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Quantitative phase imaging (QPI) has been a powerful approach in bioimaging because it can protect specimens from staining and quantify important physical properties of biological specimen, such as local thickness and refractive index. Here, a simple mechanism is proposed to implement QPI based on the quantum weak‐value theory. Two weak values are employed. One is momentum weak value, which inherently gives the phase gradient of the cells and tissues, and the other is polarization weak value leading to the biased imaging. Following the essence of weak value amplification in precision metrology, the weak value can also enhance the contrast in imaging. By combining two converse bias images and a phase gradient intensity image to capture phase gradient data, the original phase of the specimen can be quantitatively reconstructed. A proof‐of‐principle experiment is conducted by imaging the phase targets and unstained Paramecium cells. The ability to capture quantitative phase data is validated through imaging various samples with a phase resolution, demonstrating height deviations of less than 10 nm compared to atomic force microscopy (AFM). This work proposes weak‐value‐based QPI that possess the potential for improving the measurement precision and provides deep insights into physics and applications of weak value. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel protection scheme for N-qubit Greenberger–Horne–Zeilinger (GHZ) states against amplitude damping noise, using unilateral operations. The key innovation lies in the implementation of local operations on a single qubit, irrespective of the total number of qubits, thereby significantly reducing the operational complexity and resource requirements compared to existing methods. The scheme involves a unilateral rotation to transform the GHZ state into a less vulnerable configuration before exposing it to noise, followed by a weak measurement and another unilateral rotation to recover the initial state. We provide a comprehensive mathematical analysis of the proposed unilateral protection scheme, deriving expressions for both fidelity and success probability. The practical feasibility of our scheme is demonstrated through simulations using the Qiskit SDK, in which we provide the corresponding quantum circuit for performing the partial weak measurement used in our scheme. Comparative analysis with pioneer protection schemes reveals a substantial enhancement in success probability and fidelity for both GHZ and generalized GHZ states, emphasizing the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

In this work, a scheme to protect quantum entanglement from a non‐Markovian noisy environment is proposed. By applying two quantum weak measurements before and after sending the quantum state into the noisy channel, the quantum state can be "pushed" closer to a decoherence‐free state, reducing decoherence during the time evolution. Then, the second weak measurement can partially retrieve the initial quantum state from the state corrupted by the noisy environment. The study involves a non‐Markovian dynamic equation to examine the impact of the memory effect on the protection scheme's performance. Various factors affecting the residual entanglement and the success probability are analyzed. The results suggest that two measurement strengths shall be chosen approximately in a linear relation, with the best ratio determined by the memory time of the environment. Additionally, it is demonstrated that the memory effect significantly enhances the protection efficiency. Lastly, the scheme's robustness against systematic errors is evaluated. [ABSTRACT FROM AUTHOR]

In this paper, based on a remote state preparation (RSP) scheme for arbitrary single quantum bit state and a controlled quantum teleportation protocol, we discuss the decoherence suppression (DS) of weak measurement (WM) and environmentally assisted measurement (EAM). We analyze the application of the decoherence suppression strategy of WM and EAM in improving the efficiency and quality of quantum communication from the perspective of amplitude or phase damped channels. For these two types of noise, the average fidelity and the probability of success of the scheme are calculated as a function of the weak measurement before, after and the channel attenuation parameters. Provided that the decay rate of the amplitude or phase damping is completely known, one can always achieve unit fidelity even for heavy damping cases, which is the biggest advantage of proposed scheme. Influences of several paramters, including strengths of weak measurements and the decay rate of the decoherence channel, on the RSP based on decoherence suppression is discussed. The results indicate that protected CQT of an arbitrary unknown single-qubit state can be achieved with a certain probability and 100% fidelity. [ABSTRACT FROM AUTHOR]

The demand for accurate and efficient immunoassays calls for the development of precise, high-throughput analysis methods. This paper introduces a novel approach utilizing a weak measurement interface sensor for immunoassays, offering a solution for high throughput analysis. Weak measurement is a precise quantum measurement method that amplifies the weak value of a system in the weak interaction through appropriate pre- and post-selection states. To facilitate the simultaneous analysis of multiple samples, we have developed a chip with six flow channels capable of conducting six immunoassays concurrently. We can perform real-time immunoassay to determine the binding characteristics of spike protein and antibody through real-time analysis of the flow channel images and calculating the relative intensity. The proposed method boasts a simple structure, eliminating the need for intricate nano processes. The spike protein concentration and relative intensity curve were fitted using the Log-Log fitting regression equation, and R2 was 0.91. Utilizing a pre-transformation approach to account for slight variations in detection sensitivity across different flow channels, the present method achieves an impressive limit of detection(LOD) of 0.85 ng/mL for the SARS-CoV-2 the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike protein, with a system standard deviation of 5.61. Furthermore, this method has been successfully verified for monitoring molecular-specific binding processes and differentiating binding capacities. [ABSTRACT FROM AUTHOR]

This study focuses on the impact of amplitude-damping noise, which diminishes the fidelity of the teleported quantum state on an existing cyclic quantum teleportation scheme [V. Verma, D. Yadav and D. K. Mishra, Opt. Quantum Electron. 53 (2021) 1]. The CQT scheme involves three participants performing a cyclic teleportation along with a controller to supervise the protocol. We also propose weak measurement and reversal measurement operations as potential solutions to combat the noise-induced decoherence and improve the fidelity of the existing CQT scheme. The simulation results showcase the improvements achieved in the fidelity calculation when implementing the potential solutions. The findings hold immense potential for quantum information communications in practical situations. [ABSTRACT FROM AUTHOR]

