Quantum Metrology beyond the Classical Limit under the Effect of Dephasing

Abstract

Quantum sensors have the potential to outperform their classical counterparts. For classical sensing, the uncertainty of the estimation of the target fields scales inversely with the square root of the measurement time T. On the other hand, by using quantum resources, we can reduce this scaling of the uncertainty with time to 1/T. However, as quantum states are susceptible to dephasing, it has not been clear whether we can achieve sensitivities with a scaling of 1/T for a measurement time longer than the coherence time. Here, we propose a scheme that estimates the amplitude of globally applied fields with the uncertainty of 1/T for an arbitrary time scale under the effect of dephasing. We use one-way quantum-computing-based teleportation between qubits to prevent any increase in the correlation between the quantum state and its local environment from building up and have shown that such a teleportation protocol can suppress the local dephasing while the information from the target fields keeps growing. Our method has the potential to realize a quantum sensor with a sensitivity far beyond that of any classical sensor.

Single spin detection with entangled states

“…Secondly, we compare our results with the sensors to measure global magnetic fields B with L qubits in the table II. It is worth mentioning that, although we firstly analyze the performance to use the entangled states for the single spin detection, previous researches show that entangled states can enhance the performance of the global magnetic field sensors [12,[32][33][34][35][36][37][38][39][40][41][42]. From the table, we have found that the number of the qubits L to measure the global magnetic fields corresponds to the density ρ to detect the single spin.…”

“…Actually, for the single spin detection, the probe spins far from the target spin just induce noise without contributing the increase of the signal, and therefore the increase of the number of the probe spins does not necessarily improve the signal to noise ratio. This is stark contrast to the global magnetic field sensors with entangled probe spins where the signal to noise ratio is monotonically increased with increasing the number of the probe spins [12,[32][33][34][35][36][37][38][39][40][41][42].…”

“…On the other hand, it is known that, for the detection of global (spatially homogeneous) magnetic fields, an entanglement can enhance the performance of the qubitbased sensors. Especially, Greenberger-Horne-Zeilinger (GHZ) states can be used to outperform the standard quantum limit that classical sensors cannot surpass [12,[32][33][34][35][36][37][38][39][40][41][42]. There are many experimental demonstration * hakoshima-hideaki@aist.go.jp † matsuzaki.yuichiro@aist.go.jp to generate the GHZ states with several systems [12,[43][44][45].…”

Effects of counter-rotating-wave terms on the noisy frequency estimation

“…Unfortunately, the superiority of quantum metrology is commonly destroyed by decoherence [17,[23][24][25][26][27][28][29][30], which is induced by the inevitable interaction with the surrounding environment. For example, Ref.…”

Error-mitigated quantum metrology

“…The Heisenberg limit is susceptible to decoherence; for example, under the effect of Markovian dephasing, the sensitivity of entangled states scales to the standard quantum limit (SQL), as do separable states [7]. Several theoretical studies predict that scaling beyond the standard quantum limit is possible: they include the Zenoscaling under time-inhomogeneous noise model [25,26], quantum scaling by quantum teleportation [27,28], utilizing the collective effect of open quantum systems [28][29][30], and applying quantum error correction [31][32][33][34][35][36][37][38][39][40]. So far, however, scaling has been mainly discussed from the viewpoint of statistical errors under the assumption that the noise model can be fully characterized [Fig.…”