewhat elusive. We examine the role of…
Quantum discrimination and estimation are pivotal for many quantum technologies, and their performance depends on the optimal choice of probe state and measurement. Here we show that their performance can be further improved by suitably…
We study the quantum ($C^*$) convexity structure of normalized positive operator valued measures (POVMs) on measurable spaces. In particular, it is seen that unlike extreme points under classical convexity, $C^*$-extreme points of…
This tutorial introduces a systematic approach for addressing the key question of quantum metrology: For a generic task of sensing an unknown parameter, what is the ultimate precision given a constrained set of admissible strategies. The…
Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum…
Surprisingly often decoherence is due to classical fluctuations of ambient fields and may thus be described in terms of random unitary (RU) dynamics. However, there are decoherence channels where such a representation cannot exist. Based on…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
We consider how the theory of optimal quantum measurements determines the maximum information available to the receiving party of a quantum key distribution (QKD) system employing linearly independent but non-orthogonal quantum states. Such…
We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic…
Simultaneous measurement of several noncommuting observables is modeled by using semigroups of completely positive maps on an algebra with a non-trivial center. The resulting piecewise-deterministic dynamics leads to chaos and to nonlinear…
We present strictly efficient schemes for scalable measurement-based quantum computing using continuous-variable systems: These schemes are based on suitable non-Gaussian resource states, ones that can be prepared using interactions of…