Measuring small longitudinal phase shifts via weak measurement amplification

Weak measurement amplification,which is considered as a very promising scheme in precision measurement,has been applied to various small physical quantities estimations.Since many physical quantities can be converted into phase signals,it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement.Here,we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation,which is suitable for polarization interferometry.We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference.Besides,we analyze the effect of magnification error which is never considered in the previous works,and find the constraint on the magnification.Our results may find important applications in high-precision measurements,e.g.,gravitational wave detection.

Design of weak current measurement system and research on temperature impact

A dedicated weak current measurement system was designed to measure the weak currents generated by the neutron ionization chamber.This system incorporates a second-order low-pass filter circuit and the Kalman filtering algorithm to effectively filter out noise and minimize interference in the measurement results.Testing conducted under normal temperature conditions has demonstrated the system's high precision performance.However,it was observed that temperature variations can affect the measurement performance.Data were collected across temperatures ranging from -20 to 70℃,and a temperature correction model was established through linear regression fitting to address this issue.The feasibility of the temperature correction model was confirmed at temperatures of -5 and 40℃,where relative errors remained below 0.1% after applying the temperature correction.The research indicates that the designed measurement system exhibits excellent temperature adaptability and high precision,making it particularly suitable for measuring weak currents.

Protected simultaneous quantum remote state preparation scheme by weak and reversal measurements in noisy environments

We discuss a quantum remote state preparation protocol by which two parties, Alice and Candy, prepare a single-qubit and a two-qubit state, respectively, at the site of the receiver Bob. The single-qubit state is known to Alice while the two-qubit state which is a non-maximally entangled Bell state is known to Candy. The three parties are connected through a single entangled state which acts as a quantum channel. We first describe the protocol in the ideal case when the entangled channel under use is in a pure state. After that, we consider the effect of amplitude damping(AD) noise on the quantum channel and describe the protocol executed through the noisy channel. The decrement of the fidelity is shown to occur with the increment in the noise parameter. This is shown by numerical computation in specific examples of the states to be created. Finally, we show that it is possible to maintain the label of fidelity to some extent and hence to decrease the effect of noise by the application of weak and reversal measurements. We also present a scheme for the generation of the five-qubit entangled resource which we require as a quantum channel. The generation scheme is run on the IBMQ platform.

Precise measurement of a weak radio frequency electric field using a resonant atomic probe

We present a precise measurement of a weak radio frequency electric field with a frequency of ■3 GHz employing a resonant atomic probe that is constituted with a Rydberg cascade three-level atom, including a cesium ground state |6S(1/2)〉,an excited state |6P(3/2)〉, and Rydberg state |nD(5/2)〉. Two radio frequency(RF) electric fields, noted as local and signal fields, couple the nearby Rydberg transition. The two-photon resonant Rydberg electromagnetically induced transparency(Rydberg-EIT) is employed to directly read out the weak signal field having hundreds of k Hz difference between the local and signal fields that is encoded in the resonant microwave-dressed Rydberg atoms. The minimum detectable signal fields of ESmin= 1.36 ± 0.04 mV/m for 2.18 GHz coupling |68D(5/2)〉→ |69P(3/2)〉 transition and 1.33 ± 0.02 mV/m for 1.32 GHz coupling |80D(5/2)〉→ |81P(3/2)〉 transition are obtained, respectively. The bandwidth dependence is also investigated by varying the signal field frequency and corresponding -3 dB bandwidth of 3 MHz is attained. This method can be employed to perform a rapid and precise measurement of the weak electric field, which is important for the atom-based microwave metrology.

Bidirectional multi-qubit quantum teleportation in noisy channel aided with weak measurement

Recently,bidirectional quantum teleportation has attracted a great deal of research attention.However,existing bidirectional teleportation schemes are normally discussed on the basis of perfect quantum environments.In this paper,we first put forward a bidirectional teleportation scheme to transport three-qubit Greenberger-Horne-Zeilinger（GHZ） states based on controled-not（CNOT） operation and single-qubit measurement.Then,we generalize it to the teleportation of multi-qubit GHZ states.Further,we discuss the influence of quantum noise on our scheme by the example of an amplitude damping channel,then we obtain the fidelity of the teleportation.Finally,we utilize the weak measurement and the corresponding reversing measurement to protect the quantum entanglement,which shows an effective enhancement of the teleportation fidelity.

Preserving entanglement and the fidelity of three-qubit quantum states undergoing decoherence using weak measurement

We demonstrate a method to preserve entanglement and improve fidelity of three-qubit quantum states undergoing amplitude-damping decoherence using weak measurement and quantum measurement reversal. It is shown that we are able to enhance entanglement to the greatest extent, and to circumvent entanglement sudden death by increasing the weak measurement strength both for the GHZ state and the W state. The weak measurement technique can also enhance the fidelity to the quantum region and even close to 1 for the whole range of the decoherence parameter in both of the two cases. In addition, the W state can maintain more fidelity than the GHZ state in the protection protocol. However, the GHZ state has a higher success probability than the W state.

