Violation of local uncertainty relations as a signature of entanglement

By H. Hofmann, S. Takeuchi. 2002

314 citations recorded by the source corpus.

Entangled states represent correlations between two separate systems that are too precise to be represented by products of local quantum states. We show that this limit of precision for the local quantum states of a pair of N-level systems can be defined by an appropriate class of uncertainty relations. The violation of such local uncertainty relations may be used as an experimental test of entanglement generation.

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

View Paper: https://www.semanticscholar.org/paper/d3ebce33d1711dd33341ceeb6801f5a2cb519caf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Geometry of Quantum States: Index (2007, background): “27 Separability criteria not discussed here include a criterion obtained by expanding a mixed state in the Fourier basis [741], a relation between purity of a state and its maximal projection on a pure state [593], an application of uncertainty relations for non-local observables [337, 440, 370], re”
Entanglement certification from theory to experiment (2018, unknown): “Thus, by simple concavity arguments one can prove that (∆M1) 2 ρAB + (∆M2) 2 ρAB ≥ UA + UB must hold for all separable states ρAB = ∑ k pk(ρA ⊗ ρB)k [94–97].”
Experimental investigation of the entanglement-assisted entropic uncertainty principle (2010, background): “At present, the violation of uncertainty relations is implemented as a signature of entanglemen”
Quantum steering (2019, background): “Then, for separable states, the bound∑ k δ 2(Mk) ≥ CA + CB holds (Hofmann and Takeuchi, 2003).”
Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement (2010, methodology): “Uncertainty relations have been used in the past to derive entanglement witnesse”
Entanglement detection (2008, background): “The closely connected criterion of the local uncertainty relations (LURs) [107] is, however, experimentally relevant andwill be discussed in Section 7.”