Entanglement protection from noisy environments is an essential task in practical quantum information and communication. In this paper, we investigate the entanglement recovery of an amplitude-damped tripartite GHZ state by a weak-measurement reversal procedure. In particular, we emphasize the key importance of the inequivalency of probability amplitudes of the tripartite system under the recovery technique. We explore the maximal and non-maximal tripartite entangled state scenarios under amplitude damping noise in the absence and presence of weak measurement reversal procedures. Importantly, the non-maximal entangled state turns out to be a good choice for the entanglement recovery via weak-measurement reversal procedure. [ABSTRACT FROM AUTHOR]

Spin-Hall effect (SHE) of light is one of the main manifestations of the spin-orbit interaction of photons, and has been extensively studied for optical beams with homogeneous polarization. Here, we present a theoretical study of the SHE of cylindrical vector vortex beams (CVVBs) possessing inhomogeneous polarization. We derive the analytical expressions of the SHE of CVVBs reflected and refracted at a dielectric interface with radial and azimuthal polarization of incidence. The spin-dependent shifts of the SHE of light linearly depend on the topological charge of the CVVBs. In contrast to the conventional SHE of horizontally or vertically polarized beams, the SHE shifts of the CVVBs are asymmetrical when the topological charge is nonzero. This asymmetry results in the transverse Imbert–Fedorov (IF) shifts that are proportional to the topological charge. Furthermore, based on weak measurement, we propose an experimental scheme to enhance the SHE and related IF shifts with proper pre- and post-selection polarization states. Our results advance the study of the SHE of structured light and may find applications in SHE-based techniques such as precision measurement. [ABSTRACT FROM AUTHOR]

Quantum correlation is a key resource for a variety of quantum information processing and communication tasks, the efficient utilization of which has been a longstanding concern, and it is also one of the main challenges in the application of quantum technology. In this review, we focus on the interaction between quantum measurements and quantum correlations by designing appropriate measurement strategies, specifically exploring the trade-off between information gain and disturbance degree in weak measurements to ensure that quantum correlations from the same source can be shared among multiple independent observers. We introduce the basic knowledge and classification of quantum measurements, investigate the weak measurement scenario, and show the theoretical model construction of quantum correlation recycling in the original works. We summarize the theoretical and experimental development process and the latest progress in this field. Finally, we provide an outlook for more quantum resource applications that can profit from the optimization of quantum measurement strategies. [ABSTRACT FROM AUTHOR]

This paper presents a tripartite quantum teleportation protocol that incorporates feed-forward control and environment-assisted measurement, aiming to suppress the influence of arbitrary noise with at least one reversible Kraus operator. In this protocol, the feed-forward control is first utilized before the decoherence channel, such that the entangled qubit is transferred to the target state, which is more robust against noise. Next, the measurement is performed on the noise environment coupled with the entangled qubit during the decoherence channel. Finally, the reversed feed-forward control and the redesigned weak measurement reversal operator are applied after the decoherence channel. This protocol can be applied to the case where both amplitude damping and phase damping noise coexist. Based on this protocol, the analytical expressions for performance metrics including the average fidelity and the success probability are further derived. Even for the heavy damping cases, the final average teleportation fidelity can reach 1, which is independent of the magnitude of decoherence and the entanglement parameters. Furthermore, we optimize the success probability without compromising fidelity, and derive the average fidelity expression of the standard tripartite teleportation protocol through the phase damping noise channel. The effectiveness of our protocol is verified by numerical simulations.

The demand for accurate and efficient immunoassays calls for the development of precise, high-throughput analysis methods. This paper introduces a novel approach utilizing a weak measurement interface sensor for immunoassays, offering a solution for high throughput analysis. Weak measurement is a precise quantum measurement method that amplifies the weak value of a system in the weak interaction through appropriate pre- and post-selection states. To facilitate the simultaneous analysis of multiple samples, we have developed a chip with six flow channels capable of conducting six immunoassays concurrently. We can perform real-time immunoassay to determine the binding characteristics of spike protein and antibody through real-time analysis of the flow channel images and calculating the relative intensity. The proposed method boasts a simple structure, eliminating the need for intricate nano processes. The spike protein concentration and relative intensity curve were fitted using the Log-Log fitting regression equation, and R2 was 0.91. Utilizing a pre-transformation approach to account for slight variations in detection sensitivity across different flow channels, the present method achieves an impressive limit of detection(LOD) of 0.85 ng/mL for the SARS-CoV-2 the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike protein, with a system standard deviation of 5.61. Furthermore, this method has been successfully verified for monitoring molecular-specific binding processes and differentiating binding capacities.

The concept of ergotropy was previously introduced as the maximum extractable work from a quantum state. Its enhancement, which is induced by quantum correlation via projective measurement, was formulated as the daemonic ergotropy. In this work, we investigate the ergotropy in the presence of quantum correlation via weak measurement because of its elegant effects on the measured system. By considering a bipartite correlated quantum system consisting of main and ancillary systems, we demonstrate that the extractable work by the non-selective weak measurement on the ancilla is always equal to the situation captured by the strong measurement. However, the selective weak measurement interestingly reveals more work than the daemonic ergotropy and the ergotropy of the total system is greater than or equal to the daemonic ergotropy. Moreover, it is shown that for Bell diagonal states, at the cost of losing quantum correlation, the total extractable and thus non-local extractable works can be increased by using measurement. Also, we find that there is no direct relationship between quantum correlation and non-local extractable work for these cases.

