Post-selected States Research Articles

Compression of metrological quantum information in the presence of noise

In quantum metrology, information about unknown parameters θ=(θ1,...,θM) is accessed by measuring probe states ρ̂θ. In experimental settings where copies of ρ̂θ can be produced rapidly (e.g., in optics), the information-extraction bottleneck can stem from high postprocessing costs or detector saturation. In these regimes, it is desirable to compress the information encoded in ρ̂θ⊗n into m<n copies of a postselected state: ρ̂θps⊗m. Remarkably, recent works have shown that, in the absence of noise, compression can be lossless, for m/n arbitrarily small. Here, we fully characterize the family of filters that enable lossless compression. Further, we study the effect of noise on quantum-metrological information amplification. Motivated by experiments, we consider a popular family of filters, which we show is optimal for qubit probes. Further, we show that, for the optimal filter in this family, compression is still lossless if noise acts after the filter. However, in the presence of depolarizing noise before filtering, compression is lossy. In both cases, information extraction can be implemented significantly better than simply discarding a constant fraction of the states, even in the presence of strong noise. Published by the American Physical Society 2024

Weak Value Amplification Based Optical Sensor for High Throughput Real-Time Immunoassay of SARS-CoV-2 Spike Protein.

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.

Phase and amplitude reconstruction by weak measurement based on metasurface

Phase distribution is crucial for obtaining the whole information of phase object in imaging. However, due to the transparency of phase objects, the phase distribution cannot be obtained in traditional bright-field imaging. Here, we propose a phase distribution reconstruction based on the imaginary value of weak measurement, which is achieved by a Pancharatnam–Berry phase metasurface. Moreover, by adjusting the weak value to a real weak value, amplitude reconstruction can also be achieved. Different parts of weak values can be obtained by controlling the preselection and postselection states. The weak interaction is achieved by the metasurface, which is convenient to control the weak coupling and reduce the complexity of the experimental setup at the same time. Furthermore, the edge contour of objects can also be acquired by the weak measurement, and the edge sharpness is related to types of the weak values, which plays an important role in image resolution. Our method paves a way for quantitative phase imaging and unlabeled biological imaging.

Optimized weak measurement model for in-plane and out-of-plane splitting shifts of Photonic Spin Hall effect

The photonic spin Hall effect (PSHE) holds great potential for applications in the fields of precision measurement and sensing. Due to its splitting shift usually at the sub-wavelength level, the current observation and application of PSHE usually rely on weak measurement amplification technology. However, the current optimized weak measurement models are only for the out-of-plane splitting shift of PSHE, and are only applicable to certain specific situations. This greatly limits the application of PSHE in many fields such as precision measurement and sensing, and to some extent hinders the experimental research on PSHE. Based on this issue, by changing the polarization state from 0° or 90° to arbitrary linear polarization incidence, and extending the reflection coefficient from real number to complex number, a set of optimized weak measurement model with wider applicability for both in-plane and out-of-plane splitting shifts of PSHE is established in this article. It is not only applicable to the case where the pre-selection and post-selection states are arbitrary linearly polarized states, but also to the case where the reflection interface is both absorbent medium and non-absorbent medium. In addition, the correctness of this model is demonstrated through comparative verification. This work not only help to conduct more comprehensive and in-depth research on the PSHE and will also further promotes the application and development of PSHE in the fields of precision measurement and high-sensitivity sensing.

Spin-Hall Effect of Cylindrical Vector Vortex Beams

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.

High-sensitivity atomic magnetometer realized by weak-value-amplification effect

The weak-value-amplification (WVA) effect, which is also called weak measurement, has been developed extensively in various sensing systems. Here, we report the actual realization of the WVA effect in spin-exchange relaxation-free atomic magnetometer system, wherein the slight separation of transverse momentum of the probe light is amplified by introducing orthogonal pre- and post-selection states. A differential detector is used to obtain the transverse position of the probe light accurately in real time. The weak coupling of the magneto-optical interaction with atoms will be reflected in the differential signal. The WVA effect is observed and demonstrated directly and a high sensitivity of 8 fT/Hz is achieved. Also, we obtain the stable and distinct simulated magnetocardiography signal through our system. The present successful implementation of this probe method paves the way for further technical noise suppression and sensitivity improvement of quantum sensors.

