Related papers: Optimal Entropic Uncertainty Relation for Successi…
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…
We propose a class of incompatibility measures for quantum observables based on quantifying the effect of a measurement of one observable on the statistics of the outcomes of another. Specifically, for a pair of observables $A$ and $B$ with…
If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present…
Heisenberg's uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: although…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…
Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be…
Collective measurements on identical and independent quantum systems can offer advantages in information extraction compared with individual measurements. However, little is known about the distinction between restricted collective…
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…
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
Joint or simultaneous measurements of non-commuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for defining what an "optimal" joint measurement is, with…
The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We…
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…
The limitation on obtaining precise outcomes of measurements performed on two non-commuting observables of a particle as set by the uncertainty principle in its entropic form, can be reduced in the presence of quantum memory. We derive a…
The uncertainty principle is an important principle in quantum theory. Based on this principle, it is impossible to predict the measurement outcomes of two incompatible observables, simultaneously. Uncertainty principle basically is…
It is assumed that an arbitrary composite bipartite pure state in which the two subsystems are entangled is given, and it is investigated how the entanglement transmits the influence of measurement on only one of the subsystems to the state…
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for…
We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
The entropic uncertainty principle as outlined by Maassen and Uffink for a pair of non-degenerate observables in a finite level qusystem is generalized here to the case of a pair of arbitrary quantum measurements. In particular, our result…