Decoherence suppression for three-qubit W-like state using weak measurement and iteration method

Multi-qubit entanglement states are the key resources for various multipartite quantum communication tasks. For a class of generalized three-qubit quantum entanglement, W-like state, we demonstrate that the weak measurement and the reversal measurement are capable of suppressing the amplitude damping decoherence by reducing the initial damping factor into a smaller equivalent damping factor. Furthermore, we propose an iteration method in the weak measurement and the reversal measurement to enhance the success probability of the total measurements. Finally, we discuss how the number of the iterations influences the overall effect of decoherence suppression, and find that the ＂half iteration＂ method is a better option that has more practical value.

Reflectivity Measurement of Weak Fiber Bragg Grating (FBG)

One method based on the end-face reflection as a reference was used to measure weak grating reflectivity of 0.01%-1%. For measuring ultra-weak grating reflectivity, the grating group with an identical wavelength was used. By using anhydrous alcohol and deionized water as the reflecting medium, the single- pulse FBG reflectivity of a highly doped-Ge photosensitive fiber was calculated to be about 0.747% and 0.739%, respectively; and the single-pulse FBG reflectivity of ordinary SMF fiber was about 0.016% and 0.015%, respectively. The consistent results by the two different reflecting media showed that the end-face reflection method on the grating group was feasible.

Optimizing quantum correlation dynamics by weak measurement in dissipative environment

We investigate the protection of quantum correlations of two qubits in independent vacuum reservoirs by means of weak measurements. It is found that the weak measurement can reduce the amount of quantum correlation for one type of initial state at the beginning in a non-Markovian environment and meanwhile it can reduce the occurrence time of entanglement sudden death （ESD） in the process of time evolution. In a Markovian environment, the quantum entanglements of the two kinds of initial states decay rapidly and the weak measurement can further weaken the quantum entanglement, therefore in this case the entanglement cannot be optimized in the evolution process.

Protecting the entanglement of two-qubit over quantum channels with memory via weak measurement and quantum measurement reversal

Based on the quantum technique of the weak measurement and quantum measurement reversal(WMR),we propose a scheme to protect entanglement for an entangled two-qubit pure state from four typical quantum noise channels with memory,i.e.,the amplitude damping channel,the phase damping channel,the bit flip channel,and the depolarizing channel.For a given initial state |Ψ>=a |00>+d|11>,it is found that the WMR operation indeed helps to protect entanglement from the above four quantum channels with memory,and the protection effect of WMR scheme is better when the coefficient a is small.For the other initial state |φ>=b|01>+c|10>,the effect of the protection scheme is the same regardless of the coefficient b and the WMR operation can protect entanglement in the amplitude damping channel with memory.Moreover,the protection of entanglement in quantum noise channels without memory in contrast to the results of the channels with memory is more effective.For |Ψ> or |φ>,we also find that the memory parameters play a significant role in the suppression of entanglement sudden death and the initial entanglement can be drastically amplified.Another more important result is that the relationship between the concurrence,the memory parameter,the weak measurement strength,and quantum measurement reversal strength is found through calculation and discussion.It provides a strong basis for the system to maintain maximum entanglement in the nosie channel.

Extended validity of weak measurement

We introduce a modified weak value that is related to the mean value of input meter variable.With the help of the modified weak value,the validity conditions for various modified versions of weak value formalism are investigated,in terms of the dependence of the pointer shift on the mean value of the input meter.The weak value formalism,often used to represent the pointer shift,with the modified weak value is of great use in simplifying calculations and giving guidance of practical experiments whenever the mean value of the input meter variable is nonzero.The simulation in a qubit system is presented and coincident well with our theoretical result.

Dense coding capacity in correlated noisy channels with weak measurement

Capacity of dense coding via correlated noisy channel is greater than that via uncorrelated noisy channel.It is shown that the weak measurement and reversal measurement need to further improve their quantum dense coding capacity in correlated amplitude damping channel,but this improvement is very small in correlated phase damping channel and correlated depolarizing channel.

Entropy squeezing for a V-type three-level atom interacting with a single-mode field and passing through the amplitude damping channel with weak measurement

The entropy squeezing of a V-type three-level atom interacting with a single-mode field and passing through the amplitude damping channel is investigated in detail. Our results show that when coupled to the single-mode field, the atom in appropriate initial states can not only generate obvious entropy squeezing but also keep in the optimal squeezing state,while passing through the amplitude damping channel, the atom can generate entropy squeezing under the control of the weak measurement. Besides, it is proved again that as a measurement method for atomic squeezing, the entropy squeezing is precise and effective. Therefore our work is instructive for experiments in preparing three-level system information resource with ultra-low quantum noise.

Reversion of weak-measured quantum entanglement state

We theoretically study the reversible process of quantum entanglement state by means of weak measurement and corresponding reversible operation.We present a protocol of the reversion operation in two bodies based on the theory of reversion of single photon and then expend it in quantum communication channels.The theoretical results demonstrate that the protocol does not break the information transmission after a weak measurement and a reversible measurement with the subsequent process in the transmission path.It can reverse the perturbed entanglement intensity evolution to its original state.Under the condition of different weak measurement intensity the protocol can reverse the perturbed quantum entanglement system perfectly.In the process we can get the classical information described by information gain from the quantum system through weak measurement operation.On the other hand,in order to realize complete reversibility,the classical information of the quantum entanglement system must obey a limited range we present in this paper in the reverse process.

