Related papers: Tight Generalization of Robertson-Type Uncertainty…
Let $A_1,...,A_N$ be complex selfadjoint matrices and let $\rho$ be a density matrix. The Robertson uncertainty principle $$ det (Cov_\rho(A_h,A_j)) \geq det (- \frac{i}{2} Tr (\rho [A_h,A_j])) $$ gives a bound for the quantum generalized…
In this work we use the extremization method of various information-theoretic measures (Fisher information, Shannon entropy, Tsallis entropy) for $d$-dimensional quantum systems, which complementary describe the spreading of the quantum…
The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…
Viewing frames of reference as physical systems, subject to the same laws as the systems they describe, is central to the relational approach in physics. Under the assumption that quantum mechanics universally governs all physical entities,…
Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the…
The uncertainty relation for continuous variables due to Byalinicki-Birula and Mycielski expresses the complementarity between two $n$-uples of canonically conjugate variables $(x_1,x_2,\cdots x_n)$ and $(p_1,p_2,\cdots p_n)$ in terms of…
We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. There are studied uncertainty relations for sums of…
We formulate a new error-disturbance relation, which is free from explicit dependence upon variances in observables. This error-disturbance relation shows improvement over the one provided by the Branciard inequality and the Ozawa…
Heisenberg's original uncertainty relation is related to measurement effect, which is different from the preparation uncertainty relation. However, it has been shown that Heisenberg's error-disturbance uncertainty relation can be violated…
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
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.…
We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system, which provides a state-independent maximum lower bound on the direct-sum of the probability vectors in terms of…
The three ways of generalization of canonical coherent states are briefly reviewed and compared with the emphasis laid on the (minimum) uncertainty way. The characteristic uncertainty relations, which include the Schroedinger and Robertson…
What does it take for real-deterministic c-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of real-deterministic c-valued variables out of the weak values…
We establish an information gain-disturbance trade-off relation in local state discrimination. Our result demonstrates a fundamental limitation of local strategy to discriminate entangled quantum states without disturbance, which becomes…
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to…
Heisenberg's uncertainty principle is quantified by error-disturbance tradeoff relations, which have been tested experimentally in various scenarios. Here we shall report improved new versions of various error-disturbance tradeoff relations…
We derive a state dependent error-disturbance trade-off based on a statistical distance in the sequential measurements of a pair of noncommutative observables and experimentally verify the relation with a photonic qubit system. We…
The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…