Quantum Sensing with a Single-Qubit Pseudo-Hermitian System

Yaoming Chu, Yu Liu, Haibin Liu, and Jianming Cai

Phys. Rev. Lett. 124, 020501 – Published 13 January 2020

Abstract

Quantum sensing exploits the fundamental features of a quantum system to achieve highly efficient measurement of physical quantities. Here, we propose a strategy to realize a single-qubit pseudo-Hermitian sensor from a dilated two-qubit Hermitian system. The pseudo-Hermitian sensor exhibits divergent susceptibility in a dynamical evolution that does not necessarily involve an exceptional point. We demonstrate its potential advantages to overcome noises that cannot be averaged out by repetitive measurements. The proposal is feasible with the state-of-art experimental capability in a variety of qubit systems, and represents a step towards the application of non-Hermitian physics in quantum sensing.

Received 30 October 2019

DOI:https://doi.org/10.1103/PhysRevLett.124.020501

Physics Subject Headings (PhySH)

Metrology Quantum sensing

Quantum Information, Science & Technology

Authors & Affiliations

Yaoming Chu , Yu Liu, Haibin Liu , and Jianming Cai^*

School of Physics, International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China

^*jianmingcai@hust.edu.cn

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Vol. 124, Iss. 2 — 17 January 2020

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Images

Figure 1
The quantum circuit representation of our pseudo-Hermitian quantum sensing protocol. $Y (θ)$ denotes a rotation of the ancilla qubit around the $\hat{y}$ axis by an angle $θ$ to prepare the initial state. The two-qubit dilation system evolves under the Hamiltonian $H_{tot}$ . The effective dynamics of the sensor system conditioned on the postselection measurement of the ancilla qubit is described by an effective pseudo-Hermitian Hamiltonian $H_{s} (δ_{λ})$ . The outcome of the measurement on the sensor system reveals the information about the parameter $λ$ .
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Figure 2
The evolution of the normalized state population of the sensor system $S (λ, t)$ [Eq. (7)] as a function of time. Sharp dips appear at time $t_{j} = (j - 1 / 2) π / E_{λ}$ ( $j \in Z^{+}$ ) with a narrow width $Δ t = 2 \sqrt{D_{λ}} / E_{λ}$ . The comparison of the results from different values of $λ$ , including $λ = 0$ (purple) and $(λ / ϵ ω) + 2 = (0.072, 0.172, 0.272, 0.372, 0.472, 0.572, 0.672)$ (from top to bottom), demonstrate that both the location and the width of the dips are dependent on the parameter $λ$ . The inset shows an enlargement around $t_{1} |_{λ = 0}$ (red dashed line). The other parameters are $ϵ = 0.01$ , $ω = 1$ .
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Figure 3
Pseudo-Hermitian quantum sensing with the dilated Hamiltonian in Eq. (3) for the estimation of the parameter $λ$ . (a) The normalized state population $S (λ, τ)$ of a fixed evolution time $τ = π / (2 E)$ as a function of $λ / (ϵ ω)$ shows a sharp peak located at $λ_{m} = - 2 ϵ ω$ . The derived analytical result in Eq. (7) (blue line) agrees well with numerical simulation (red circle). In the proximity of the peak, the approximation of the state population in Eq. (8) (green) allows us to derive the peak width $Δ λ ≃ 3 π ϵ^{3 / 2} ω$ . (b) The peak width as a function of the parameter $ϵ$ , becomes ultrasharp as $ϵ \to 0$ . The full peak width $Δ λ = Δ λ_{+} + λ_{-}$ (orange dots) is obtained by numerically solving $S (λ_{m} + Δ λ_{+}) = S (λ_{m} - Δ λ_{-}) = 1 / 2$ , which is well fitted by $Δ λ = 3 π ϵ^{3 / 2} ω$ (red dashed). (c) The susceptibility reaches the maximum value ${| χ_{s} (λ) |}_{\max} ≃ 0.14 ϵ^{- 3 / 2} ω^{- 1}$ at the optimal measurement working point. The solid line is calculated exactly from Eq. (7) and the dashed line corresponds to an approximate analytical result [58]. The other parameters are $ω = 1$ , $ϵ = 0.01$ , and $κ = δ$ .
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Figure 4
Numerical simulations of the dephasing effect. (a) The population signal $S (λ, τ)$ of a fixed evolution time $τ = π / (2 E)$ under the influence of dephasing at a rate of $γ$ . (b) Susceptibility at working point $| χ_{s} (λ_{o}) |$ as a function of the different dephasing rate $γ$ . The other parameters are the same as Fig. 3.
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