A perfect teleportation protocol requires pure maximally shared entangled states. While in reality the shared entanglement is drastically degraded due to the inevitable interaction with the noisy environment. Here, we propose a teleportation protocol to teleport an unknown qubit through amplitude damping channels with a fidelity up to one with a single copy of the entangled state. Our proposed teleportation protocol, while illustrated using the Bell and W entangled states as examples, can be utilized with any type of entangled states. In our protocol, we utilize environment-assisted measurement (EAM) during the entanglement distribution, and further modify the original teleportation protocol to apply weak measurement in the last step of teleportation. We find a balance between teleportation fidelity and success probability by varying the strength of the weak measurement. Furthermore, we investigate the protection of third-party assisted teleportation protocols, where all the qubits of the entangled state pass through the amplitude damping channel. In particular, for the third-party assisted teleportation with the W state, the decoherence of the shared entanglement can be totally suppressed by using EAM, hence no weak measurement is required to achieve an average teleportation fidelity of unity. The numerical simulation results reveal that our proposed teleportation protocol outperforms both the weak measurement based probabilistic teleportation protocol and the original teleportation protocols without protection.

In this work, we study quantum versions of attribute-based encryption schemes. Attribute-based encryption enables fine-grained access control of encrypted data using authorization policies. The secret key of a user and the ciphertext are dependent upon attributes, and the decryption of a ciphertext is possible only if the set of attributes of the user key matches the attributes of the ciphertext. Most of the existing classical attribute-based schemes are based on the hardness of the bilinear Diffie–Hellman problem, which has been proven to be vulnerable against Shor's algorithm. No efficient quantum attribute-based encryption scheme has been reported till date. In this backdrop, we propose quantum attribute-based encryption schemes exploiting quantum key distribution and quantum error-correcting codes. Attribute-based scheme is a special case of a more general functional encryption scheme whose quantum version we consider next hence giving this work a unifying framework. We present two constructions of quantum functional encryption schemes. The first construction generalizes the traditional notion of functional encryption and can handle multiple functions. The second construction utilizes the quantum query complexities of different Boolean functions. As applications, we present a quantum progressive functional encryption scheme to suitably encrypt an image to be shared among data users with hierarchical relations between them and outline a connection between quantum functional encryption schemes and obfuscated quantum states. In this work, we use weak measurements, which help us to expand our horizon to include encryption schemes in the dishonest model and quantum communication in the presence of an adversary. Our methods are unconditional and do not depend on the known difficulty of problems like lattice-based problems. Finally, we discuss various advantages of our methods and results. [ABSTRACT FROM AUTHOR]

The generalized amplitude damping (GAD) noise models the dynamical map of a qubit in contact with a non-zero temperature bosonic reservoir. When two qubits successively pass through the same GAD channel, correlation effects should be taken into account. Therefore, the dynamical map is modeled as correlated GAD (CGAD) noise. In this paper, we investigate the teleportation of quantum Fisher information (QFI) under CGAD noise. We first show that the correlation effects in CGAD noise can enhance the teleported QFI. We then present two probabilistic schemes to improve the teleportation of QFI in CGAD noise by weak measurement (WM) and environment-assisted measurement (EAM). We find the correlation effects of CGAD noise serve to improve the teleportation of QFI and increase the probability of success. Contrary to intuition, the thermal average photon number n does not always play a negative role in our probabilistic schemes. Although a larger n will cause the teleported QFI to decay faster, the corresponding probability of success will be higher. Finally, we introduce a quantity called average QFI to demonstrate that the EAM scheme is superior to the WM scheme with respect to QFI improvement under CGAD noise.

The approach to question answering is challenging because it usually requires finding useful information from within and between question and answer sentences for sentence semantic matching. The key information mined from existing question and answer sentences, as a supplement to semantic information, maybe helpful for this task. However, capturing the intra-sentence and inter-sentence semantic interactions is somewhat difficult given the implicit interrelationships between question and answer sentences. Although the learning effect of multi-layer neural network is good, it lacks explanatory and theoretical support. This paper mainly studies how to select the best answer sentence from a set of question and answer sentences, mine information more effectively, perform semantic matching, and have a certain interpretability. Therefore, we propose a hierarchical attention network (QHAN) based on the mathematical framework of quantum theory, which integrates the attention mechanism under quantum measurement and density matrix (DMATT) and the attention mechanism under quantum weak measurement and weak value (WMATT) in one in a unified model framework. QHAN can not only discover key sentences in a set of question and answer sentences and key words in a sentence, but also perform sentence semantic matching quickly and accurately. Furthermore, QHAN has the advantage of interpretability in terms of models due to the physical meaning and attentional full weight distribution implied by quantum theory. Extensive experiments on the question answering dataset show that our method is comparable to the baselines and can explain why the selected question and answer sentence is the best option in terms of intra-sentence and inter-sentence attention distributions. [ABSTRACT FROM AUTHOR]

