Multiqubit matter-wave interferometry under decoherence and the Heisenberg scaling recovery

Abstract

Most matter-wave interferometry (MWI) schemes for quantum sensing have so far been evaluated in ideal situations without noises. In this work, we provide assessments of generic multiqubit MWI schemes under Markovian dephasing noises. We find that for certain classes of the MWI schemes with scale factors that are nonlinearly dependent on the interrogation time, the optimal precision of maximally entangled probes decreases with increasing the particle number N , for both independent and collective dephasing situations. This result challenges the conventional wisdom found in dephasing Ramsey-type interferometers. We initiate the analyses by investigating the optimal precision of multiqubit Sagnac atom interferometry for rotation sensing. And we show that due to the competition between the unconventional interrogation-time quadratic phase accumulation and the exponential dephasing processes, the Greenberger-Horne-Zeilinger (GHZ) state, which is the optimal input state in noiseless scenarios, leads to vanishing quantum Fisher information in the large-N regime. Then our assessments are further extended to generic MWI schemes for quantum sensing with entangled states and under decoherence. Finally, a quantum error-correction logical GHZ state is tentatively analyzed, which could have the potential to recover the Heisenberg scaling and improve the sensitivity. arXiv:1808.04632v3 [quant-ph]

Gaussian quantum metrology in a dissipative environment

“…( 11) that F +,BMA κ (∞) = 0, which indicates that the metrology error becomes divergent and the corresponding metrology scheme completely breaks down in the long-encoding time regime. A similar result is also reported in many previous works [16][17][18][19][20][21][22][23][24]. It is understandable based on the fact that the information of κ in ρ(t) under the Born-Markovian approximation unidirectionally flows from the probe to the environment such that no message can be extracted in the long-encoding-time regime.…”

“…This result is qualitatively consistent with the Born-Markovian approximate result in Eq. ( 11) and many previous studies [16][17][18][19][20][21][22][23][24]. In sharp contrast to this, Fig.…”

“…Such amazing result is caused by the anomalous equilibrium state induced by the bound state: the message of κ is partially preserved in the steady state ρ(∞) and can be persistently enlarged by prolonging the encoding time. Therefore, we can completely overcome the error-divergency problem appearing in many previous studies [16][17][18][19][20][21][22][23][24] with the help of the bound state mechanism. Moreover, one can find from Eq.…”

“…It results in the deterioration of the performance of quantum metrology. It was found that the metrology error generally becomes divergent in the longencoding-time regime under the influence of decoherence caused by environments [16][17][18][19][20][21][22][23][24]. Such phenomenon is called no-go theorem of noisy quantum metrology [21,25] and is the main bottleneck for achieving a high-precision quantum metrology in practice.…”

Optimal Scheme for Quantum Metrology

“…Metrology, which studies the precision limit of measurement and estimation, plays a central role in science and technology. Recently quantum metrology, which exploits quantum mechanical effects to achieve far better precision than classical schemes , has gained increasing attention and has found wide applications in various fields, such as gravitational wavedetection [19,[23][24][25][26][27], quantum phase estimation [5,[28][29][30][31], quantum magnetometer [32,33], quantum ranging [34][35][36], quantum spectroscopy [37][38][39][40], quantum imaging [41][42][43][44][45][46][47], quantum target-detection [48,49], quantum gyroscope [50,51], distributed quantum sensing [52][53][54], atomic clocksynchronization [55][56][57][58][59][60][61], and even biological measurements [62].…”