Measurement-device-independent multi-party quantum key agreement

Quantum key agreement (QKA) is an important quantum cryptography primitive. In a QKA protocol, two or more untrusted parties can agree on an identical key in such a way that they equally influence the key and no subset can decide it alone. However, in practical QKA, the imperfections of the participant’s detectors can be exploited to compromise the security and fairness of QKA. To remove all the detector-side-channel loopholes, a measurement-device-independent multi-party QKA protocol is proposed. The protocol exploits the post-selected GHZ states to generate a secure agreement key between legitimate participants, while ensuring the fairness of key agreement. Our protocol provides a new clue for the design of practical QKA protocols.

Quantum-coherence-free precision metrology by means of difference-signal amplification

The novel weak-value-amplification (WVA) scheme of precision metrology is deeply rooted in the quantum nature of destructive interference between the pre- and post-selection states. And, an alternative version, termed as joint WVA (JWVA), which employs the difference-signal from the post-selection accepted and rejected results, has been found possible to achieve even better sensitivity (two orders of magnitude higher) under some technical limitations (e.g. misalignment errors). In this work, after erasing the quantum coherence, we analyze the difference-signal amplification (DSA) technique, which serves as a classical counterpart of the JWVA, and show that similar amplification effect can be achieved. We obtain a simple expression for the amplified signal, carry out characterization of precision, and point out the optimal working regime. We also discuss how to implement the post-selection of a classical mixed state. The proposed classical DSA technique holds similar technical advantages of the JWVA and may find interesting applications in practice.

Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems

Observations in quantum weak measurements are determined by complex numbers called weak values. We present a geometrical interpretation of the argument of weak values of general Hermitian observables in N-dimensional quantum systems in terms of geometric phases. We formulate an arbitrary weak value in terms of three real vectors on the unit sphere in N 2 − 1 dimensions, . These vectors are linked to the initial and final states, and to the weakly measured observable, respectively. We express pure states in the complex projective space of N − 1 dimensions, , which has a non-trivial representation as a 2N − 2 dimensional submanifold of (a generalization of the Bloch sphere for qudits). The argument of the weak value of a projector on a pure state of an N-level quantum system describes a geometric phase associated to the symplectic area of the geodesic triangle spanned by the vectors representing the pre-selected state, the projector and the post-selected state in . We then proceed to show that the argument of the weak value of a general observable is equivalent to the argument of an effective Bargmann invariant. Hence, we extend the geometrical interpretation of projector weak values to weak values of general observables. In particular, we consider the generators of SU(N) given by the generalized Gell–Mann matrices. Finally, we study in detail the case of the argument of weak values of general observables in two-level systems and we illustrate weak measurements in larger dimensional systems by considering projectors on degenerate subspaces, as well as Hermitian quantum gates. To conclude, we discuss the interpretation and usefulness of geometric phases in weak values in connection to weak measurements.

Multiple-weak-value quantum measurement for precision estimation of time delay

In quantum weak measurement, a weak value is a quantity related to a pointer shift of a measuring device which is usually determined by pre- and postselection states. For conventional weak measurement, a single weak-value model has been well addressed in precision metrology of time delay, but it only holds for a narrowband light source. To further improve the measurement accuracy, a broad-spectrum light source is needed. We find that the single weak-value model no longer holds, due to the occurrence of modified preselection states. Here, a multiple weak-value model is established by introducing the modified preselection states in the estimation of time delay. For broad-spectrum light source with 50-nm spectral width, the multiple weak-value scheme enables us to achieve a high resolution of $1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.16em}{0ex}}\mathrm{as}$. Our proposed multiple weak-value amplification may have important applications in various fields involving precise time-delay detection.

Optimal weak measurement in the photonic spin Hall effect for arbitrary linear polarization incidence

The photonic spin Hall effect (SHE) has great potential in precision metrology due to its unique spin modulation characteristics. To improve its potential, the effective enhancement of detection precision has become an important issue. In this work, we theoretically and experimentally demonstrate the optimal weak measurement (optimal overlap of pre-selected and post-selected states) with arbitrary linear polarization incidence for both amplified transverse and in-plane shift. Also, based on photonic SHE, a method for arbitrary linear polarization angle detection is then proposed experimentally with a detection accuracy of 0.04 degree. It can provide a guidance for the weak measurement and enlarge the potential application of photonic SHE in field of precision measurement.

