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Register a new userMulti-parameter Quantum Magnetometry with Spin States in coarsened measurement reference
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We investigate the simultaneous estimation of the intensity and the orientation of a magnetic field by the multi-parameter quantum Fisher information matrix. A general expression is achieved for the simultaneous estimation precision of the intensity and the orientation, which is better than the independent estimation precision for the given number of spin states. Moreover, we consider an imperfect measurement device, coarsened measurement reference. For the case of the measurement reference rotating around the $y-$axis randomly, the simultaneous estimation always performs better than the independent estimation. For all other cases, the simultaneous estimation precision will not perform better than the independent estimation when the coarsened degree is larger than a certain value.
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We describe the formalism for optimally estimating and controlling both the state of a spin ensemble and a scalar magnetic field with information obtained from a continuous quantum limited measurement of the spin precession due to the field. The full quantum parameter estimation model is reduced to a simplified equivalent representation to which classical estimation and control theory is applied. We consider both the tracking of static and fluctuating fields in the transient and steady state regimes. By using feedback control, the field estimation can be made robust to uncertainty about the total spin number.
It has been found that the quantum-to-classical transition can be observed independent of macroscopicity of the quantum state for a fixed degree of fuzziness in the coarsened references of measurements. Here, a general situation, that is the degree of fuzziness can change with the rotation angle between two states (different rotation angles represent different references), is researched based on the reason that the fuzziness of reference can come from two kinds: the Hamiltonian (rotation frequency) and the timing (rotation time). Our results show that, for the fuzziness of Hamiltonian alone, the degree of fuzziness for reference will change with the rotation angle between two states and the quantum effects can still be observed no matter how much degree of fuzziness of Hamiltonian; for the fuzziness of timing, the degree of coarsening reference is unchanged with the rotation angle. Moreover, during the rotation of the measurement axis, the decoherence environment can also help the classical-to-quantum transition due to changing the direction of measurement axis.
We argue that it is possible in principle to reduce the uncertainty of an atomic magnetometer by double-passing a far-detuned laser field through the atomic sample as it undergoes Larmor precession. Numerical simulations of the quantum Fisher information suggest that, despite the lack of explicit multi-body coupling terms in the systems magnetic Hamiltonian, the parameter estimation uncertainty in such a physical setup scales better than the conventional Heisenberg uncertainty limit over a specified but arbitrary range of particle number N. Using the methods of quantum stochastic calculus and filtering theory, we demonstrate numerically an explicit parameter estimator (called a quantum particle filter) whose observed scaling follows that of our calculated quantum Fisher information. Moreover, the quantum particle filter quantitatively surpasses the uncertainty limit calculated from the quantum Cramer-Rao inequality based on a magnetic coupling Hamiltonian with only single-body operators. We also show that a quantum Kalman filter is insufficient to obtain super-Heisenberg scaling, and present evidence that such scaling necessitates going beyond the manifold of Gaussian atomic states.
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Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is a novel protocol which eliminates all possible attacks on detector side and necessity of reference-frame alignment in source sides. However, its performance may degrade notably due to statistical fluctuations, since more parameters, e.g. yields and error rates for mismatched-basis events, must be accumulated to monitor the security. In this work, we find that the original decoy-states method estimates these yields over pessimistically since it ignores the potential relations between different bases. Through processing parameters of different bases jointly, the performance of RFI-MDI-QKD is greatly improved in terms of secret key rate and achievable distance when statistical fluctuations are considered. Our results pave an avenue towards practical RFI-MDI-QKD.
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