Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j . We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5 . The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j .Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j . We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5 . The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j .

arXiv:1909.08355QuantumJun 22, 202034 citations

A quantum measurement of the spin direction

G.M. D'Ariano, P. Lo Presti, M.F. Sacchi

arXiv:quant-ph/0110065Physics Letters AJan 1, 200221 citations

Ultrasensitive Optical Rotation Detection With Closed-Loop Suppression of Spin Polarization Error

Xing Heng, Kai Wei, Tian Zhao +6 more

Optical rotation detection system (ORDS) utilizing quantum nondemolition (QND) measurement methods is widely applied in the field of quantum metrology and quantum information. However, the sensitivity of ORDS is limited by the uncertainty from optical-couple noise during the measurement of the atomic spin ensemble. In this study, we specifically analyze the mechanism of optical-couple noise caused by the fluctuations of probe light’s polarization in the modulated ORDS with a new model established to describe atomic spin precession in this particular condition. It is discovered that transverse electron-spin polarization errors are generated by the residual probe photon spin polarization in the ORDS, which results in extra coupling magnetic noise. In order to suppress this noise, a novel in situ method is proposed that the resultant electron-spin errors are reduced by a specifically designed closed-loop system. The results are verified through the ORDS in a co-magnetometer. After zeroing the extra probe photon spin polarization, an angular sensitivity better than $1 \times 10 ^{\mathrm {-8}}$ rad/Hz $^{\mathrm {1/2}}$ is achieved for frequencies higher than 5 Hz, demonstrating a probe background noise of 0.26 fT/Hz $^{\mathrm {1/2}}$ @14.5 Hz, approaching electronic noise and photon shot noise (PSN). With closed-loop control, the optical rotation bias instability is promoted by 4.2 times (from 107.9 to$25.7 \mu $rad/h), and the angular noise of the ORDS is reduced by 2.4 times at 1–100 Hz. The measurement uncertainty of the realized ORDS nears the standard quantum limit, paving the road for long-term ultrasensitive measurements for new physics explorations.Optical rotation detection system (ORDS) utilizing quantum nondemolition (QND) measurement methods is widely applied in the field of quantum metrology and quantum information. However, the sensitivity of ORDS is limited by the uncertainty from optical-couple noise during the measurement of the atomic spin ensemble. In this study, we specifically analyze the mechanism of optical-couple noise caused by the fluctuations of probe light’s polarization in the modulated ORDS with a new model established to describe atomic spin precession in this particular condition. It is discovered that transverse electron-spin polarization errors are generated by the residual probe photon spin polarization in the ORDS, which results in extra coupling magnetic noise. In order to suppress this noise, a novel in situ method is proposed that the resultant electron-spin errors are reduced by a specifically designed closed-loop system. The results are verified through the ORDS in a co-magnetometer. After zeroing the extra probe photon spin polarization, an angular sensitivity better than$1 \times 10 ^{\mathrm {-8}}$rad/Hz$^{\mathrm {1/2}}$is achieved for frequencies higher than 5 Hz, demonstrating a probe background noise of 0.26 fT/Hz$^{\mathrm {1/2}}$@14.5 Hz, approaching electronic noise and photon shot noise (PSN). With closed-loop control, the optical rotation bias instability is promoted by 4.2 times (from 107.9 to$25.7 \mu $rad/h), and the angular noise of the ORDS is reduced by 2.4 times at 1–100 Hz. The measurement uncertainty of the realized ORDS nears the standard quantum limit, paving the road for long-term ultrasensitive measurements for new physics explorations.

IEEE Transactions on Instrumentation and MeasurementJan 1, 202319 citations

Quantum Spin Systems

Ola Bratteli, Derek W. Robinson

Springer eBooksJan 1, 19970 citations

Generalized GHZ entanglement states for optimal rotation detection of quantum spin systems using majorana representation

Yousef Mafi, Payman Kazemikhah, Ali Kookani +2 more

Abstract A multitude of engineering and scientific applications require the estimation of an unknown axis’ rotation, known as the reference frame alignment problem. These problems can be categorized using the quantum Cramer–Rao bound. Detecting rotations is typically focused on smaller angles, as errors are more significant in this range. Therefore, selecting the optimal combination of measurement techniques based on a quantum entangled state for a particular setup is a critical step. This paper proposes a linear combination of anticoherence and coherence measures based on the generalized GHZ entanglement states. The anticoherence measures, optimizes the spin system’s average fidelity in detecting rotated states, while the overlap between states in any spin number is minimal. The optimal quantum rotosensors are characterized by the minimal average fidelity given by the overlap before and after averaging over all directions. The individual subsystems’ states have substantial overlap with GHZ states, making the generalized GHZ state the entanglement quantum spin-j state with coherence decay rate ϵ beneficial in finding the optimal rotation detection on noncoherent entanglement state.Abstract A multitude of engineering and scientific applications require the estimation of an unknown axis’ rotation, known as the reference frame alignment problem. These problems can be categorized using the quantum Cramer–Rao bound. Detecting rotations is typically focused on smaller angles, as errors are more significant in this range. Therefore, selecting the optimal combination of measurement techniques based on a quantum entangled state for a particular setup is a critical step. This paper proposes a linear combination of anticoherence and coherence measures based on the generalized GHZ entanglement states. The anticoherence measures, optimizes the spin system’s average fidelity in detecting rotated states, while the overlap between states in any spin number is minimal. The optimal quantum rotosensors are characterized by the minimal average fidelity given by the overlap before and after averaging over all directions. The individual subsystems’ states have substantial overlap with GHZ states, making the generalized GHZ state the entanglement quantum spin-j state with coherence decay rate ϵ beneficial in finding the optimal rotation detection on noncoherent entanglement state.

Physica ScriptaJan 11, 20240 citations

1 \times 10 ^{\mathrm {-8}}

rad/Hz

^{\mathrm {1/2}}

is achieved for frequencies higher than 5 Hz, demonstrating a probe background noise of 0.26 fT/Hz

^{\mathrm {1/2}}

@14.5 Hz, approaching electronic noise and photon shot noise (PSN). With closed-loop control, the optical rotation bias instability is promoted by 4.2 times (from 107.9 to$25.7 \mu $rad/h), and the angular noise of the ORDS is reduced by 2.4 times at 1–100 Hz. The measurement uncertainty of the realized ORDS nears the standard quantum limit, paving the road for long-term ultrasensitive measurements for new physics explorations.