Quantum metrology including state preparation and readout times

Abstract

There is growing belief that the next decade will see the emergence of sensing devices based on the laws of quantum physics that outperform some of our current sensing devices. For example, in frequency estimation, using a probe prepared in an entangled state can, in principle, lead to a precision gain compared to a probe prepared in a separable state. Even in the presence of some forms of decoherence, it has been shown that the precision gain can increase with the number of probe particles N . Usually, however, the entangled and separable state preparation and readout times are assumed to be negligible. We find that a probe in a maximally entangled (GHZ) state can give an advantage over a separable state only if the entangled state preparation and readout times are lower than a certain threshold. When the probe system suffers dephasing, this threshold is much lower (and more difficult to attain) than it is for an isolated probe. Further, we find that in realistic situations the maximally entangled probe gives a precision advantage only up to some finite number of probe particles N cutoff that is lower for a dephasing probe than it is for an isolated probe.

Fundamental limits to frequency estimation: a comprehensive microscopic perspective

“…Importantly, in contrast to phase estimation tasks in optical interferometry [4], in frequency estimation one must explicitly account for the finite time-scale over which ω 0 is imprinted on the probes. In particular, t in equation (1) that constitutes the encoding time specifies also the duration of a single round (repetition) of the protocol-we assume throughout this work that both the preparation and measurement stages in figure 1 take negligible durations (see [48] for a generalisation). As a result, when optimising the protocol to maximise the precision attained, one must take into account the fact that, although the total duration of an experiment, T, can always be assumed to be significantly larger than the duration of a single protocol round (T?t), by decreasing t the total number of repetitions, ν=T/t, is increased.…”

“…In figure 4 we illustrate the different dynamics geometrically by comparing the different evolutions of the open system for the NPC dynamics described by equation (48) and the PC dynamics fixed by equation (50), respectively, see appendix C.1. In figures 4(a)-(c), we report the evolution for the same dynamics (i.e., the same ω 0 , ω c , λ, β and J), for the three different initial conditions which correspond to the three canonical orthogonal axes in the Bloch sphere.…”

“…In this paragraph we examine the behavior of the QFI for finite times, when the dynamics are dictated by the master equation expressed in equations (48) and (50). This will allow us to analyze more in detail the difference between the NPC and the PC contributions to the QFI.…”

“…The starting point is the master equation given by equation (48). In particular, we considered three different NPC noise scenarios: the first two cases of a purely transversal noise, i.e., J = 0, for a non-semigroup (see figure 7(a)) and for a semigroup (figure 7(b)) dynamics.…”

“…NPC noise, which might be seen as a 'purely NPC noise'. For any J ¹ 0, the dissipative part of the master equation given in equation (48) together with the resulting dynamical maps, will have a component longitudinal to the parameter imprinting, fixing the asymptotic scaling to the less favorable one proper to PC dynamics and hence extending the Zeno regime recalled in section 2.3 to the scenario governed by NPC noise. This result, already known for the semigroup regime [37] (see also section 2.3), is here extended to the non-semigroup case.…”