Spin squeezing and entanglement

TL;DR

This paper derives comprehensive inequalities involving collective spin measurements to detect entanglement in spin-1/2 systems, establishing a clear link between spin squeezing and entanglement, and demonstrating their effectiveness in various spin models.

Contribution

It introduces a complete set of generalized spin squeezing inequalities for entanglement detection applicable to systems with collective spin measurements, expanding previous criteria.

Findings

Inequalities can detect all entangled states based on collective measurements.

The criteria can identify bound entanglement in spin models.

Comparison shows how spin squeezing relates to entanglement in reduced two-qubit states.

Abstract

What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular momentum components J_k. They can be used for the experimental detection of entanglement in a system of spin-1/2 particles in which the spins cannot be individually addressed. We present various sets of inequalities that can detect all entangled states that can be detected based on the knowledge of: (i) the mean values and variances of J_k in three orthogonal directions, or (ii) the variances of J_k in three orthogonal directions, or (iii) the mean values of J_k^2 in three orthogonal directions or (iv) the mean values and variances of J_k in arbitrary directions. We compare our inequalities to known spin squeezing entanglement criteria and discuss to which extent spin squeezing is related to entanglement in the reduced two-qubit states. Finally, we apply our criteria for the detection of entanglement in spin models, showing that they can be used to detect bound entanglement in these systems.