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Mean spin direction and spin squeezing in superpositions of spin coherent states

100%

Yan D. , Wang X. , Song L. , Zong Z.

Open Physics

2007

tom 5

nr 3

367-376

We consider the mean spin direction (MSD) of superpositions of two spin coherent states (SCS) | ± μ〉, and superpositions of | μ〉 and | μ*〉 with a relative phase. We find that the azimuthal angle exhibits a π transition for both states when we vary the relative phase. The spin squeezing of the states, and the bosonic counterpart of the mean spin direction are also discussed.

Quantum estimation of a two-phase spin rotation

80%

Vaneph C. , Tufarelli T. , Genoni M. G.

Quantum Measurements and Quantum Metrology

2013

tom 1

12-20

system, characterised by two unknown phases, and compare the estimation precision achievable with two different strategies. The first is a standard ‘joint estimation’ strategy, in which a single probe state is used to estimate both parameters, while the second is a ‘sequential’ strategy in which the two phases are estimated separately, each on half of the total number of system copies. In the limit of small angles we show that, although the joint estimation approach yields in general a better performance, the two strategies possess the same scaling of the total phase sensitivity with respect to the spin number j, namely ΔΦ≃ 1/j. Finally, we discuss a simple estimation strategy based on spin squeezed states and spin measurements, and compare its performance with the ultimate limits to the estimation precision that we have derived above.