Related papers: Higher-order uncertainty bounds for mixed states
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner-Yanase skew information. The variances in this uncertainty relation does not involve any classical mixing uncertainty,…
Entropic uncertainty relations in a finite dimensional Hilbert space are investigated. Making use of the majorization technique we derive explicit lower bounds for the sum of R\'enyi entropies describing probability distributions associated…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
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…
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
Uncertainty principle is the basis of quantum mechanics. It reflects the basic law of the movement of microscopic particles. Wigner-Yanase skew information, as a measure of quantum uncertainties, is used to characterize the intrinsic…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
We analyze entropic uncertainty relations in a finite dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the…
A closed-form expression for Wigner-Yanase skew information in mixed-state quantum systems is derived. It is shown that limit values of the mixing coefficients exist such that Wigner-Yanase information is equal to Helstrom information. The…
Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between…
We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states,…
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…
We present a new uncertainty relation by defining a measure of uncertainty based on skew information. For bipartite systems, we establish uncertainty relations with the existence of a quantum memory. A general relation between quantum…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…
We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density…
Uncertainty relations for mixed quantum states (precisely, purity-bounded position-momentum relations, developed by Bastiaans and then by Man'ko and Dodonov) are studied in general multi-dimensional case. An expression for family of mixed…