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.

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.

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.

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.

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.

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.

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.

Effect of weak measurement on quantum correlations

We investigate the local quantum uncertainty(LQU)in weak measurement.An expression of weak LQU is explicitly determined.Also,we consider some cases of three special X states,Werner state,circulant two-qubit states,and Heisenberg model via LQU in normal and weak measurements.We find that the LQU in weak measurement is weaker than the case of strong measurement.

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.

Statistical Mechanics for Weak Measurements and Quantum Inseparability

In weak measurement thought experiment, an ensemble consists of M quantum particles and N states. We observe that separability of the particles is lost, and hence we have fuzzy occupation numbers for the particles in the ensemble. Without sharply measuring each particle state, quantum interferences add extra possible configurations of the ensemble, this explains the Quantum Pigeonhole Principle. This principle adds more entropy to the system;hence the particles seem to have a new kind of correlations emergent from particles not having a single, well-defined state. We formulated the Quantum Pigeonhole Principle in the language of abstract Hilbert spaces, then generalized it to systems consisting of mixed states. This insight into the fundamentals of quantum statistical mechanics could help us understand the interpretation of quantum mechanics more deeply, and possibly have implication on quantum computing and information theory.

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.

Observation of tiny polarization rotation rate in total internal reflection via weak measurements

In this paper,we examine the tiny polarization rotation effect in total internal reflection due to the spin–orbit interaction of light.We find that the tiny polarization rotation rate will induce a geometric phase gradient,which can be regarded as the physical origin of photonic spin Hall effect.We demonstrate that the spin-dependent splitting in position space is related to the polarization rotation in momentum space,while the spin-dependent splitting in momentum space is attributed to the polarization rotation in position space.Furthermore,we introduce a quantum weak measurement to determine the tiny polarization rotation rate.The rotation rate in momentum space is obtained with 118 nm,which manifests itself as a spatial shift,and the rotation rate in position space is achieved with 38 μrad∕λ,which manifests itself as an angular shift.The investigation of the polarization rotation characteristics will provide insights into the photonic spin Hall effect and will enable us to better understand the spin–orbit interaction of light.

Measuring the temperature of the spin via weak measurement

In this study,we give a new proposal to measure the temperature of the spin in a sample in a magnetic resonance force microscopy system by using postselected weak measurement,and investigating the Fisher information to estimate the precision of the scheme.We show that in a high temperature regime the temperature of the spin can be measured via a weak measurement technique with proper postselection and our scheme is able to increase the precision of temperature estimation.

Ultrasensitive Protein Concentration Characterization Based on Weak Measurements

An optical rotation bio-sensor based on the photonic spin Hall effect was established and applied to detecting the concentration varieties of chiral molecules.The optical rotation,introduced by sample solutions,was exploited to modulate the postselected polarization of a weak measurement system.Much work has been done in the case of glucose and fructose.However,little attention has been paid for biomolecules,such as proteins and amino acids.With this modulation,the optical rotation can be determined through the direction and spin accumulation of light spots,thus mirroring the concentration of solutions.A resolution of 2×10^(-4) degree was achieved.

Determination of the focused beam waist of lasers with weak measurements

In this Letter, a method for detecting the focused beam waist of lasers is proposed by using weak measurements based on the so-called weak-value amplification. We establish a propagation model to describe the quantitative relation between the beam waist and the amplified shift of the spin Hall effect of light(SHEL), which is sensitive to the variation of the beam waist. We experimentally measure the amplified shift corresponding to a different beam waist and the experimental data agrees well with theoretical calculation. These results confirm the rationality and feasibility of our method.

Temporally Modulated Phase Retrieval Method for Weak Temporal Phase Measurement of Laser Pulses

We propose a simple iterative algorithm based on a temporally movable phase modulation process to retrieve the weak temporal phase of laser pulses. This unambiguous method can be used to achieve a high accuracy and to simultaneously measure the weak temporal phase and temporal profile of pulses, which are almost transform- limited. A detailed analysis shows that this iterative method has valuable potential applications in the charac- terization of pulses with weak temporal phase.