Toward Heisenberg scaling in non-Hermitian metrology at the quantum regime.

Non-Hermitian quantum metrology, an emerging field at the intersection of quantum estimation and non-Hermitian physics, holds promise for revolutionizing precision measurement. Here, we present a comprehensive investigation of non-Hermitian quantum parameter estimation in the quantum regime, with a special focus on achieving Heisenberg scaling. We introduce a concise expression for the quantum Fisher information (QFI) that applies to general non-Hermitian Hamiltonians, enabling the analysis of estimation precision in these systems. Our findings unveil the remarkable potential of non-Hermitian systems to attain the Heisenberg scaling of 1/t, where t represents time. Moreover, we derive optimal measurement conditions based on the proposed QFI expression, demonstrating the attainment of the quantum Cramér-Rao bound. By constructing non-unitary evolutions governed by two non-Hermitian Hamiltonians, one with parity-time symmetry and the other without specific symmetries, we experimentally validate our theoretical analysis. The experimental results affirm the realization of Heisenberg scaling in estimation precision, marking a substantial milestone in non-Hermitian quantum metrology.

Optimal Strategies of Quantum Metrology with a Strict Hierarchy.

One of the main quests in quantum metrology is to attain the ultimate precision limit with given resources, where the resources are not only of the number of queries, but more importantly of the allowed strategies. With the same number of queries, the restrictions on the strategies constrain the achievable precision. In this Letter, we establish a systematic framework to identify the ultimate precision limit of different families of strategies, including the parallel, the sequential, and the indefinite-causal-order strategies, and provide an efficient algorithm that determines an optimal strategy within the family of strategies under consideration. With our framework, we show there exists a strict hierarchy of the precision limits for different families of strategies.

Information Geometry under Hierarchical Quantum Measurement.

In most quantum technologies, measurements need to be performed on the parametrized quantum states to transform the quantum information to classical information. The measurements, however, inevitably distort the information. The characterization of the discrepancy is an important subject in quantum information science, which plays a key role in understanding the difference between the structures of quantum and classical informations. Here we analyze the difference in terms of the Fisher information metric and present a framework that can provide analytical bounds on the discrepancy under hierarchical quantum measurements. Specifically, we present a set of analytical bounds on the difference between the quantum and classical Fisher information metric under hierarchical p-local quantum measurements, which are measurements that can be performed collectively on at most p copies of quantum states. The results can be directly transformed to the precision limit in multiparameter quantum metrology, which leads to characterizations of the trade-off among the precision of different parameters. The framework also provides a coherent picture for various existing results by including them as special cases.

Interfacial transport modulation by intrinsic potential difference of janus TMDs based on CsPbI3/J-TMDs heterojunctions.

Although perovskite/two-dimensional (2D) materials heterojunctions have been employed to improve the optoelectronic performance of perovskite photodetectors and solar cells, effects of the intrinsic potential difference (ΔV in ) of asymmetrical 2D materials, like Janus TMDs (J-TMDs), were not revealed yet. Herein, by investigating the optoelectronic properties of CsPbI3/J-TMDs heterojunctions, we find a reversible type-II band alignment related to the intensity and direction of ΔV in , suggesting that carrier transport paths can be reversed by modulating the contact configuration of J-TMDs in the heterojunctions. Meanwhile, the band offset, carrier transfer efficiency and optical properties of those heterojunctions are directly determined by the intensity and direction of ΔV in . Overall, CsPbI3/MoSSe heterojunction is suggested in this work with a tunneling probability of 79.65%. Our work unveils the role of ΔV in in asymmetrical 2D materials on the optoelectronic performances of lead halide perovskite devices, and provides a guideline to design high performance perovskite optoelectronic devices.

Reveal the Humidity Effect on the Phase Pure CsPbBr3 Single Crystals Formation at Room Temperature and Its Application for Ultrahigh Sensitive X-Ray Detector.

