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.

arXiv comment5+2 pages, 11 figures

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• Entanglement detection
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• Quantum spin squeezing
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• Entanglement and Extreme Spin Squeezing
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• Variance-based uncertainty relations
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• Asymptotic entropic uncertainty relations
• Measurement Uncertainty for Finite Quantum Observables
• Preparational Uncertainty Relations for $N$ Continuous Variables

Cited by in corpus (35)

• Quantum Steering
• Entanglement Certification $-$ From Theory to Experiment
• Improved tripartite uncertainty relation with quantum memory
• Simultaneous tracking of spin angle and amplitude beyond classical limits
• Device-Independent Quantum Key Distribution with Random Key Basis
• Holevo Bound of Entropic Uncertainty in Schwarzschild Spacetime
• Uncertainty from Heisenberg to Today
• Quantum Complementarity through Entropic Certainty Principles
• The Optimal Uncertainty Relation
• State-independent preparation uncertainty relations
• Observing geometry of quantum states in a three-level system
• Tight $N$-observable uncertainty relations and their experimental demonstrations
• Experimental investigation of multi-observable uncertainty relations
• Uncertainty relations from graph theory
• Entanglement detection by violations of noisy uncertainty relations: A proof of principle
• State independent uncertainty relations from eigenvalue minimization
• The Uncertainty Principle of Quantum Processes
• Incompatibility of Observables as State-Independent Bound of Uncertainty Relations
• Entanglement Criteria Based on Quantum Fisher Information
• State-independent Uncertainty Relations and Entanglement Detection
• Experimental Test of Tight State-Independent Preparation Uncertainty Relations for Qubits
• Probing Uncertainty Relations in Non-Commutative Space
• Uncertainty regions of observables and state-independent uncertainty relations
• Standard symmetrized variance with applications to coherence, uncertainty and entanglement
• Mutual Uncertainty, Conditional Uncertainty and Strong Sub-Additivity
• Tight bounds from multiple-observable entropic uncertainty relations
• $su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems
• Multiparticle Entanglement Resolution Analyzer based on Quantum-Control-Assisted Uncertainty Relation
• Efficient detection for quantum states containing fewer than $k$ unentangled particles in multipartite quantum systems
• Probability density functions of quantum mechanical observable uncertainties
• An Effective Way to Determine the Separability of Quantum State
• Uncertainty relation and the constrained quadratic programming
• State-independent uncertainty relations on multipartite spin $1/2$-systems
• Universal witnesses of vanishing energy gap
• Sequences of lower bounds for entropic uncertainty relations from bistochastic maps