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Communications in Theoretical Physics

Parity-symmetric phase sensing in one- and two-axis twisting spin systems

Guang-Ri Jin, Yi Yang, Hang Li, Likun Zhou, Wen Yang

Published Jul 23, 2026• 0 citations
Publisher

Abstract

Abstract We investigate spin squeezing and optimal phase sensing in parity-conserving one-axis twisting (OAT) and two-axis twisting (TAT) spin systems. For the OAT model, we analytically identify a plateau regime where the quantum Fisher information (QFI) reaches 0.5 N 2 with a fixed y -axis sensing direction—a configuration well-suited for standard interferometry. For an even number of particles N , it is essential to switch the sensing direction from the y -axis to the z -axis to further enhance the QFI to N 2 . In contrast, for odd N , the y -axis remains nearly optimal without such a directional transition. We analytically demonstrate that this transition in the optimal sensing direction is exclusive to the even- N case. For the TAT model, we demonstrate a discontinuous jump in the optimal sensing direction from the anti-squeezing direction to the z -axis, enabling the QFI to reach a peak value ∼ 0.93 N 2 , thereby exceeding the earlier benchmark of 0.64 N 2 . Our results reveal the important role of the sensing direction transition in achieving a high-precision quantum phase estimation.

DOI
10.1088/1572-9494/ae8f1f

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Abstract We investigate spin squeezing and optimal phase sensing in parity-conserving one-axis twisting (OAT) and two-axis twisting (TAT) spin systems. For the OAT model, we analytically identify a plateau regime where the quantum Fisher information (QFI) reaches 0.5 N 2 with a fixed y -axis sensing direction—a configuration well-suited for standard interferometry. For an even number of particles N , it is essential to switch the sensing direction from the y -axis to the z -axis to further enhance the QFI to N 2 . In contrast, for odd N , the y -axis remains nearly optimal without such a directional transition. We analytically demonstrate that this transition in the optimal sensing direction is exclusive to the even- N case. For the TAT model, we demonstrate a discontinuous jump in the optimal sensing direction from the anti-squeezing direction to the z -axis, enabling the QFI to reach a peak value ∼ 0.93 N 2 , thereby exceeding the earlier benchmark of 0.64 N 2 . Our results reveal the important role of the sensing direction transition in achieving a high-precision quantum phase estimation.
We study a variational class of generalized Ramsey protocols that include two one-axis twisting (OAT) operations, one performed before the phase imprint and the other after. In this framework, we optimize the axes of the signal imprint, the OAT interactions, and the direction of the final projective measurement. We distinguish between protocols that exhibit symmetric or antisymmetric dependencies of the spin projection signal on the measured phase. Our results show that the quantum Fisher information, which sets the limits on the sensitivity achievable with a given one-axis twisted input state, can be saturated within our class of variational protocols for almost all initial twisting strengths. By incorporating numerous protocols previously documented in the literature, our approach creates a unified framework for Ramsey echo protocols with OAT states and measurements.
We study a variational class of generalized Ramsey protocols that include two one-axis twisting (OAT) operations, one performed before the phase imprint and the other after. In this framework, we optimize the axes of the signal imprint, the OAT interactions, and the direction of the final projective measurement. We distinguish between protocols that exhibit symmetric or antisymmetric dependencies of the spin projection signal on the measured phase. Our results show that the quantum Fisher information, which sets the limits on the sensitivity achievable with a given one-axis twisted input state, can be saturated within our class of variational protocols for almost all initial twisting strengths. By incorporating numerous protocols previously documented in the literature, our approach creates a unified framework for Ramsey echo protocols with OAT states and measurements.
We study a variational class of generalised Ramsey protocols that include two one-axis twisting (OAT) operations, one performed before the phase imprint and the other after. In this framework, we optimise the axes of the signal imprint, the OAT interactions, and the direction of the final projective measurement. We distinguish between protocols that exhibit symmetric or antisymmetric dependencies of the spin projection signal on the measured phase. Our results show that the quantum Fisher information, which sets the limits on the sensitivity achievable with a given uniaxially twisted input state, can be saturated within our class of variational protocols for almost all initial twist strengths. By incorporating numerous protocols previously documented in the literature, our approach creates a unified framework for Ramsey echo protocols with OAT states and measurements.
A detailed analysis of the quantum Fisher information (QFI) and spin squeezing (SS) of the non-Hermitian one-axis twisting model is conducted. The results show that the non-Hermitian model achieves significant entanglement in many-body systems, which is quite different from the Hermitian case, and achieves more SS than the optimal value of the Hermitian counterpart. Furthermore, we investigate the effect of dephasing, which is induced by external field fluctuations, and find out to what extent it weakens QFI and SS of the non-Hermitian one-axis twisting model.
In the absence of decay, the conditional dynamics for an open system is often describable by a non-Hermitian Hamiltonian. This study investigates spin squeezing (SS) in a non-Hermitian one-axis twisting (OAT) model. Somewhat surprisingly, SS close to the limit of Hermitian two-axis counter twisting (TACT) Hamiltonian is achievable for some parameters, which significantly improves upon the optimal value realizable by the Hermitian OAT model. The drawback is like with all conditional schemes, it takes on average longer time to evolve into a steady state, and the probability of no decay or success decreases as the number of atoms (spins) increases. The result above for the steady-state SS in a non-Hermitian OAT Hamiltonian is thus limited to small systems. For other parameter regimes, however, desirable SS arrives dynamically before a steady state is achieved, with a greatly shortened evolution time and enhanced probability of success, while still remains significantly improved over the limit of Hermitian OAT.
We develop a framework for describing the effects of systematic state-preparation error in quantum-enhanced atom interferometry on sensing performance. We do this in the context of both spin-squeezed and non-Gaussian states for the two-axis-twisting (TAT), one-axis-twisting (OAT), and twist-and-turn (TNT) state-preparation schemes, and derive general conditions for robustness and susceptibility of quantum states to state-preparation error. In the spin-squeezing regime, we find that OAT is more susceptible to state-preparation error than TAT due to its parameter-dependent phase-space rotation. In the non-Gaussian regime, we find that OAT is robust to state-preparation errors, which can be explained by a small ratio of off-diagonal to diagonal elements in its Fisher-covariance matrix. In contrast, TNT does not exhibit this robustness. We find that the single-parameter unbiased estimators that are habitually used in quantum-enhanced atom interferometry are not always optimal, and that there may be occasions where biased estimators, or two-parameter unbiased estimators, lead to lower net error.