Related papers: Position measuring interactions and the Heisenberg…
It is shown that the well-defined unbiased measurement or disturbance of a dynamical variable is not maintained for the precise measurement of the conjugate variable, independently of uncertainty relations. The conditionally valid…
Quantum theory famously entails the existence of incompatible measurements; pairs of observables which cannot be simultaneously measured to arbitrary precision. Incompatibility is widely regarded to be a uniquely quantum phenomenon, linked…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not…
We ask which is the best strategy to reveal uncertainty relations between comple- mentary observables of a continuous variable system for coarse-grained measurements. This leads to the derivation of new uncertainty relations for…
A rigorous lower bound is obtained for the average resolution of any estimate of a shift parameter, such as an optical phase shift or a spatial translation. The bound has the asymptotic form k_I/<2|G|> where G is the generator of the shift…
Heisenberg's uncertainty principle implies that if one party (Alice) prepares a system and randomly measures one of two incompatible observables, then another party (Bob) cannot perfectly predict the measurement outcomes. This implication…
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
When a measurement is made on a system that is not in an eigenstate of the measured observable, it is often assumed that some conservation law has been violated. Discussions of the effect of measurements on conserved quantities often…
I discuss some of the main interpretations given to explain the indeterministic nature of quantum measurements and show that all has some loopholes in one corner or another. I propose an alternative interpretation based on the notion of…
Incompatible observables underlie pillars of quantum physics such as contextuality and entanglement. The Heisenberg uncertainty principle is a fundamental limitation on the measurement of the product of incompatible observables, a `joint'…
The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary…
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form $(\Delta P)(\Delta Q)\geq C\hbar$, where the `uncertainties' quantify the difference between the marginals of the…
We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…
In the general theory of quantum measurement, one associates a positive semidefinite operator on a $d$-dimensional Hilbert space to each of the $n$ possible outcomes of an arbitrary measurement. In the special case of a projective…
Precision metrology underpins scientific and technological advancements. Quantum metrology offers a pathway to surpass classical sensing limits by leveraging quantum states and measurement strategies. However, measuring multiple…
The uncertainty relation, which displays an elementary property of quantum theory, was originally described by Heisenberg as the relation between error and disturbance. Ozawa presented a more rigorous expression of the uncertainty relation,…
The uncertainty principle places a fundamental limit on the accuracy with which we can measure conjugate physical quantities. However, the fluctuations of these variables can be assessed in terms of different estimators. We propose a new…
The effects of any quantum measurement can be described by a collection of measurement operators {M_m} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the…
The Heisenberg uncertainty inequality is used to derive a rigorous lower bound to the amount of isospin impurities in $N=Z$ atomic nuclei, caused by the violation of isospin symmetry. The bound is fixed by the difference between the neutron…