The quantum coherence of a two‐qubit system in which each qubit is coupled to its own hierarchical environment is studied. The effect of the hierarchical environment is explored in order to improve the coherence effectively. It is discovered that the dynamics of coherence can be manipulated by the number N of the second‐layer cavities (mn$m_{n}$), the coupling strengths Ω0, Ω, κ, respectively for the qubit‐cavity (m0), nearest‐neighbor, and m0‐mn$m_{n}$ cavities. It depends also on the decay rate Γ of second‐layer cavities. Furthermore, an effective scheme for enhancing coherence is proposed by using weak measurement and weak measurement reversal. The explicit conditions of the optimal measurement strengths to improve the coherence comparatively are derived. It is seen that the final stable value of the coherence is independent of the number N of second‐layer cavities but is related to the weak measurement strength m when the coupling strength between two nearest‐neighbor cavities is taken into account. [ABSTRACT FROM AUTHOR]

In this paper, a weak measurement scheme with double pointers (mean value shift and intensity shift of the post-selected light) is presented to simultaneously measure the tiny polarization change (phase and amplitude) of light in a single experimental apparatus. Furthermore, rather than using charge-coupled-device (CCD) to measure the pointer shift, we use the two-channel photoreceiver combined with lock-in amplifier (LIA) to measure the intensities of a split-Gaussian mode in this work. In this way, we introduce two intensity contrast ratios (ICRs) as special pointers to characterize the mean value and intensity shifts. As a result, the measurement precision of the polarization rotation is on the order of magnitude of $\,10^{-7}rad$ in the experiment. These findings provide a distinctive insight into the weak measurement and have important implications for the accurate measurement of complex optical parameters.

Time-symmetric formulation of quantum mechanics—the two-state vector formalism—is presented as a tool for studying past behaviour of quantum systems. A role of weak measurement and weak values in the Cheshire Cat effect and a nested (Vaidman) three-path interferometer are discussed. Interpretation of a particle’s faint trace indicating possibility of discontinuous paths of particles passing the Vaidman interferometer is given. Consistent histories are presented as one of alternative approaches. Multitude of controversial issues is briefly reviewed and discussed.

The spin Hall effect of light, i.e., the microscopic and spin-dependent transverse splitting of linearly polarized light into circular polarizations at an optical interface, has been considered as a promising candidate for high-precision measurement when combined with a weak measurement technique. However, in those previous demonstrations, the precision is determined by the interface of interest, hindering its versatility. Here, by leveraging the direct correlation of precision with the spin Hall shift, we propose nanophotonic-assisted approaches to increase the precision of the weak measurement by controlling the spin Hall effect of light at the target interface. The refractive index sensing of an isotropic medium is demonstrated as a proof of concept, in which the precision can be increased, in principle, to infinity by placing an index-below-unity slab in the vicinity of the target interface. Furthermore, a single-layer metasurface comprising two-dimensional subwavelength patterns is introduced as an experimentally favorable platform. This study lays the foundation for nondestructive and high-precision investigation of unknown parameters of interfaces and will find wide sensing applications in material science, medical engineering, and other interdisciplinary fields.

Since the initial discovery of quantum teleportation, it is devoted to transferring unknown quantum states from one party to another distant partner. However, in the scenarios of remote sensing, what people truly care about is the information carried by certain parameters. The problem of multiparameter estimation in the framework of qutrit teleportation under amplitude damping (AD) noise is studied. Particularly, two schemes are proposed to battle against AD noise and enhance the precision of multiparameter estimation by utilizing weak measurement (WM) and environment‐assisted measurement (EAM). For two‐phase parameters encoded in a qutrit state, the analytical formulas of the quantum Fisher information matrix can be obtained. The results prove that the scheme of EAM outperforms the WM one in the improvements of both independent and simultaneous estimation precision. Remarkably, the EAM scheme can completely ensure the estimation precision against the contamination by AD noise. The reason should be attributed to the fact that EAM is carried out after the AD noise. Thus, it extracts information from both the system and the environment. The findings show that the techniques of WM and EAM are helpful for remote quantum sensing and can be generalized to other qutrit‐based quantum information tasks under AD decoherence. [ABSTRACT FROM AUTHOR]

Spin-Hall effect (SHE) of light is one of the main manifestations of the spin-orbit interaction of photons, and has been extensively studied for optical beams with homogeneous polarization. Here, we present a theoretical study of the SHE of cylindrical vector vortex beams (CVVBs) possessing inhomogeneous polarization. We derive the analytical expressions of the SHE of CVVBs reflected and refracted at a dielectric interface with radial and azimuthal polarization of incidence. The spin-dependent shifts of the SHE of light linearly depend on the topological charge of the CVVBs. In contrast to the conventional SHE of horizontally or vertically polarized beams, the SHE shifts of the CVVBs are asymmetrical when the topological charge is nonzero. This asymmetry results in the transverse Imbert–Fedorov (IF) shifts that are proportional to the topological charge. Furthermore, based on weak measurement, we propose an experimental scheme to enhance the SHE and related IF shifts with proper pre- and post-selection polarization states. Our results advance the study of the SHE of structured light and may find applications in SHE-based techniques such as precision measurement.

