Related papers: Tight Entropic Uncertainty Relations
Under the scenario of generalized measurements, it can be questioned how much of quantum uncertainty can be attributed to measuring device, independent of the uncertainty in the measured system. On the course to answer the question, we…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
The sum of entropic uncertainties for the measurement of two non-commuting observables is not always reduced by the amount of entanglement (quantum memory) between two parties, and in certain cases may be impacted by quantum correlations…
We derive an asymptotic lower bound on the Shannon entropy $H$ of sums of $N$ arbitrary iid discrete random variables. The derived bound $H \geq \frac{r(X)}{2}\log(N) + {\it cst}$ is given in terms of the incommensurability rank $r(X)$ of…
Recently, an entropic uncertainty relation for multiple measurements has been proposed by Liu et al. in [Phys. Rev. A 91, 042133 (2015)]. However, the lower bound of the relation is not always tight with respect to different measurements.…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
It is well known that the entropy $H(X)$ of a discrete random variable $X$ is always greater than or equal to the entropy $H(f(X))$ of a function $f$ of $X$, with equality if and only if $f$ is one-to-one. In this paper, we give tight…
The uncertainty principle has been established within the framework of locally compact quantum groups in recent years. This paper demonstrates that entropic uncertainty relations can be strengthened under localizations on discrete quantum…
We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when…
We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation…
Uncertainty relations are pivotal in delineating the limits of simultaneous measurements for observables. In this paper, we derive four novel uncertainty and reverse uncertainty relations for the sum of variances of two incompatible…
We derive several entanglement criteria for bipartite continuous variable quantum systems based on the Shannon entropy. These criteria are more sensitive than those involving only second-order moments, and are equivalent to well-known…
Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
The uncertainty principle determines the distinction between the classical and quantum worlds. This principle states that it is not possible to measure two incompatible observables with the desired accuracy simultaneously. In quantum…
The Shannon entropy in the atomic, molecular and chemical physics context is presented by using as test cases the hydrogenic-like atoms $H_c$, ${He_c}^+$ and ${Li_c}^{2+}$ confined by an impenetrable spherical box. Novel expressions for…
A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should use when doing any calculation using the entangled wave function of the pair. This new…
In this paper, we compute uncertainty relations for non-commutative space and obtain a better lower bound than the standard one obtained from Heisenberg's uncertainty relation. We also derive the reverse uncertainty relation for product and…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…
We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the B\"ottcher-Wenzel inequality. The first relation is mathematically proven, while the second, tighter relation is…