Studying Heisenberg-like Uncertainty Relation with Weak Values in One-dimensional Harmonic Oscillator

As one of the fundamental traits governing the operation of quantum world, the uncertainty relation, from the perspective of Heisenberg, rules the minimum deviation of two incompatible observations for arbitrary quantum states. Notwithstanding, the original measurements appeared in Heisenberg’s principle are strong such that they may disturb the quantum system itself. Hence an intriguing question is raised: What will happen if the mean values are replaced by weak values in Heisenberg’s uncertainty relation? In this work, we investigate the question in the case of measuring position and momentum in a simple harmonic oscillator via designating one of the eigenkets thereof to the pre-selected state. Astonishingly, the original Heisenberg limit is broken for some post-selected states, designed as a superposition of the pre-selected state and another eigenkets of harmonic oscillator. Moreover, if two distinct coherent states reside in the pre- and post-selected states respectively, the variance reaches the lower bound in common uncertainty principle all the while, which is in accord with the circumstance in Heisenberg’s primitive framework.

Restrictions on the existence of weak values in quantum mechanics: Weak quantum evolution concept

It is shown, that the Aharonov-Albert-Vaidman concept of weak values appears to be a consequence of a more general quantum phenomenon of weak quantum evolution. Here the concept of weak quantum evolution is introduced and discussed for the first time. In particular, it is shown on the level of quantum evolution that there exist restrictions on the applicability of weak quantum evolution- and, hence, weak values approach. These restrictions connect the size of a given quantum ensemble with the parameters of pre- and post-selected quantum states. It is shown, that the latter requirement can be fulfilled for the model system, where the concept of weak values was initially introduced by Aharonov, Albert and Vaidman. Moreover, the deep connection between weak quantum evolution and conventional probability of quantum transition between two non-orthogonal quantum states is established for the first time. It is found that weak quantum evolution of quantum system between its two non-orthogonal quantum states is inherently present in the measurement-determined definition of quantum transition probability between these two quantum states.

Enhancing signal and signal-to-noise ratio with post-selection and nonclassical states

We propose a weak measurement scheme with post-selection based on the cross-Kerr interaction between two optical fields. We demonstrate that our scheme can measure smaller physical effects and obtain a larger signal-to-noise ratio compared to the weak measurement scheme without post-selection. We also show that the initial pointer states with nonclassical properties can increase the successful post-selection probability, offer a bigger signal-to-noise ratio compared to the coherent states.

Weak measurement of Berry’s phase

Quantum measurements can be generalized to include complex quantities. It is possible to relate the quantum weak values of projection operators to the third order Bargmann invariants. The argument of the weak value becomes, up to a sign, equal to the Berry’s phase associated with the three state vectors. In case of symmetric informationally complete, positive operator valued measures, this relation takes a particularly simple form. Alternating strong and weak measurements can be used to determine Berry’s phase directly, which demonstrates that not only their real and imaginary parts but also moduli and arguments of weak values have a physical significance. For an arbitrary projection operator, weak value is real when the projector, pre- and post-selected states lie on a so-called null phase curve which includes the geodesic containing the three states as a special case.

Hamiltonian estimation based on adaptive weak value amplification

Hamiltonian estimation is a cardinal task in applications of quantum metrology, quantum computation, quantum simulation, etc. When the evolution time is short in order to suppress noise and enhance sensitivity, the measurement and postprocessing may incur high cost. In this paper, we propose an adaptive weak measurement scheme for Hamiltonian estimation, which adjusts the pre- and post-selection according to the difference of the mean shift between two orthogonal post-selected states. According to the angle of the post-selected state, the proposed scheme can change from weak value amplification (WVA) to joint weak measurement (JWM). A study of the quantum Fisher information shows that the JWM situation is always optimal. Meanwhile, the WVA approach loses a little information but it can inherit the WVA’s technical advantages, which are suitable for short evolution times. The widely applicable scope of the proposed scheme makes us believe that it offers a new path for the understanding of unknown Hamiltonians.

