Deterministic preparation of supersinglets with collective spin projections

TL;DR

This paper presents a new measurement-based protocol for efficiently generating supersinglet states, which are highly entangled, total spin zero states, useful for quantum metrology, with fast convergence and no postselection.

Contribution

The authors introduce a collective spin measurement scheme that reliably produces supersinglet states from arbitrary initial states without postselection.

Findings

Fast convergence to zero spin variance achieved.

Protocol works regardless of initial state.

Numerical simulations confirm effectiveness.

Abstract

We introduce a procedure to generate supersinglets, the multipartite generalization of angular momentum singlet states. A supersinglet is defined as a total spin zero state consisting of $ N $ spin-$ j $ particles. They are highly entangled and have zero spin variance in any direction, and as such are potentially useful for quantum metrology. Our scheme is based on projective measurements that measure the collective spin of the whole spin ensemble. A local unitary rotation is applied conditionally on the measurement outcome, such as to maximize the probability of obtaining spin zero on the subsequent measurement. The sequence is repeated in the $ z $- and $ x $-basis until convergence is obtained towards the supersinglet state. Our sequence works regardless of the initial state, and no postselection is required. Due to the use of strong projective measurements, very fast convergence towards zero spin variance is obtained. We discuss an example implementation using quantum nondemolition measurements in atomic ensembles, and perform numerical simulations to demonstrate the procedure.