The photonic spin Hall effect (SHE) refers to the transverse spin separation of photons with opposite spin angular momentum, after the beam passes through an optical interface or inhomogeneous medium, manifested as the spin-dependent splitting. It can be considered as an analogue of the SHE in electronic systems: the light’s right-circularly polarized and left-circularly polarized components play the role of the spin-up and spin-down electrons, and the refractive index gradient replaces the electronic potential gradient. Remarkably, the photonic SHE originates from the spin-orbit interaction of the photons and is mainly attributed to two different geometric phases, i.e., the spin-redirection Rytov-Vlasimirskii-Berry in momentum space and the Pancharatnam-Berry phase in Stokes parameter space. The unique properties of the photonic SHE and its powerful ability to manipulate the photon spin, gradually, make it a useful tool in precision metrology, analog optical computing and quantum imaging, etc. In this review, we provide a brief framework to describe the fundamentals and advances of photonic SHE, and give an overview on the emergent applications of this phenomenon in different scenes.

In this paper we propose a tripartite teleportation protocol to teleport an unknown quantum state via noisy quantum channels with fidelity equal to one even with a non-maximally entangled state. In our protocol we utilize environment-assisted measurement during entanglement distribution and further modify the standard teleportation protocol to apply weak measurement reversal in the last step of teleportation. We design the weak measurement reversal operators to make the teleportation fidelity equal to one, independent of the magnitude of decoherence or the shared entangled state parameters. Since the teleportation fidelity is always equal to one, we can optimize the teleportation success probability without affecting the fidelity. Moreover, we give the detailed procedure of the standard tripartite teleportation protocol in the presence of amplitude damping and derive the final expression of the average standard teleportation fidelity. [ABSTRACT FROM AUTHOR]

The public health concern of antibiotic residues in animal-origin food has been a long-standing issue. In this work, we present a novel method for antibiotic detection, leveraging optical weak value amplification and harnessing an indirect competitive inhibition assay, which significantly boosts the system's sensitivity in identifying small molecule antibiotics. We chose chloramphenicol as a model compound and mixed it with chloramphenicol-bovine serum albumin conjugates to bind to the chloramphenicol antibody competitively. We achieved a broad linear detection range of up to 3.24 ng/mL and a high concentration resolution of 33.20 pg/mL. To further validate the universality of our proposed detection methodology, we successfully applied it to testing gibberellin and tetracycline. Moreover, we conducted regeneration experiments and real-sample correlation studies. This study introduces a novel strategy for the label-free optical sensing of small molecule antibiotics, greatly expanding the range of applications for sensors utilizing optical weak value amplification. • The sensor utilizes optical weak value amplification. • The label-free sensor enables real-time monitoring. • Indirect competitive inhibition assay enhances the sensitivity to low signals. • The sensor achieves a chloramphenicol concentration resolution of 33.20 pg/mL. • The sensing scheme is both universal and highly selective. [ABSTRACT FROM AUTHOR]

In quantum metrology, the famous result of Heisenberg limit, scaling as 1 / N (with N the number of probes), can be surpassed by considering nonlinear coupling measurement. In this work, we consider the most practice-relevant quadratic nonlinear coupling and show that the metrological precision can be enhanced from the 1 / N 3 2 super-Heisenberg scaling to 1 / N 2 , by simply employing a pre- and post-selection (PPS) strategy, but not using any expensive quantum resources such as quantum entangled state of probes. • Post-selection and nonlinear coupling probe were analyzed for parameter estimation. • Super-Heisenberg scaling was enhanced from 1 / N 3 / 2 to 1 / N 2 by means of the post-selection technique. • Unexpected result that the weak-value-amplification scheme can intrinsically outperform the conventional measurement was uncovered. • Detailed numerical results were carried out and comprehensive understandings were presented. [ABSTRACT FROM AUTHOR]

Elliptic curves are planar curves which can be used to define an abelian group. The computation of this group's addition operation, as well as related operations such as the discrete logarithm, could be performed on quantum computing devices, potentially leading to better performance. Currently, however, thousands of logical qubits are required for elliptic curve group addition, putting this application out of reach for near-term quantum hardware. Here we give an algorithm for computing elliptic curve group addition (over the real numbers) using a single continuous-variable mode, based on weak measurements of a system with a cubic potential energy. This result could lead to improvements in the efficiency of elliptic curve operations using a quantum device. • Encoding elliptic curves in discrete-variable quantum systems requires thousands of qubits. • An elliptic curve (over the reals) can be encoded in a single continuous-variable mode. • The group operation on elliptic curve points can be estimated using weak measurements. • This is a novel kind of quantum algorithm taking advantage of the geometry of the Wigner function. [ABSTRACT FROM AUTHOR]

The continued interest in placing bounds on the neutron's Electric Dipole Moment (EDM) is due to the implications regarding the characteristics of the strong interaction and, in particular, its behavior under the CP symmetry. In this work, we discuss the apparent tension resulting from the discrepancy of about 13 orders of magnitude between the current bounds and the expected quantum uncertainty in the relevant quantity. We offer a resolution of the "puzzle" in terms of the notion of a weak measurement, using a version of the corresponding formalism adapted to consideration of the nEDM experiment at the Spallation Neutron Source at the Oak Ridge National Laboratory. • The main focus of our article is the compatibility of basic aspects of quantum theory with actual practice. • The paper presents a situation that seems paradoxical at first but is carefully analyzed to show there is no conflict with quantum theory. • We mentioned some possible paths to study BSM sources of CP violation leading to an observable nEDM. [ABSTRACT FROM AUTHOR]

Quantum correlation is a key resource for a variety of quantum information processing and communication tasks, the efficient utilization of which has been a longstanding concern, and it is also one of the main challenges in the application of quantum technology. In this review, we focus on the interaction between quantum measurements and quantum correlations by designing appropriate measurement strategies, specifically exploring the trade-off between information gain and disturbance degree in weak measurements to ensure that quantum correlations from the same source can be shared among multiple independent observers. We introduce the basic knowledge and classification of quantum measurements, investigate the weak measurement scenario, and show the theoretical model construction of quantum correlation recycling in the original works. We summarize the theoretical and experimental development process and the latest progress in this field. Finally, we provide an outlook for more quantum resource applications that can profit from the optimization of quantum measurement strategies.