WEAK LIMITS OF EMPIRICAL MEASURES FOR A FAMILY OF DIFFUSION PROCESSES

This paper considers diffusion processes {X^(?)(t)} on R^2, which are perturbations of dynamical system {X(t)} (dX(t)=b(X(t))dt) on R^2. By means of weak convergence of probability measures, the authors characterize the limit behavior for empirical measures of {X^(?)(t)} in a neighborhood domain of saddle point of the dynamical system as the perturbations tend to zero.

Enhancing the precision of phase estimation by weak measurement and quantum measurement reversal

The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement （WM） and quantum measurement reversal （QMR）. We derive the exact expressions of the optimal quantum Fisher information （QFI） and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.

Dynamics of super-quantum discord and direct control with weak measurement in open quantum system

Super-quantum discord（SQD） with weak measurement is regarded as a kind of quantum correlation in quantum information processing. We compare and analyze the dynamical evolutions of SQD, quantum discord（QD）, and quantum entanglement（QE） between two qubits in the correlated dephasing environmental model. The results indicate that（i） owing to the much smaller influence of weak measurement on the coherence of the system than that of von Neumann projection measurement, SQD with weak measurement is larger than QD, and（ii） dynamical evolution of QD or QE monotonically goes to zero with time, while SQD monotonically tends to a stable value and a freezing phenomenon occurs. The stable value after freezing mainly depends on the measurement strength and the purity of the initial quantum state.

MEASURES OF WEAK NONCOMPACTNESS AND FIXED POINT THEORY FOR 1-SET WEAKLY CONTRACTIVE OPERATORS ON UNBOUNDED DOMAINS

The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F（x） = αx （α≥〉 1） for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for the nonlinear operator equation F（x） = αx （α≥1） for such class of operators. As consequences, the main results general- ize and improve the relevant results, which are obtained by O＇Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive （μ-nonexpansive） and weakly semi-closed operators at the origin and their generalizations. The main condition in our results is formulated in terms of axiomatic measures of weak compactness.

Implementation of nonlocal Bell-state measurement and quantum information transfer with weak Kerr nonlinearity

We propose a protocol to implement the nonlocal Bell-state measurement, which is nearly determinate with the help of weak cross-Kerr nonlinearities and quantum non-destructive photon number resolving detection. Based on the nonlocal Bell-state measurement, we implement the quantum information transfer from one place to another. The process is different from conventional teleportation but can be regarded as a novel form of teleportation without entangled channel and classic communication.

Atom interferometers with weak-measurement path detectors and their quantum mechanical analysis

According to the orthodox interpretation of quantum physics, wave-particle duality(WPD) is the intrinsic property of all massive microscopic particles. All gedanken or realistic experiments based on atom interferometers(AI) have so far upheld the principle of WPD, either by the mechanism of the Heisenberg’s position-momentum uncertainty relation or by quantum entanglement. In this paper, we propose and make a systematic quantum mechanical analysis of several schemes of weak-measurement atom interferometer(WM-AI) and compare them with the historical schemes of strongmeasurement atom interferometer(SM-AI), such as Einstein’s recoiling slit and Feynman’s light microscope. As the critical part of these WM-AI setups, a weak-measurement path detector(WM-PD) deliberately interacting with the atomic internal electronic quantum states is designed and used to probe the which-path information of the atom, while only inducing negligible perturbation of the atomic center-of-mass motion. Another instrument that is used to directly interact with the atomic center-of-mass while being insensitive to the internal electronic quantum states is used to monitor the atomic centerof-mass interference pattern. Two typical schemes of WM-PD are considered. The first is the micromaser-cavity path detector, which allows us to probe the spontaneously emitted microwave photon from the incoming Rydberg atom in its excited electronic state and record unanimously the which-path information of the atom. The second is the optical-lattice Bragg-grating path detector, which can split the incoming atom beam into two different directions as determined by the internal electronic state and thus encode the which-path information of the atom into the internal states of the atom. We have used standard quantum mechanics to analyze the evolution of the atomic center-of-mass and internal electronic state wave function by directly solving Schr¨odinger’s equation for the composite atom-electron-photon system in these WM-AIs. We have also compared our analysis with the theoretical and experimental studies that have been presented in the previous literature. The results show that the two sets of instruments can work separately, collectively, and without mutual exclusion to enable simultaneous observation of both wave and particle nature of the atoms to a much higher level than the historical SM-AIs, while avoiding degradation from Heisenberg’s uncertainty relation and quantum entanglement. We have further investigated the space–time evolution of the internal electronic quantum state, as well as the combined atom–detector system and identified the microscopic origin and role of quantum entanglement, as emphasized in numerous previous studies. Based on these physics insights and theoretical analyses, we have proposed several new WM-AI schemes that can help to elucidate the puzzling physics of the WPD of the atoms. The principle of WM-AI scheme and quantum mechanical analyses made in this work can be directly extended to examine the principle of WPD for other massive particles.