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Spin squeezing in symmetric multiqubit states with two non-orthogonal Majorana spinors

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Abstract

Enhanced precision measurements using entangled many particle states are crucial for their technological applications in quantum information science and metrology. Squeezed spin states are a class of permutation symmetric N particle entangled states, which exhibit reduced quantum fluctuation in their collective spin angular momentum in a certain direction, and they are useful for quantum enhanced metrology. Permutation symmetric states attract attention as they offer significant test grounds for the description of entanglement in multipartite quantum systems, which is crucial for processing complex quantum information tasks. Spin squeezing serves as an experimentally amenable collective criterion of entanglement in symmetric multiqubit systems. In this paper, we explore spin-squeezing behavior in different classes of N-qubit symmetric states consisting of all permutations of two distinct spinors. We employ Majorana geometric representation of multiqubit states obeying exchange symmetry for this purpose. We prove that N qubit symmetric states consisting of two distinct non-orthogonal spinors do exhibit spin squeezing, thus expanding the avenues of their applicability in quantum enhanced sensing tasks.

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Notes

  1. For states belonging to the class \(\{ \mathcal{D}_{N-k,k}\}\) with different values of \(k=2,3,\ldots \), we find that (i) the mean spin direction (denoted by the unit vector \(\hat{n}_0\)) lies in the XZ plane and (ii) the \(2\times 2\) block \(T_\bot \) of correlation matrix T, which is expressed in the basis \(({\hat{n}}_1, \hat{n}_2)\) orthogonal to the mean spin direction \(\hat{n}_0\), is diagonal, i.e., \({\widetilde{\hat{n}}_{1}}\, T \, {\hat{n}}_{2}=0\). It is seen that \({\mathrm{min}}\left( \widetilde{\hat{n}}_{1}\, T\, {\hat{n}}_{1},\, \widetilde{\hat{n}}_{2}\,T\,{\hat{n}}_{2}\right) =\widetilde{\hat{n}}_{2}\,T\,{\hat{n}}_{2}\). Thus, the spin-squeezing parameter [see Eqs. (6) and (11)] takes the form \(\xi =\sqrt{1+(N-1)\, (\widetilde{\hat{n}}_{2}\,T\,{\hat{n}}_{2})}\) for any k and N.

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Acknowledgements

KSA would like to thank the University Grants Commission for providing a BSR-RFSMS fellowship during the present work. ARU acknowledges the support of UGC MRP (Ref. MRP-MAJOR-PHYS-2013-29318). We thank Professor A. K. Rajagopal for insightful discussions.

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Authors and Affiliations

  1. Department of Studies in Physics, University of Mysore, Manasagangotri, Mysuru, Karnataka, 570006, India

    K. S. Akhilesh & K. S. Mallesh

  2. Department of Physics, Tunga Mahavidyalaya, Thirthahalli, Karnataka, 577432, India

    B. G. Divyamani

  3. Department of Physics, Kuvempu University, Shankaraghatta, Shimoga, 577 451, India

    Sudha

  4. Inspire Institute Inc., Alexandria, VA, 22303, USA

    Sudha & A. R. Usha Devi

  5. Department of Physics, Bangalore University, Bangalore, 560 056, India

    A. R. Usha Devi

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  1. K. S. Akhilesh
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Akhilesh, K.S., Divyamani, B.G., Sudha et al. Spin squeezing in symmetric multiqubit states with two non-orthogonal Majorana spinors. Quantum Inf Process 18, 144 (2019). https://doi.org/10.1007/s11128-019-2244-3

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