{
  "abstract": "In this paper, we study two bosonic modes that exchange pairs of quanta, which realize two-axis twisting exactly: within a sector of fixed particle number the exchange operator is proportional to the two-axis twisting generator, with a fixed factor of two. Because any real nonlinear medium supplies a local Kerr nonlinearity alongside this operator, the two merge into one twisting Hamiltonian governed by a single dimensionless ratio $r=χ_s/χ_e$ of the Kerr strength to the exchange strength. Two conditions then decide how much of the ideal behavior survives this constraint, and they must be met separately. The first concerns speed: the exponential squeezing rate follows in closed form, vanishes exactly at $r=\\pm1$, and recovers as the square root of the distance from that point. The second concerns depth: the smallest attainable squeezing parameter depends only on the anisotropy of the mean-field saddle, attaining the full two-axis-twisting value at $r=0$ and $r=\\pm3$ regardless of the rate, so that settings sharing the same anisotropy but differing twofold in rate reach the same depth. The two conditions address different targets, and a system may squeeze quickly yet terminate at a shallow optimum; only $r=0$ is optimal in both respects. The closed-form Gaussian solution reveals a further systematic bias: because the early-time decay rate of the variance exceeds twice the exponential rate, a fit to short-time data overestimates the rate by more than a factor of two. Since an isotropic cubic nonlinearity imposes $r=1$, the value at which the rate vanishes, the two strengths must be mismatched, and a moderate mismatch already restores most of the optimal depth. Finally, the constraint is invisible at low excitation: at two quanta the Kerr term shifts both coupled states equally, so the two Hamiltonians are indistinguishable until four quanta.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15774",
  "author_total": 5,
  "authors": [
    {
      "name": "Qing Yu"
    },
    {
      "name": "Ying Li"
    },
    {
      "name": "Cuilu Zhai"
    },
    {
      "name": "Shiqing Tang"
    },
    {
      "name": "Wangjun Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aetc64yrxs0zh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15774",
  "fulltext_url": null,
  "id": "aetc64yrxs0zh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15774",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7221788838",
  "pdf_url": "https://arxiv.org/pdf/2610.15774",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aetc64yrxs0zh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2610.15774",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15774"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Rate and depth of two-axis twisting by pair exchange under the self-Kerr constraint",
  "title_text": "Rate and depth of two-axis twisting by pair exchange under the self-Kerr constraint",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/aetc64yrxs0zh",
  "venue": "arXiv",
  "versions": []
}