Quantum Cheshire cat: a physically realistic interpretation by invoking entangled correlations

The phenomenon of the quantum Cheshire cat (QCC) and its interpretation by Aharanov et al. [New J. Phys. 15, 113015 (2013)NJOPFM1367-263010.1088/1367-2630/15/11/113015], with the conjecture that any quantum entity can be disembodied from its physical attributes, has resulted in a heated debate leading to interpretational controversy as well as practical consequences. Here, we propose an experimentally testable and physically more realistic and logically plausible interpretation. We utilize a specifically engineered Mach–Zehnder-type interferometeric setup that is quite similar to the original QCC setup but with the slight difference that now a single-photon, bipartite entangled state traverses the interferometer such that each path is designated to a photon with different tags. With this specific setup, we demonstrate that the photon’s polarization is never physically separated from the photon itself. Rather, it becomes dormant and hence inaccessible along the designated interferometric path. We also generalize the schematics and show that any precisely oriented photon’s polarization that stands inaccessible or dormant re-emerges along the same spatially separated and isolated arm as we tune the polarization vector away from the selected angle. Thus our proposal persuasively proves that polarization is never stripped off the photon itself and instead becomes inaccessible along the interferometeric arm for a certain particularly selected orientation. The schematics further reveal that this inaccessibility of the photon’s polarization is not permanent, fixed, and universal, but rather it is entirely constrained to a specific orientation in the Hilbert space, governed by the particular pre- and post-selected state under two-state vector formalism.

Maximum a posteriori path for open quantum systems

In this work, the Stratonovich stochastic differential equation is considered in the derivation of the maximum a posteriori path (MAP) for an open quantum system. We have derived the modified Onsager-Machlup (OM) function for a stochastic process, which plays an analogous role of the Lagrangian in the conventional classical mechanics. Variational method is applied to obtain the Euler-Lagrange equations. We show that the MAP trajectory is close to the quantum most-likely path obtained by Chantasri et al. [1], but in general not exactly the same. For an open quantum system subject to a no-knowledge measurement, both methods produce the same most-likely path. Numerical simulations for both the modified OM and the quantum most-likely path methods agree very well with theoretical predictions, regardless of the evolution time and different post-selected states.

The A Satellite-to-Ground Quantum Key Distribution Protocol Based on Orbital Angular Momentum of Light

The orbital angular momentum (OAM) of light has been considered as a promising degree of freedom (DoF) that gives access to a higher-dimensional Hilbert space, which may lead to potential higher capacity quantum communications. Due to the fragility of the OAM state, the traditional view is that turbulence will make OAM-QKD infeasible in satellite-to-ground channels. However, based on the detailed phase screen simulations of the expected atmospheric turbulence, we find that quantum key distribution (QKD) using OAM of the light is feasible in certain system configurations, especially if quantum channel in-formation is utilized in the processing of post-selected states. Therefore, we propose a satellite-to-ground quantum key distribution protocol based on the orbital angular momentum of the light, which uses the principle that OAM-QKD can only be used in high-altitude ground stations with larger receiver apertures with-out using classic optical probes. At the same time, the classically entangled light is used as a probe of the quantum channel and reasonably-sized transmitter-receiver apertures are also employed. Numerical simulation results show that this protocol can lead to positive secret key rates even under circumstances where a sea-level ground station with a reasonable-sized aperture is used. We also found that quantum channel conjugation enables a key rate advantage provided by the higher dimensions of the protocol to be realized.

Parameter accuracy analysis of weak-value amplification process in the presence of noise* *Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0305200), the National Natural Science Foundation of China (Grant Nos. 11674234 and 11605205), the Natural Science Foundation of Chongqing (Grant Nos. cstc2015jcyjA00021 and cstc2018jcyjAX0656), the Innovation Project of Sichuan University (Grant No. 2018SCUH0021), the

We theoretically introduce the statistical uncertainty of photon number and phase error to discuss the precision of parameters to be measured based on weak measurements. When the photon counting scheme is used, we discuss the relative accuracy of the system in the presence of phase error by using the orthogonal and nonorthogonal pre- and post-selected states, respectively. When using the measurement scheme of pointer shift, we discuss the measurement accuracy in the presence of phase error, pointer resolution, and statistical uncertainty. These results give a guide way to get the smallest relative precision and deepen our understanding about weak measurement.