Generally, growing phase pure CsPbBr3 single crystals is challenging, and CsPb2 Br5 or Cs4 PbBr6 by-products are usually formed due to the different solubilities of CsBr and PbBr2 in the single solvent. Herein, the growth of high-quality phase pure CsPbBr3 perovskite single crystals at room temperature by a humidity controlled solvent evaporation method is reported first. Meanwhile, the room temperature phase transition process from three dimensional (3D) cubic CsPbBr3 to two dimensional (2D) layered tetragonal CsPb2 Br5 and the detailed mechanism induced by humidity are revealed. Moreover, compared with the organic-inorganic perovskite, the prepared CsPbBr3 single crystals are much more stable under high humidity, which satisfies the long-term working conditions of X-ray detectors. The X-ray detectors based on CsPbBr3 single crystals show a high sensitivity and a low detection limit of 1.89 µGyair s-1 , all of which meet the needs of medical diagnosis.

Impacts of the Electron Transport Layer Surface Reconstruction on the Buried Interface in Perovskite Optoelectronic Devices.

Using density functional theory combined with ab initio molecular dynamics, we comprehensively investigated the performance enhancement mechanism of the device after surface reconstruction by passivating different halogen groups (i.e., F or Cl) at the ETL/perovskite interface. We demonstrated that the halogen group at the ETL layer could stabilize the geometric structure of the perovskite surface by balancing the interfacial interaction, ionic migration, and lead iodide framework. Even though halogen passivation decreased and increased the interface charge transfer at the O- and SnO-terminated MAPbI3/SnO2 interfaces, respectively, halogen passivation optimized surface reconstruction and could theoretically relieve the interface carrier recombination according to the changes in conduction band offsets generated by halogen passivation. Furthermore, the interfacial carrier recombination of the MAPbI3/SnO2 interface was also connected to the interfacial gap states, which were smaller for O-terminated MAPbI3/SnO2 interfaces with halogen passivation-induced surface reconstruction but larger for the SnO-terminated cases. Hence, our findings have implications for the design of buried interface optimization in perovskite optoelectronic devices.

"Super-Heisenberg" and Heisenberg Scalings Achieved Simultaneously in the Estimation of a Rotating Field.

The Heisenberg scaling, which scales as N^{-1} in terms of the number of particles or T^{-1} in terms of the evolution time, serves as a fundamental limit in quantum metrology. Better scalings, dubbed as "super-Heisenberg scaling," however, can also arise when the generator of the parameter involves many-body interactions or when it is time dependent. All these different scalings can actually be seen as manifestations of the Heisenberg uncertainty relations. While there is only one best scaling in the single-parameter quantum metrology, different scalings can coexist for the estimation of multiple parameters, which can be characterized by multiple Heisenberg uncertainty relations. We demonstrate the coexistence of two different scalings via the simultaneous estimation of the magnitude and frequency of a field where the best precisions, characterized by two Heisenberg uncertainty relations, scale as T^{-1} and T^{-2}, respectively (in terms of the standard deviation). We show that the simultaneous saturation of two Heisenberg uncertainty relations can be achieved by the optimal protocol, which prepares the optimal probe state, implements the optimal control, and performs the optimal measurement. The optimal protocol is experimentally implemented on an optical platform that demonstrates the saturation of the two Heisenberg uncertainty relations simultaneously, with up to five controls. As the first demonstration of simultaneously achieving two different Heisenberg scalings, our study deepens the understanding on the connection between the precision limit and the uncertainty relations, which has wide implications in practical applications of multiparameter quantum estimation.

Zero-trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations.

Quantum estimation of a single parameter has been studied extensively. Practical applications, however, typically involve multiple parameters, for which the ultimate precision is much less understood. Here, by relating the precision limit directly to the Heisenberg uncertainty relation, we show that to achieve the highest precisions for multiple parameters at the same time requires the saturation of multiple Heisenberg uncertainty relations simultaneously. Guided by this insight, we experimentally demonstrate an optimally controlled multipass scheme, which saturates three Heisenberg uncertainty relations simultaneously and achieves the highest precisions for the estimation of all three parameters in SU(2) operators. With eight controls, we achieve a 13.27-dB improvement in terms of the variance (6.63 dB for the SD) over the classical scheme with the same loss. As an experiment demonstrating the simultaneous achievement of the ultimate precisions for multiple parameters, our work marks an important step in multiparameter quantum metrology with wide implications.

