Spin squeezing and pairwise entanglement for symmetric multiqubit states

By Xiaoguang Wang, Barry C. Sanders. 2003

173 citations recorded by the source corpus.

We show that spin squeezing implies pairwise entanglement for arbitrary symmetric multiqubit states. If the squeezing parameter is less than or equal to 1, we demonstrate a quantitative relation between the squeezing parameter and the concurrence for the even and odd states. We prove that the even states generated from the initial state with all qubits being spin down, via the one-axis twisting Hamiltonian, are spin squeezed if and only if they are pairwise entangled. For the states generated via the one-axis twisting Hamiltonian with an external transverse field for any number of qubits greater than 1 or via the two-axis countertwisting Hamiltonian for any even number of qubits, the numerical results suggest that such states are spin squeezed if and only if they are pairwise entangled.

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

View Paper: https://www.semanticscholar.org/paper/1c889b8834ce7000c80dfd0ff888baa8cda5c6b1

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Citations in the corpus

Quantum spin squeezing (2010, background): “(53) reduces to [15] ξ(2) S = 2 N (〈 J(2) x + J 2 y 〉 − ∣∣〈J2 −〉∣∣) .”
Entanglement detection (2008, background): “[502] that if a symmetric state violates Eq.”
Entanglement in many-body systems (2007, background): “It is interesting that CR can be related to, the so called, spin squeezing parameter Σ = 2 √ ∆Sn⊥ (Wang and Sanders, 2003), measuring the spin fluctuations in a quantum correlated state (he subscript n⊥ indicates a perpendicular axes to 〈S〉).”
Quantum-enhanced measurements without entanglement (2017, background): “…Holland and Burnett, 1993; Kacprowicz et al., 2010; Kitagawa and Ueda, 1993; Korbicz et al., 2005; Pezzè and Smerzi, 2009; Sanders and Milburn, 1995; Sørensen et al., 2001; Tóth et al., 2009; Uys and Meystre, 2007; Wang and Sanders, 2003; Wineland et al., 1994; Yurke, 1986; Yurke et al., 1986)).”
Quantum metrology with nonclassical states of atomic ensembles (2016, background): “The Mølmer-Sørensen gate (Mølmer and Sørensen, 1999; Sørensen and Mølmer, 2000) is obtained setting Ô = 12 ∑N i=1 σ̂ (i) y = Ĵy (or Ô = Ĵx).”