Error estimation of different schemes to measure spin-squeezing
inequalities
- URL: http://arxiv.org/abs/2311.17845v1
- Date: Wed, 29 Nov 2023 17:49:10 GMT
- Title: Error estimation of different schemes to measure spin-squeezing
inequalities
- Authors: Jan Lennart B\"onsel, Satoya Imai, Ye-Chao Liu, Otfried G\"uhne
- Abstract summary: In this paper, we focus on the measurement of spin-squeezing inequalities in multi-qubit systems.
We show that spin-squeezing inequalities can not only be evaluated by measurements of the total angular momentum but also by two-qubit correlations.
For this purpose, we discuss how error bounds can be derived for non-linear estimators with the help of their variances.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: How can we analyze quantum correlations in large and noisy systems without
quantum state tomography? An established method is to measure total angular
momenta and employ the so-called spin-squeezing inequalities based on their
expectations and variances. This allows to detect metrologically useful
entanglement, but efficient strategies for estimating such non-linear
quantities have yet to be determined. In this paper, we focus on the
measurement of spin-squeezing inequalities in multi-qubit systems. We show that
spin-squeezing inequalities can not only be evaluated by measurements of the
total angular momentum but also by two-qubit correlations, either involving all
pair correlations or randomly chosen pair correlations. Then we analyze the
estimation errors of our approaches in terms of a hypothesis test. For this
purpose, we discuss how error bounds can be derived for non-linear estimators
with the help of their variances, characterizing the probability of falsely
detecting a separable state as entangled. Our methods can be applied for the
statistical treatment of other non-linear parameters of quantum states.
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