State-independent Uncertainty Relations and Entanglement Detection in Noisy Systems

Abstract

Quantifying quantum mechanical uncertainty is vital for the increasing number of experiments that reach the uncertainty limited regime. We present a method for computing tight variance uncertainty relations, i.e., the optimal state-independent lower bound for the sum of the variances for any set of two or more measurements. The bounds come with a guaranteed error estimate, so results of pre-assigned accuracy can be obtained straightforwardly. Our method also works for POVM measurements. Therefore, it can be used for detecting entanglement in noisy environments, even in cases where conventional spin squeezing criteria fail because of detector noise.

5+2 pages, 11 figures

References in corpus (5)

• Entanglement detection
• Twin matter waves for interferometry beyond the classical limit
• Stronger uncertainty relations for the sum of variances
• Detecting multiparticle entanglement of Dicke states
• Heisenberg Uncertainty Relation for Three Canonical Observables

Cited by in corpus (15)

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• Simultaneous tracking of spin angle and amplitude beyond classical limits
• Uncertainty from Heisenberg to Today
• Uncertainty relations from graph theory
• Experimental investigation of multi-observable uncertainty relations
• Entanglement Criteria Based on Quantum Fisher Information
• Uncertainty regions of observables and state-independent uncertainty relations
• Standard symmetrized variance with applications to coherence, uncertainty and entanglement
• Tight bounds from multiple-observable entropic uncertainty relations
• $su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems
• Probability density functions of quantum mechanical observable uncertainties
• Uncertainty relation and the constrained quadratic programming
• An Effective Way to Determine the Separability of Quantum State
• Efficient detection for quantum states containing fewer than $k$ unentangled particles in multipartite quantum systems
• State-independent uncertainty relations on multipartite spin $1/2$-systems