Entanglement, Non-linear Dynamics, and the Heisenberg Limit

Abstract

We show that the quantum Fisher information provides a sufficient condition to recognize multi-particle entanglement in a $N$ qubit state. The same criterion gives a necessary and sufficient condition for sub shot-noise phase sensitivity in the estimation of a collective rotation angle $\theta$. The analysis therefore singles out the class of entangled states which are {\it useful} to overcome classical phase sensitivity in metrology and sensors. We finally study the creation of useful entangled states by the non-linear dynamical evolution of two decoupled Bose-Einstein condensates or trapped ions.

Phys. Rev. Lett. 102, 100401 (2009)

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• Quantum Phase Estimation Algorithm with Gaussian Spin States
• Bounds on quantum Fisher information and uncertainty relations for thermodynamically conjugate variables
• Entanglement in the symmetric subspace: mapping multipartite to bipartite states
• Multiparameter quantum metrology with postselection measurements
• Transfer of quantum-enhanced information through a many-body system
• Bootstrapping entanglement in quantum spin systems
• Multipartite entanglement in quantum phase transitions
• Optimal finite-dimensional probe states for quantum phase estimation
• Quantum Information Approaches to Quantum Gravity
• General quantum resources providing advantages in work-extraction tasks