We address the use of entangled qubits as quantum probes to characterize the noise induced by complex environments. In particular, we show that a joint measurement on entangled probes can improve estimation of the correlation time for a broad class of environmental noises compared to sequential strategies involving single-qubit preparation. The enhancement appears when the noise is faster than a threshold value, a regime which may always be achieved by tuning the coupling between the quantum probe and the environment inducing the noise. Our scheme exploits time-dependent sensitivity of quantum systems to decoherence and does not require dynamical control on the probes. We derive the optimal interaction time and the optimal probe preparation, showing that it corresponds to multiqubit Greenberger-Horne-Zeilinger states when entanglement is useful. We also show the robustness of the scheme against depolarization or dephasing of the probe, and discuss simple measurements approaching optimal precision.
We address the use of entangled qubits as quantum probes to characterize the noise induced by complex environments. In particular, we show that a joint measurement on entangled probes can improve estimation of the correlation time for a broad class of environmental noises compared to sequential strategies involving single-qubit preparation. The enhancement appears when the noise is faster than a threshold value, a regime which may always be achieved by tuning the coupling between the quantum probe and the environment inducing the noise. Our scheme exploits time-dependent sensitivity of quantum systems to decoherence and does not require dynamical control on the probes. We derive the optimal interaction time and the optimal probe preparation, showing that it corresponds to multiqubit Greenberger-Horne-Zeilinger states when entanglement is useful. We also show the robustness of the scheme against depolarization or dephasing of the probe, and discuss simple measurements approaching optimal precision.
The dynamics of quantum systems are unavoidably influenced by their environment, but in turn observing a quantum system (probe) can allow one to measure its environment: Measurements and controlled manipulation of the probe such as dynamical decoupling sequences as an extension of the Ramsey interference measurement allow to spectrally resolve a noise field coupled to the probe. Here, we introduce fast and robust estimation strategies for the characterization of the spectral properties of classical and quantum dephasing environments. These strategies are based on filter function orthogonalization, optimal control filters maximizing the relevant Fisher Information and multi-qubit entanglement. We investigate and quantify the robustness of the schemes under different types of noise such as finite-precision measurements, dephasing of the probe, spectral leakage and slow temporal fluctuations of the spectrum.
We explore the ability of a qubit probe to characterize unknown parameters of its environment. By resorting to the quantum estimation theory, we analytically find the ultimate bound on the precision of estimating key parameters of a broad class of ubiquitous environmental noises ("baths") which the qubit may probe. These include the probe-bath coupling strength, the correlation time of generic types of bath spectra, and the power laws governing these spectra, as well as their dephasing times T2. Our central result is that by optimizing the dynamical control on the probe under realistic constraints one may attain the maximal accuracy bound on the estimation of these parameters by the least number of measurements possible. Applications of this protocol that combines dynamical control and estimation theory tools to quantum sensing are illustrated for a nitrogen-vacancy center in diamond used as a probe.
We address the use of simple quantum probes for the spectral characterization of classical noisy environments. In our scheme a qubit interacts with a classical stochastic field describing environmental noise and is then measured after a given interaction time in order to estimate the characteristic parameters of the noise. In particular, we address estimation of the spectral parameters of two relevant kinds of non-Gaussian noise: random telegraph noise with a Lorentzian spectrum and colored noise with a $1/{f}^{\ensuremath{\alpha}}$ spectrum. We analyze in detail the estimation precision achievable by quantum probes and prove that population measurement on the qubit is optimal for noise estimation in both cases. We also evaluate the optimal interaction times for the quantum probe, i.e., the values maximizing the quantum Fisher information (QFI) and the quantum signal-to-noise ratio. For random telegraph noise the QFI is inversely proportional to the square of the switching rate, meaning that the quantum signal-to-noise ratio is constant and thus the switching rate may be uniformly estimated with the same precision in its whole range of variation. For colored noise, the precision achievable in the estimation of ``color,'' i.e., of the exponent $\ensuremath{\alpha}$, strongly depends on the structure of the environment, i.e., on the number of fluctuators describing the classical environment. For an environment modeled by a single random fluctuator estimation is more precise for pink noise, i.e., for $\ensuremath{\alpha}=1$, whereas by increasing the number of fluctuators, the quantum signal-to-noise ratio has two local maxima, with the largest one drifting towards $\ensuremath{\alpha}=2$, i.e., brown noise.
Quantum metrology promises to surpass classical precision limits by leveraging quantum resources such as entanglement. Maximally entangled Greenberger-Horne-Zeilinger (GHZ) states are theoretically optimal probes for quantum metrology. However, they are fragile to environmental noise, severely limiting their practical utility. To overcome this limitation, we propose and experimentally realize a noise-adaptive quantum metrology scheme that autonomously identifies optimal probes without any prior information of the noise. This is achieved by combining a variational quantum circuit that optimizes available resources with an efficient strategy for evaluating the sensing performance. Using a seven-qubit nuclear spin sensor, we identify optimal probe states that achieve precision improvements up to 0.698 dB over GHZ states when sensing a fixed magnetic field. Furthermore, we show that the learned probe state exhibits cross-parameter robustness, maintaining superior performance over a broad range of magnetic field frequencies. The proposed scheme is model-free, hardware-efficient, and scalable, providing a practical route to noise-resilient quantum metrology on near-term quantum devices.
Abstract Quantum probing is the art of exploiting simple quantum systems interacting with a complex environment to extract precise information about some environmental parameters, e.g. the temperature of the environment or its spectral density. Here we analyze the performance of a single-qubit probe in characterizing Ohmic bosonic environments at thermal equilibrium. In particular, we analyze the effects of tuning the interaction Hamiltonian between the probe and the environment, going beyond the traditional paradigm of pure dephasing. In the weak-coupling and short-time regime, we address the dynamics of the probe analytically, whereas numerical simulations are employed in the strong coupling and long-time regime. We then evaluate the quantum Fisher information for the estimation of the cutoff frequency and the temperature of the environment. Our results provide clear evidence that pure dephasing is not optimal, unless we focus attention to short times. In particular, we found several working regimes where the presence of a transverse interaction improves the maximum attainable precision, i.e. it increases the quantum Fisher information. We also explore the role of the initial state of the probe and of the probe characteristic frequency in determining the estimation precision, thus providing quantitative guidelines to design optimized detection to characterize bosonic environments at the quantum level.
We address a particular instance where open quantum systems may be used as quantum probes for an emergent property of a complex system, as the temperature of a thermal bath. The inherent fragility of the quantum probes against decoherence is the key feature making the overall scheme very sensitive. The specific setting examined here is that of quantum thermometry, which aims to exploit decoherence as a resource to estimate the temperature of a sample. We focus on temperature estimation for a bosonic bath at equilibrium in the Ohmic regime (ranging from sub-Ohmic to super-Ohmic), by using pairs of qubits in different initial states and interacting with different environments, consisting either of a single thermal bath or of two independent ones at the same temperature. Our scheme involves pure dephasing of the probes, thus avoiding energy exchange with the sample and the consequent perturbation of temperature itself. We discuss the role of correlations among the probes and the presence of a local versus a global bath. We show that entanglement improves thermometry at short times if the two qubits are embedded in a common bath, whereas if the interaction time is not constrained, then coherence rather than entanglement is the key resource in quantum thermometry.