Minimal Tradeoff and Ultimate Precision Limit of Multiparameter Quantum Magnetometry under the Parallel Scheme.

The precise measurement of a magnetic field is one of the most fundamental and important tasks in quantum metrology. Although extensive studies on quantum magnetometry have been carried out over past decades, the ultimate precision that can be achieved for the estimation of all three components of a magnetic field under the parallel scheme remains unknown. This is largely due to the lack of understandings on the incompatibility of the optimal probe states for the estimation of the three components. Here we provide an approach to characterize the minimal tradeoff among the precisions of multiple parameters that arise from the incompatibility of the optimal probe states, which leads to the identification of the ultimate precision limit for the estimation of all three components of a magnetic field under the parallel scheme. The optimal probe state that achieves the ultimate precision is also explicitly constructed. The obtained precision sets a benchmark on the precision of the multiparameter quantum magnetometry under the parallel scheme, which is of fundamental interest and importance in quantum metrology.

Control-Enhanced Sequential Scheme for General Quantum Parameter Estimation at the Heisenberg Limit.

The advantage of quantum metrology has been experimentally demonstrated for phase estimations where the dynamics are commuting. General noncommuting dynamics, however, can have distinct features. For example, the direct sequential scheme, which can achieve the Heisenberg scaling for the phase estimation under commuting dynamics, can have even worse performances than the classical scheme when the dynamics are noncommuting. Here we realize a scalable optimally controlled sequential scheme, which can achieve the Heisenberg precision under general noncommuting dynamics. We also present an intuitive geometrical framework for the controlled scheme and identify sweet spots in time at which the optimal controls used in the scheme can be prefixed without adaptation, which simplifies the experimental protocols significantly. We successfully implement the scheme up to eight controls in an optical platform and demonstrate a precision near the Heisenberg limit. Our work opens the avenue for harvesting the power of quantum control in quantum metrology, and provides a control-enhanced recipe to achieve the Heisenberg precision under general noncommuting dynamics.

Modeling of Structure Effect for Ferroelectric Capacitor Based on Poly(vinylidene fluoride-trifluoroethylene) Ultrathin Films.

The characteristics of ferroelectric capacitors with poly(vinylidene fluoride-trifluoroethlene) (P(VDF-TrFE)) films have been studied at different structures of cell electrodes. It is suggested that the effect of electrode structures could induce changes of performance. Remarkably, cells with line electrodes display a better polarization and fatigue resistance than those with flat electrodes. For P(VDF-TrFE) ultrathin films with different electrode structures, the models of charge compensation mechanism for depolarization field and domain fatigue decomposition are used to explain the effect of electrode structure. Furthermore, the driving voltage based on normal speed-functionality is designed, and the testing results show that the line electrode structure could induce a robust switching, which is determined by the free charges concentration in active layer. These findings provide an effective route to design the optimum structure for a ferroelectric capacitor based on P(VDF-TrFE) copolymer ultrathin film.

Sequential Feedback Scheme Outperforms the Parallel Scheme for Hamiltonian Parameter Estimation.

Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find the highest achievable precision with the given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in the quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter, we show that the sequential feedback scheme has a threefold improvement over the parallel scheme for Hamiltonian parameter estimations on two-dimensional systems, and an order of O(d+1) improvement for Hamiltonian parameter estimation on d-dimensional systems. We also show that, contrary to the conventional belief, it is possible to simultaneously achieve the highest precision for estimating all three components of a magnetic field, which sets a benchmark on the local precision limit for the estimation of a magnetic field.

Optimal feedback scheme and universal time scaling for Hamiltonian parameter estimation.

Time is a valuable resource and it is expected that a longer time period should lead to better precision in Hamiltonian parameter estimation. However, recent studies in quantum metrology have shown that in certain cases more time may even lead to worse estimations, which puts this intuition into question. In this Letter we show that by including feedback controls this intuition can be restored. By deriving asymptotically optimal feedback controls we quantify the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit under the optimal feedback scheme. Our study reveals an intriguing connection between noncommutativity in the dynamics and the gain of feedback controls in Hamiltonian parameter estimation.