We propose a high-resolution scheme for determining the kinetic parameters of sucrose hydrolysis based on the weak measurement, and the parameters including rate constant, half-life, activation energy and pre-exponential factor are experimentally determined. In the scheme, the postselection state of weak measurement is modified by the optical rotation angle in the process of sucrose hydrolysis, and the amplified spin-Hall shift acts as a probe for determining the kinetic parameters. The rate constant and half-life are obtained based on the time variations of amplified spin-Hall shifts under different reaction conditions of temperatures and hydrochloric acid concentrations. The corresponding activation energy and pre-exponential factor are also evaluated for explaining the physical mechanism which influences the rate constant and analyzing how to adjust the reaction conditions to predict or control the rate. The high resolution for optical rotation angle is achieved in our scheme, which can reach ${\rm {4}}{\rm {.9}} \times {\rm {10}}^{\rm {-4}}$ degree with one order of magnitude improvement over the polarimeter. These results can provide a possibility for the determination of chemical kinetic parameters with high-precision, real-time, label-free and convenient effects.

Due to the coupling with the noisy environment, the quantum state in the target quantum communication system will undergo decoherence and reduce the fidelity. To diminish the noise effect, we utilized weak measurement (WM) and weak measurement reversal (MWR) to enhance the fidelity of controlled quantum teleportation (CQT). The CQT protocol was first proposed, in which Alice prepared an eight-qubit entangled state as a quantum channel. With controller Bob’s permission, an arbitrary two-qubit state can be transmitted to Charlie. Then We extend the CQT protocol for an arbitrary two-qubit state to an unknown 2N-qubit state. Then we separately analyzed that the two CQT protocols process were influenced by amplitude damping (AD) noise, leading to an inevitable reduction in its fidelity. In both cases, WM and WMR operations respectively were performed before and after undergoing the noise channel. Our results showed that the fidelity of transmitting the two-qubit state with two measurement operations is improved, which can hold true in the entire evolutionary field. However, when N is greater than 1, the fidelity of transmitting the 2N-qubit state does not always increase with WM and WMR operations but will be lower than without those operations in a certain value range of noise factor and weak measurement strength. [ABSTRACT FROM AUTHOR]

In this paper, the technique of weak measurement is employed in order to enhance the fidelity of joint remote state preparation (JRSP) protocol under decoherence. We design a quantum circuit of joint remote preparation of a single-qubit state through a GHZ state. Then, we analytically derive the average fidelity of the JRSP protocol under four types of noise usually encountered in real-world implementations of quantum communication protocols, i.e. the phase-flip, depolarizing, amplitude-damping and bit-flip noise. Our study shows that the application of weak measurement and measurement reversal could enhance the average fidelity of the JRSP process under the influence of phase-flip, depolarizing, amplitude-damping noise for most values of the decoherence parameters. If the JRSP process suffers from the bit-flip noise, the weak measurement technique is not useful for increasing the average fidelity. [ABSTRACT FROM AUTHOR]

High-dimensional quantum communication plays an important role in long-distance quantum communication. It is shown that two-qubit quantum entanglement can be protected from amplitude damping decoherence. We study the effect of amplitude damping decoherence on two-qubit high-dimensional quantum entanglement. The negativity for high-dimensional quantum entanglement with or without quantum weak measurement and the reversal in amplitude damping decoherence are presented. We found that nonmaximally entangled state may have better performance than maximally entangled state in amplitude damping decoherence. Moreover, we show that arbitrary high-dimensional quantum entanglement can be protected from amplitude damping decoherence by weak measurement and the reversal. The results of our protocol are in agreement with previous analysis for the case of qubits and qutrits. [ABSTRACT FROM AUTHOR]

The problem of combating de-coherence by weak measurements has already been studied for the amplitude damping channel and for specific input states. We generalize this to a large four-parameter family of qubit channels and for the average fidelity over all pure states. As a by-product we classify all the qubit channels which have one invariant pure state and show that the parameter manifold of these channels is isomorphic to S 2 Ă— S 1 Ă— S 1 and contains many interesting sub-classes of channels. By tuning the parameter of the weak measurement, we show that it is possible to increase the average inputâ€"output fidelity without blocking too many particles to pass through the channel. Quantitative analysis reveals that the increase of average fidelity can be up to 0.3, by blocking less than half of the particles. [ABSTRACT FROM AUTHOR]

One of the crucial tasks in quantum systems is to reduce the effects of decoherence due to the unavoidable interactions between a system and its environment. Many protection schemes have been proposed recently, among them the weak measurement quantum measurement reversal (WMQMR), weak measurement-based quantum feedback control (QFBC) and quantum feedforward control (QFFC) are reviewed in this paper. By considering weak measurement, the aim is to find a balance between information gain and disturbance of the system caused by the measurement. We classify different types of measurement and give the definition of noise sources and their effects on the state of the system. Finally, we compare and analyze the performance of the discussed protection schemes for different noise sources by numerical simulations. [ABSTRACT FROM AUTHOR]

