Fisher information and multiparticle entanglement

By P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, Harald Weinfurter, L. Pezz'e, Augusto Smerzi. 2010

473 citations recorded by the source corpus.

The Fisher information F gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on F for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry. We further compute similar bounds on the average Fisher information F for collective spin operators, where the average is performed over all possible spin directions. We show that these criteria detect different sets of states and illustrate their strengths by considering several examples, also using experimental data. In particular, the criterion based on F is able to detect certain bound entangled states.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/79d51a1eaf42e30a614a4cbfb725d19f2ff7d574

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum limits in optical interferometry (2014, background): “Above results imply that QFI, or precision, can be interpreted as a particle-entanglement witness, i.e. all states that give precision scaling better than the shot noise must be particleentangled (Hyllus et al., 2012; Tóth, 2012).”
Simulating quantum many-body dynamics on a current digital quantum computer (2019, background): “The QFI is an entanglement witness [65–67], and for our chosen deﬁ-nition in Eq.”
Entanglement certification from theory to experiment (2018, background): “Entanglement depth criteria similar to the above have also been derived for different target states, like Dicke states [108, 285] and planar quantum squeezed states [109, 286], and also based on other quantities, like the QFI [179, 287–290].”
At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited (2017, background): “The rotation scenario serves also as a powerful entanglement detector [23,24] that can detect a vanishing fraction of entanglement [25] or even bound entanglement [26] with scaling close to the Heisenberg limit.”
Quantum metrology with nonclassical states of atomic ensembles (2016, background): “The inequalities (48) have been generalized to arbitrary spin systems (Vitagliano et al., 2014, 2011) and to systems of fluctuating numbers of particles (Hyllus et al., 2012b).”
Measuring multipartite entanglement through dynamic susceptibilities (2015, methodology): “The multipartite entanglement that the QFI detects has an immediate interpretation as a resource for quantum metrology [8, 9].”
Quantum-enhanced measurements without entanglement (2017, background): “If ρ is k-producible, i.e., it is a convex mixture of pure states which are tensor products of at most k-qubit states, then the quantum Fisher information is bounded above as follows (Hyllus et al., 2012; Tóth, 2012), Iθ(ρ, Jl) ≤ nk2 + (N − nk)2 , (18) where n is the integer part of N/k.”
Macroscopic quantum states: Measures, fragility, and implementations (2017, background): “An effective size of Neff & k implies genuine entanglement within groups of at least k spins (this statement can be made fully rigorous including O(1) correction terms (Hyllus et al., 2012; Tóth, 2012)).”