We analyze the role of entanglement among probes and with external ancillas in quantum metrology. In the absence of noise, it is known that unentangled sequential strategies can achieve the same Heisenberg scaling of entangled strategies and that external ancillas are useless. This changes in the presence of noise; here we prove that entangled strategies can have higher precision than unentangled ones and that the addition of passive external ancillas can also increase the precision. We analyze some specific noise models and use the results to conjecture a general hierarchy for quantum metrology strategies in the presence of noise.
We analyze the role of entanglement among probes and with external ancillas in quantum metrology. In the absence of noise, it is known that unentangled sequential strategies can achieve the same Heisenberg scaling of entangled strategies and that external ancillas are useless. This changes in the presence of noise; here we prove that entangled strategies can have higher precision than unentangled ones and that the addition of passive external ancillas can also increase the precision. We analyze some specific noise models and use the results to conjecture a general hierarchy for quantum metrology strategies in the presence of noise.
Entanglement-assisted quantum communication employs preshared entanglement between sender and receiver as a resource. We apply the same framework to quantum metrology, introducing shared entanglement between the probe and the ancilla in the preparation stage and allowing entangling operations at the measurement stage, i.e., using some entangled ancillary system that does not interact with the system to be sampled. This is known to be useless in the noiseless case, but was recently shown to be useful in the presence of noise [R. Demkowicz-Dobrzanski and L. Maccone, Phys. Rev. Lett. 113, 250801 (2014); W. D\"ur, M. Skotiniotis, F. Fr\"owis, and B. Kraus, Phys. Rev. Lett. 112, 080801 (2014); E. M. Kessler, I. Lovchinsky, A. O. Sushkov, and M. D. Lukin, Phys. Rev. Lett. 112, 150802 (2014); R. Demkowicz-Dobrza\ifmmode \acute{n}\else \'{n}\fi{}ski and J. Kolodynski, New J. Phys. 15, 073043 (2013)]. Here we detail how and when it can be of use. For example, surprisingly it is useful when two channels are randomly alternated, for both of which ancillas do not help (depolarizing). We show that it is useful for all levels of noise for many noise models and propose a simple optical experiment to test these results.
This thesis explores various protocols which can be applied to quantum metrology, such that precision of the measurement can beat the best classical approaches. We first demonstrate that ancilla-assisted schemes can improve phase estimation in the presence of noise, and we propose an experiment to demonstrate these effects. Given that the use of ancillae helps, it is no surprise that there are noisy channels for which the optimal strategy may depend on the noise level. We show that there is a non-trivial crossover between the ancilla-assisted strategy and the parallel-entangled strategy for Pauli noise channels and the amplitude damping channel. We see that under certain circumstances, the environment cannot access the parameter of interest. We then integrated techniques from quantum communication, to derive a general framework that renders quantum metrology protocols into cryptographic ones. Here the protocol is unconditionally secure if the trusted parties wish only to achieve the standard quantum limit. If Heisenberg-limited precision is to be achieved, they sacrifice some security, where adversaries can access information, but only at the risk of getting caught at it (cheat-sensitivity). In many scenarios, the quantum Fisher information is achieved for only one value of the phase. In a particular phase estimation scheme that measures the parity at the output of a Mach-Zehnder interferometer where the input is a two-mode squeezed vacuum, this problem is particularly imminent. We apply an adaptive technique to resolve this issue, showing that one can achieve precisions substantially below the shot noise limit. The key to a quadratically enhanced improvement in quantum metrology is entanglement. Finally, we demonstrate in a photonic system how high-dimensional entanglement can be certified, and provide an alternate interpretation of entanglement from an information-theoretic perspective.
For phase estimation using qubits, we show that for some noise channels, the optimal entanglement-assisted strategy depends on the noise level. We note that there is a nontrivial crossover between the parallel-entangled strategy and the ancilla-assisted strategy: in the former the probes are all entangled; in the latter the probes are entangled with a noiseless ancilla but not among themselves. The transition can be explained by the fact that separable states are more robust against noise and therefore are optimal in the high-noise limit, but they are in turn outperformed by ancilla-assisted ones.
The Heisenberg scaling is an ultimate precision limit of parameter estimation allowed by the principles of quantum mechanics, with no counterpart in the classical realm, and has been a long-pursued goal in quantum metrology. It has been known that interactions between the probes can help reach the Heisenberg scaling without entanglement. In this paper, we show that interactions between the probes and the additional dimensions of an ancillary system may also increase the precision of parameter estimation to surpass the standard quantum limit and attain the Heisenberg scaling without entanglement, if the measurement scheme is properly designed. The quantum Fisher information exhibits periodic patterns over the evolution time, implying the existence of optimal time points for measurements that can maximize the quantum Fisher information. By implementing optimizations over the Hamiltonian, the initial states of the probes and the ancillary system, the interaction strength, and the time points for measurements, our protocol achieves the Heisenberg scaling for the parameter of the probe Hamiltonian, in terms of both evolution time and probe number. Our protocol features two aspects: (i) the Heisenberg scaling can be achieved by a product state of the probes and (ii) mere local measurement on the ancilla is sufficient, both of which reduce the quantum resources and the implementation complexity to achieve the Heisenberg scaling. The paper is concluded by the investigation of the effects of noise on this protocol.
The primary challenge in advancing practical quantum technology is the presence of noise, which can lead to decoherence and undermine the advantages of quantum systems. However, it is worth noting that noise can also contain information that can be harnessed to improve performance in certain quantum information tasks. This has been explored for specific types of noise, but the full potential of informative noise within general dynamics remains largely unknown. Here we demonstrate that informative noise can be transformed into a valuable resource for enhancing precision limits in quantum metrology. We provide necessary and sufficient conditions under which the precision achieved in the presence of informative noise can attain Heisenberg scaling. Our research offers a fresh perspective on the role of noise in quantum metrology and opens up avenues for achieving higher precision beyond the previously anticipated ultimate limit.
The advent of quantum entanglement has revolutionized metrology, enabling the development of ultra-precise measurement techniques that surpass the limitations of classical systems. However, the delicate nature of entangled states makes them vulnerable to various noise sources, significantly impeding their metrological utility. To address this challenge, we delve into the intricate relationship between noise and the metrological usefulness of highly entangled multiqubit systems. By studying the impact of various factors, we aim to unravel the fundamental limits of quantum metrology and devise strategies to enhance the resilience of quantum systems against noise. Our investigation reveals that increasing the number of qubits in an entangled state can significantly enhance its noise robustness, particularly for certain entangled states. Furthermore, we uncover the surprising advantage of utilizing different local operators, surpassing the robustness offered by the conventional identical-operator approach. Additionally, by employing a technique that utilizes multiple copies of the quantum state, we identified many states with latent metrological usefulness and demonstrated their hidden noise robustness. While these strategies significantly enhance the robustness of many studied states, it is crucial to note that generalizations may not apply universally. Therefore, validating these findings for each specific state is essential before practical implementation. Our findings proved that by rigorously assessing noise susceptibility and adopting appropriate strategies, we can achieve substantial gains in precision and noise robustness. This paves the way for the development of more robust and reliable quantum metrological techniques, offering valuable insights across a wide range of applications, from fundamental physics to cutting-edge technologies like quantum computing, sensing, and communication.