This study addresses the critical need for high purity chiral molecules in biological systems by overcoming the challenges associated with the quantitative detection of chiral molecules and their enantiomeric mixtures. We developed an innovative detection approach that leverages the two-dimensional information gleaned from natural optical rotation (NOR) and Faraday optical rotation (FOR) under magnetic fields in chiral molecules, combined with an ultrahigh-resolution weak measurement sensor. This novel weak measurement system achieves unparalleled accuracy in detecting spin angles, with a precision of 1.86 × 10−5°. Notably, our method introduces no chemical reactions or interference with the substances under test. It offers enhanced discrimination capabilities through the dual-dimensional analysis of both natural and Faraday optical rotation, alongside a simple and compact sensor design. Conclusively, our study introduces a novel, high-precision, and multi-dimensional optical detection paradigm for chiral molecules. By incorporating Faraday rotation in the presence of a magnetic field, we expand the informational dimensionality accessible to the original weak measurement sensor, facilitating the quantitative analysis of chiral molecules and their enantiomers. This breakthrough not only furnishes a novel instrument for the exploration and development of chiral pharmaceuticals but also propels the advancement of weak measurement sensing technology forward. This study introduces a novel detection system that utilizes both natural and Faraday optical rotations under magnetic fields to accurately and quantitatively detect chiral molecules, achieving an unprecedented precision of 1.86 × 10−5° without chemical interference. [Display omitted] • Developed a novel chiral molecule detection system combining NOR and FOR under magnetic fields for enhanced accuracy. • Achieved detection precision of 1.86×10⁻⁵° without chemical reactants, preserving substance integrity. • Compact sensor design simplifies use in pharmaceutical and biochemical labs. • Offers a powerful tool for precise synthesis and analysis of chiral drugs, impacting drug purity testing. • Advances weak measurement technology by adapting it for multi-dimensional data, setting a new standard. [ABSTRACT FROM AUTHOR]

From the perspective of quantum information transmission, one may be interested in the teleportation of quantum Fisher information (QFI) which provides the optimal precision of parameter estimation. In this paper, we investigate the teleportation of QFI under the correlated amplitude damping (CAD) decoherence. It is found that the correlated effects play a positive role in improving the teleported QFI, but the impact of decoherence is still serious. Therefore, we propose two schemes, which are based on weak measurement (WM) and environment-assisted measurement (EAM), to enhance the teleportation of QFI under the CAD decoherence. The results show that both schemes can significantly improve the teleported QFI with a certain success probability. The findings of our study suggest that the correlated effects can significantly increase the success probabilities of these two schemes. A detailed comparison confirms that the EAM scheme is more efficient than the WM scheme in improving the teleportation of QFI.

A high-sensitivity detection method is proposed for ethanol concentration based on weak measurement system with Faraday effect, and the improvement law of the sensitivity is studied. Different from chiral solution determination, the post-selection angle of the system is modified by the Faraday rotation angle of ethanol solution. The amplified photonic spin Hall effect acts as a probe for detecting the ethanol concentration in the system, and the sensitivity of ethanol concentration increases linearly with the increasing magnetic field intensity. Then we use the method to determine the ethanol concentration of commercial liquor, whose determination values are consistent with the label values and Raman spectroscopy results. Compared to other methods such as Raman spectrometry, the method has the advantages of real time, non-invasiveness, low cost and high sensitivity. Finally, the sensitivity of ethanol concentration can be further improved by designing of a suitable BK7-medium structure, and the sensitivity of 9.72 /vol% is achievable for the range 0 vol% ∼100 vol% of ethanol solutions. • We propose a new method for the highly sensitive detection of ethanol solution based on weak measurement with Faraday effect. • We establish a quantitative relationship between PSHE and ethanol concentration, and determine the ethanol content of commercial liquor. • The method provides a new way for the detection of achiral molecular solutions. [ABSTRACT FROM AUTHOR]

Weak-value amplification (WVA) is a metrological protocol that effectively amplifies ultra-small physical effects, making it highly applicable in the fields of quantum sensing and metrology. However, the amplification effect is achieved through post-selection, which leads to a significant decrease in signal intensity. Consequently, there is a heated debate regarding the trade-off between the amplification effect and the success probability of post-selection, questioning whether WVA surpasses conventional measurement (CM) in terms of measurement precision. Extensive research indicates that the specific theoretical assumptions and experimental conditions play crucial roles in determining the respective advantages of WVA and CM. WVA provides new perspectives for recognizing the important role of post-selection in precision metrology. It demonstrates significant advantages in two aspects: (i) WVA based on the phase space interaction provides feasible strategies to practically achieve the Heisenberg-scaling precision using only classical resources. (ii) WVA exhibits robustness against certain types of technical noise and imperfections of detectors. Moreover, WVA allows for various modifications to extend the applicable scope and enhance the metrological performance in corresponding situations. Despite substantial progress in recent years, the inherent connection between the advantages of WVA and its unique features remains incompletely understood. In this paper, we systematically review the recent advances in the WVA scheme, with a particular focus on the ultimate precision of WVA under diverse conditions. Our objective is to provide a comprehensive perspective on the benefits of WVA in precision measurement and facilitate the realization of its full potential. [ABSTRACT FROM AUTHOR]

