Entanglement detection in the stabilizer formalism

By Géza Tóth, O. Guehne. 2005

217 citations recorded by the source corpus.

We investigate how stabilizer theory can be used for constructing sufficient conditions for entanglement. First, we show how entanglement witnesses can be derived for a given state, provided some stabilizing operators of the state are known. These witnesses require only a small effort for an experimental implementation and are robust against noise. Second, we demonstrate that also nonlinear criteria based on uncertainty relations can be derived from stabilizing operators. These criteria can sometimes improve the witnesses by adding nonlinear correction terms. All our criteria detect states close to Greenberger-Horne-Zeilinger states, cluster and graph states. We show that similar ideas can be used to derive entanglement conditions for states which do not fit the stabilizer formalism, such as the three-qubit W state. We also discuss connections between the witnesses and some Bell inequalities.

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

View Paper: https://www.semanticscholar.org/paper/9ef33fde7eaeb5980c1b1c307156de210ced418b

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

A quantum processor based on coherent transport of entangled atom arrays (2021, unknown): “probe the resultant twelve-qubit cluster state we measure the stabilizer set {Si} = {Zi−1XiZi+1} through readout in two measurement settings, given by a local π/2 rotation on either the odd or even sublattice before projective measurement [33].”
Observation of entangled states of a fully-controlled 20 qubit system (2017, methodology): “(A.6c) Since the spectra of all six operators are {±1} (with twofold degeneracy), we further have 〈OiOi+1 〉2 ≤ 1, and the ACT theorem hence tells us that 〈X1X2 〉2ρ + 〈Y2Y3 〉 2 ρ ≤ 1 , (A.7a) 〈Y1Y2 〉2ρ + 〈Z2Z3 〉 2 ρ ≤ 1 , (A.7b) 〈Z1Z2 〉2ρ + 〈X2X3 〉 2 ρ ≤ 1 .”
Entanglement detection (2008, methodology): “Using these operators, and the strategy from above, one can find now the witness [397]”
Quantum steering (2019, background): “Note that similar bounds on sums of squared mean values are known for many cases of anticommuting observables or mutually unbiased bases (Tóth and Gühne, 2005; Wehner and Winter, 2010; Wu et al., 2009), so one can directly generalize the criteria from above to broader classes of observables on…”
Logical quantum processor based on reconfigurable atom arrays (2023, methodology): “Animations of all of our programmed circuits are attached as Supplementary Videos.”
Entanglement certification from theory to experiment (2018, methodology): “Apart from this generically applicable method, most available GME witnesses are tailored towards detecting specific states, such as graph states [270] or stabilizer states [186–188], Dicke states [271], or generally symmetric states [272].”