Related papers: State independent uncertainty relations from eigen…
Accuracy of a relativistic weak-coupling expansion procedure for solving the Hamiltonian bound-state eigenvalue problem in theories with asymptotic freedom is measured using a well-known matrix model. The model is exactly soluble and simple…
We derive lower bounds on the time needed for a quantum annealer to prepare the ground state of a target Hamiltonian. These bounds do not depend on the annealing schedule and can take the local structure of the Hamiltonian into account.…
Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson,…
The uncertainty relations (URs) of two arbitrary Hermitian and non-Hermitian incompatible operators represented by the product of variances have been confirmed theoretically and experimentally in various physical systems. However, the lower…
We explain several separability criteria which rely on uncertainty relations. For the derivation of these criteria uncertainty relations in terms of variances or entropies can be used. We investigate the strength of the separability…
We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices.…
The complicated interactions in presence of disorder lead to a correlated randomization of states. The Hamiltonian as a result behaves like a multi-parametric random matrix with correlated elements. We show that the eigenvalue correlations…
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 aim of the work is to give the explicit proofs of the Renyi-entropy uncertainty relations presented in the previous work [A. Rastegin, arXiv:0805.1777]. The relations with both the state-dependent and state-independent entropic bounds…
We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a…
We consider any noncontextuality inequality, and the state preparation scheme which consists in performing any von Neumann measurement on any initial state. For an inequality which is not always satisfied, and Hilbert space dimensions…
We ask which is the best strategy to reveal uncertainty relations between comple- mentary observables of a continuous variable system for coarse-grained measurements. This leads to the derivation of new uncertainty relations for…
Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually…
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…
In this paper we investigate the problem of minimization the Heisenberg's uncertainty relation by the trajectory-coherent states. The conditions of minimization for Hamiltonian and trajectory are obtained. We show that the…
Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present…
We establish the tightest possible Robertson-type preparation uncertainty relation, which explicitly depends on the eigenvalues of the quantum state. The conventional constant $ \tfrac{1}{4} $ is replaced by a state-dependent coefficient…
We propose algorithms, based on the multi-scale entanglement renormalization ansatz, to obtain the ground state of quantum critical systems in the presence of boundaries, impurities, or interfaces. By exploiting the theory of minimal…
We obtain a necessary and sufficient condition for the orthomartingale-coboundary decomposition. We establish a sufficient condition for the approximation of the partial sums of a strictly stationary random fields by those of stationary…
We explore the possibility of entanglement detection in continuous variable systems by entanglement witnesses based on covariance matrices, constructible from random homodyne measurements. We propose new linear constraints characterizing…