bibkey: volkoff2016pairtunnelling authors: T. J. Volkoff year: 2016 title: “Optimal and near-optimal probe states for quantum metrology of number conserving two-mode bosonic Hamiltonians” doi: null url: https://arxiv.org/abs/1610.05807v1 claim: “We conjecture that for each N ≥ 4 there exists a value c_N for which |ω_+(c_N)⟩ or |ω_−(c_N)⟩ is the exact ground state.” strata_touched:

• D5/S3/Quantum/Dynamics/PairTunnelingAnsatzGroundStateRefutation license: citation-only triage: anchor

Volkoff pair-tunnelling ansatz

T. J. Volkoff, Optimal and near-optimal probe states for quantum metrology of number conserving two-mode bosonic Hamiltonians, arXiv:1610.05807v1 (2016), §V.A, pp. 6–7. Eq. (20) and the even-sector assumption are on p. 6; the conjecture is on p. 7.

We conjecture that for each N ≥ 4 there exists a value c_N for which |ω_+(c_N)⟩ or |ω_−(c_N)⟩ is the exact ground state.

The source defines

|ω_±(c)⟩ := 1/𝒩 [(a₀†² + 2ic a₀†a₁† − a₁†²)^M ± (a₀†² − 2ic a₀†a₁† − a₁†²)^M]|0,0⟩,

with c ∈ ℝ and M = N/2, for even N. The Hamiltonian is a₀†²a₁² + h.c.

Verified locator

• URL: https://arxiv.org/abs/1610.05807v1
• PDF: https://arxiv.org/pdf/1610.05807v1 (Section V.A, pp. 6–7).