Enhancement of frequency estimation by spatially correlated environments

Abstract

In metrological tasks, employing entanglement can quantitatively improve the precision of parameter estimation. However, susceptibility of the entanglement to decoherence fades this capability in the realistic metrology and limits ultimate quantum improvement. One of the most destructive decoherence-type noise is uncorrelated Markovian noise which commutes with the parameter-encoding Hamiltonian and is modelled as a semigroup dynamics, for which the quantum improvement is constrained to a constant factor. It has been shown [Phys. Rev. Lett. 109, 233601 (2012)] that when the noisy time evolution is governed by a local and non-semigroup dynamics (e.g., induced by an uncorrelated non-Markovian dephasing), emerging the Zeno regime at short times can result in the Zeno scaling in the precision. Here, by considering the impact of the correlated noise in metrology, we show that spatially correlated environments which lead to a nonlocal and non-semigroup dynamics can improve the precision of a noisy frequency measurement beyond the Zeno scaling. In particular, it is demonstrated that one can find decoherence-free subspaces and subsequently achieve the Heisenberg precision scaling for an approximated dynamics induced by spatially correlated environments.

Practical quantum metrology in noisy environments

“…A similar qualitative behavior has been recently reported under other types of (nonunital) noise, such as erasure, spontaneous emission, and phase damping [37,38].…”

“…This will be the subject of future work. [38,39] does hold in general, although it is not necessarily a tight bound. If the maximization were not restricted to vectorized physical states |ˆ , but extended to all normalized four-dimensional vectors in Liouville space, we would end up calculating the op-…”

“…To that end, we aim to bound the QFI from below. In general, one may use [38,39], which is not necessarily tight. Luckily, for the family of channels encompassed by our ϕ , a tighter bound f N (ϕ) stemming from …”

Noisy metrology: a saturable lower bound on quantum Fisher information

“…In the case of semigroup dynamics, the noise type is one of the most destructive noise due to constraining the quantum enhancement to a constant factor [12,14,21]. However, this is not the case for a non-semigroup dynamics [16,[22][23][24][25]. Regarding U ω as the encoding unitary map and J as the parameter-independent noise map, the state of N probes at any instant is described as…”

Estimating phase with a random generator: Strategies and resources in multiparameter quantum metrology

“…However, a central aspect of phase sensing in a real-world scenario is the interaction between the probing system and the environment. Unfortunately, when this is taken into account, the promised quantum advantage is severely affected, with the enhancement becoming, at best, a constant factor in the asymptotic limit of large N , under most commonly encountered noise models [10][11][12][13]. This motivates one to examine more carefully the practical regime of finite N , where some form of advantage may remain [2,11,14].…”