quantum-computing

From spin squeezing to fast state discrimination

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⚡ Quantum Brief

From spin squeezing to fast state discrimination

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AbstractThere is great interest in generating and controlling entanglement in Bose-Einstein condensates and similar ensembles for use in quantum computation, simulation, and sensing. One class of entangled states useful for enhanced metrology are spin-squeezed states of $N$ two-level atoms. After preparing a spin coherent state of width $1/\sqrt{N}$ centered at coordinates $( \theta, \phi) $ on the Bloch sphere, atomic interactions generate a nonlinear evolution that shears the state's probability density, stretching it to an ellipse and causing squeezing in a direction perpendicular to the major axis. Here we consider the same setup but in the $N \rightarrow \infty $ limit . This shrinks the initial coherent state to zero area. Large $N$ also suppresses two-particle entanglement and squeezing, as required by a monogamy bound. The torsion (1-axis twist) is still present, however, and the center of the large $N$ coherent state evolves as a qubit governed by a two-state Gross-Pitaevskii equation. The resulting nonlinearity is known to be a powerful resource in quantum computation. It can be used to implement single-input quantum state discrimination, an impossibility within linear one-particle quantum mechanics. We obtain a solution to the discrimination problem in terms of a Viviani curve on the Bloch sphere. We also consider an open-system variant containing both Bloch sphere torsion and dissipation. In this case it should be possible to generate two basins of attraction within the Bloch ball, having a shared boundary that can be used for a type of autonomous state discrimination. We explore these and other connections between spin squeezing in the large $N$ limit and nonlinear quantum gates, and argue that a two-component condensate is a promising platform for realizing a nonlinear qubit.► BibTeX data@article{Geller2026fromspinsqueezingto, doi = {10.22331/q-2026-05-20-2108}, url = {https://doi.org/10.22331/q-2026-05-20-2108}, title = {From spin squeezing to fast state discrimination}, author = {Geller, Michael R.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2108}, month = may, year = {2026} }► References [1] C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle. Rev. Mod. Phys., 52: 341, 1980. 10.1103/RevModPhys.52.341. https://doi.org/10.1103/RevModPhys.52.341 [2] V. Giovannetti, S. Lloyd, and L. 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Cambridge University Press, Cambridge, England, 2000.Cited byCould not fetch Crossref cited-by data during last attempt 2026-05-20 09:02:44: Could not fetch cited-by data for 10.22331/q-2026-05-20-2108 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-05-20 09:02:44: Cannot retrieve data from ADS due to rate limitations.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractThere is great interest in generating and controlling entanglement in Bose-Einstein condensates and similar ensembles for use in quantum computation, simulation, and sensing. One class of entangled states useful for enhanced metrology are spin-squeezed states of $N$ two-level atoms. After preparing a spin coherent state of width $1/\sqrt{N}$ centered at coordinates $( \theta, \phi) $ on the Bloch sphere, atomic interactions generate a nonlinear evolution that shears the state's probability density, stretching it to an ellipse and causing squeezing in a direction perpendicular to the major axis. Here we consider the same setup but in the $N \rightarrow \infty $ limit . This shrinks the initial coherent state to zero area. Large $N$ also suppresses two-particle entanglement and squeezing, as required by a monogamy bound. The torsion (1-axis twist) is still present, however, and the center of the large $N$ coherent state evolves as a qubit governed by a two-state Gross-Pitaevskii equation. The resulting nonlinearity is known to be a powerful resource in quantum computation. It can be used to implement single-input quantum state discrimination, an impossibility within linear one-particle quantum mechanics. We obtain a solution to the discrimination problem in terms of a Viviani curve on the Bloch sphere. We also consider an open-system variant containing both Bloch sphere torsion and dissipation. In this case it should be possible to generate two basins of attraction within the Bloch ball, having a shared boundary that can be used for a type of autonomous state discrimination. We explore these and other connections between spin squeezing in the large $N$ limit and nonlinear quantum gates, and argue that a two-component condensate is a promising platform for realizing a nonlinear qubit.► BibTeX data@article{Geller2026fromspinsqueezingto, doi = {10.22331/q-2026-05-20-2108}, url = {https://doi.org/10.22331/q-2026-05-20-2108}, title = {From spin squeezing to fast state discrimination}, author = {Geller, Michael R.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2108}, month = may, year = {2026} }► References [1] C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle. Rev. Mod. Phys., 52: 341, 1980. 10.1103/RevModPhys.52.341. https://doi.org/10.1103/RevModPhys.52.341 [2] V. Giovannetti, S. Lloyd, and L. 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