Noiseless quantum channels are critical to share a pure maximally entangled state for performing an ideal teleportation protocol. However, in reality the shared entanglement severely degraded due to decoherence. In this paper, we propose a quantum teleportation channel protection scheme to enhance the teleportation fidelity in presence of decoherence. Before the entangled pair enters the decoherence channel, the weak measurement and flip operations are applied to transfer the qubit to a more robust state to the effects of the noise. After the decoherence channel the reversed flip operations and weak measurement reversal are applied to recover the initial state. We illustrate our protected teleportation scheme and compare it with a protocol based on weak measurement reversal. The numerical results show that the average teleportation fidelity of our proposed scheme can be significantly improved. Although the proposed entanglement protection scheme is probabilistic, after a successful entanglement transmission, we use the standard teleportation protocol which has probability one. [ABSTRACT FROM AUTHOR]

In this paper, we propose a quantum state recovery scheme based on environment assisted measurement with weak measurements and flip operations. Before the decoherence channel the weak measurement and flip operators are applied to gain some information about the state of the system and transfer it to a more robust state. Then we utilize environment assisted measurement and post-flip operations to bring the system as close as possible to its initial state. We illustrate our scheme and compare it with a scheme based on environment assisted measurement and weak measurement reversal in the case of a decoherence channel. We show that the success probability of our proposed scheme is significantly improved for all initial states. The proposed scheme is applicable for recovery of N-qubit state from any type of decoherence with at least one invertible Kraus operator. Also, the explicit formula of total fidelity and success probability for recovery of N-qubit GHZ state are derived. [ABSTRACT FROM AUTHOR]

The dynamical behaviour of quantum correlations captured by different forms of Measurement-Induced Nonlocality (MIN) between two atoms coupled with thermal reservoirs is investigated and compared with the entanglement. It is shown that the MIN quantities are more robust, while noise causes sudden death in entanglement. Further, we quantified the quantum correlation with weak measurement and the effect of measurement strength is observed. The role of mean photon number and weak measurements on quantum correlation is also highlighted. [ABSTRACT FROM AUTHOR]

We first put forward a scheme to teleport circularly arbitrary single-qubit states in a noise quantum channel. In our scheme, each sender preforms local nondemolition parity analysis based on cross-Kerr nonlinearities and publicizes the achieved outcome; the nearby receiver executes appropriate Pauli operation on his/her own qubit to obtain the original state. Due to the implementation of nondemolition parity analysis rather than Bell state measurement, the resource of Bell state can be achieved and applied to other potential tasks of quantum information processing. Further, we discuss the influence of quantum noise by the example of an amplitude damping channel and obtain the fidelity of the cyclic teleportation. Finally, we use the weak measurement and the corresponding reversing measurement to protect the quantum entanglement, which shows an effective enhancement of the cyclic teleportation fidelity. [ABSTRACT FROM AUTHOR]

Quantum teleportation as a key protocol for quantum communication and quantum computing demonstrates the stark difference between quantum and classical information transmission. An ideal teleportation protocol requires pure maximally entangled state as the teleportation channel, while in real implementations the shared entanglement is severely degraded due to decoherence. In this letter, we propose a scheme to protect the quantum teleportation from decoherence by means of environment assisted measurement with weak measurements and flip operations. We show that the teleportation fidelity of our proposed scheme is significantly improved compared to teleportation with no protection and a teleportation protocol based on quantum measurement reversal. Also, the explicit formula of average teleportation fidelity and success probability of the entanglement protection are derived. [ABSTRACT FROM AUTHOR]

An effective approach for general measurement based on weak value amplification using non-Gaussian broadband light sources is demonstrated. This scheme can reduce the difficulty of preparing the measurement apparatus and correcting the systematic error caused by the imperfection of device's wave function, thus making the weak-value amplification scheme more convenient and robust for practical field applications. The influence of several common noise sources in a general application based on weak value amplification is analyzed theoretically and examined experimentally. A purely imaginary weak-value phase measurement system is considered for the noise model verification experimentally. In this we show how to optimize the precision of measurement in a unique solution that takes into account the interplay between precision and uncertainty, and explicate the ramifications of such a compromising and pragmatic approach.

In this study, a method to improve the detection accuracy of a “weak measurement” system of optical rotation was proposed by determining the optimal total phase difference of the system. Analysis of the characteristics of weak measurement regime of the system under different total phase differences provided the total phase difference corresponding to the regime with the smallest ratio of system noise level to sensitivity (that is, the highest system resolution). In this regime, an optical rotation resolution of 5.522 × 10−6° was obtained, which is nearly an order of magnitude higher than the original system.

Chiroptical signals (generally very weak) play significant roles in chiral discrimination that bring great benefits in biochemistry, pharmacy, chemical, and so on. But, high-precise chiroptical detection is still a challenge. In this paper, a high-precise measurement of optical rotatory dispersion (ORD) based on weak value amplification (WVA) is presented. We proposed ORD detection method with parameter separation: by introducing complex coupling strength and dimensionless parameter “intensitiy contrast ratio” pointer, the ORD is only associated with the imaginary part of the weak value while circular dichroism (CD) is only associated with the real part. By designing a suitable WVA scheme, the ORD and CD can be measured separately. In the experiment, the reliability of the parameter separation method for ORD measurement is verified, and the precision reach the order of $10^{-6}$ rad. This method has a broad application prospect in biomedical sensing, medicine, chemical analysis and other fields.