Related papers: Uncertainty relations for general unitary operator…
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…
We investigate entropic uncertainty relations for two or more binary measurements, for example spin-$\frac{1}{2}$ or polarisation measurements. We argue that the effective anti-commutators of these measurements, i.e. the anti-commutators…
The problem of optimally estimating an unknown unitary quantum operation with the aid of entanglement is addressed. The idea is to prepare an entangled pair, apply the unknown unitary to one of the two parts and then measure the joint…
We discuss some applications of various versions of uncertainty relations for both discrete and continuous variables in the context of quantum information theory. The Heisenberg uncertainty relation enables demonstration of the EPR paradox.…
It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…
We derive entropic uncertainty relations for successive generalized measurements by using general descriptions of quantum measurement within two {distinctive operational} scenarios. In the first scenario, by merging {two successive…
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain…
We investigate the product form uncertainty relations of variances for $n\,(n\geq 3)$ quantum observables. In particular, tight uncertainty relations satisfied by three observables has been derived, which is shown to be better than the ones…
We construct steering inequalities which exhibit unbounded violation. The concept was to exploit the relationship between steering violation and uncertainty relation. To this end we apply mutually unbiased bases and anti-commuting…
The idea to base the uncertainty relation for photons on the electromagnetic energy distribution in space enabled us to derive a sharp inequality that expresses the uncertainty relation [Phys. Rev. Lett. {\bf 108}, 140401 (2012)]. An…
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…
Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields…
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…
Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is…
A survey on the generalizations of Heisenberg uncertainty relation and a general scheme for their entangled extensions to several states and observables is presented. The scheme is illustrated on the examples of one and two states and…
We investigate the fine-grained uncertainty relations for qubit system by measurements corresponding respectively to two and three spin operators. Then we derive the general bound for a combination of two probabilities of projective…
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension…
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,…
In quantum mechanics, joint measurements of non-commuting observables are only possible if a minimal unavoidable measurement uncertainty is accepted. On the other hand, correlations between non-commuting observables can exceed classical…
We revisit the Extended Uncertainty Principle (EUP) from an operational viewpoint, replacing wavefunction-based widths with apparatus-defined position constraints such as a finite slit of width $\Delta x$ or a geodesic ball of radius $R$.…