Weak Quantum Measurement Research Articles

Weak measurement-based state estimation of Gaussian states of one-variable quantum systems

We present a scheme to estimate Gaussian states of one-dimensional continuous variable systems, based on weak (unsharp) quantum measurements. The estimation of a Gaussian state requires us to find position (q), momentum (p) and their second order moments. We measure q weakly and follow it up with a projective measurement of p on half of the ensemble, and on the other half we measure p weakly followed by a projective measurement of q. In each case we use the state twice before discarding it. We compare our results with projective measurements and demonstrate that under certain conditions such weak measurement-based estimation schemes, where recycling of the states is possible, can outperform projective measurement-based state estimation schemes. We establish beyond statistical fluctuations that our method works better for small ensemble sizes.

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.

Weak values obtained from mass-energy equivalence

Quantum weak measurement, measuring some observable quantities within the selected subensemble of the entire quantum ensemble, can produce many interesting results such as the superluminal phenomena. An outcome of such a measurement is the weak value which has been applied to amplify some weak signals of quantum interactions in lots of previous references. Here, we apply the weak measurement to the system of relativistic cold atoms. According to mass-energy equivalence, the internal energy of an atom will contribute its rest mass and consequently the external momentum of center of mass. This implies a weak coupling between the internal and external degrees of freedom of atoms moving in the free space. After a duration of this coupling, a weak value can be obtained by post-selecting an internal state of atoms. We show that the weak value can change the momentum uncertainty of atoms and consequently help us to experimentally measure the weak effects arising from mass-energy equivalence.

Quantized photonic spin Hall effect in graphene

We examine the photonic spin Hall effect (SHE) in a graphene-substrate system with the presence of external magnetic field. In the quantum Hall regime, we demonstrate that the in-plane and transverse spin-dependent splittings in photonic SHE exhibit different quantized behaviors. The quantized SHE can be described as a consequence of a quantized geometric phase (Berry phase), which corresponds to the quantized spin-orbit interaction. Furthermore, an experimental scheme based on quantum weak value amplification is proposed to detect the quantized SHE in terahertz frequency regime. By incorporating the quantum weak measurement techniques, the quantized photonic SHE holds great promise for detecting quantized Hall conductivity and Berry phase. These results may bridge the gap between the electronic SHE and photonic SHE in graphene.

Freezing quantum coherence with weak measurement

We show how to optimally protect quantum states and freeze coherence under incoherent channels using a quantum weak measurement and quantum measurement reversal. In particular, we present explicit formulas for the conditions for freezing quantum coherence in a given quantum state.

The protection of qudit states by weak measurement

Liao Xiang-Ping et al.(Chin. Phys. B 23 020304, 2014) pointed out that the method of weak measurement and quantum weak measurement reversal can protect entanglement and improve the fidelity of three-qubit quantum state. We generalize the method of weak measurement to the case of qudit state in this paper. By using the operation of weak measurement and quantum weak measurement reversal, we investigate the evolution dynamics of fidelity and fidelity improvement for qudit state under amplitude damping decoherence. We compare two kinds of operations: one is to let the input qudit state cross the amplitude damping decoherence directly, and the other one is that we first make a weak measurement operation on the input qudit state, then through the amplitude damping decoherence, finally an operation of quantum weak measurement reversal is done with the output qudit state. We discuss the GHZ state, W state, CL state and some special separable states exactly and obtain the analytic expressions of fidelity and fidelity improvement for qudit state before and after the weak measurement and quantum weak measurement reversal operation. According to the analytic expressions we plot the evolution curves against its corresponding parameters. The effects of corresponding parameters are discussed and a susceptible protection region of the qudit state is also given in the context. The results show that the structure of qudit state is the determined factor to the effect of weak measurement and quantum weak measurement reversal. There are some different effects on the different structured qudit states. For entangled state, the fidelity of qudit GHZ state can be protected in a relatively big evolution region, most part of the fidelity improvement is in the upper part of the zero reference plane. While the fidelity of qudit W state can be improved effectively in the whole evolution region, which is a perfect protection. The evolution regulations of qudit CL state and Dick state are between evolution regulations of the GHZ state and W state. When we input some special separable qudit states which have similar structures to W state, their fidelity and fidelity improvement are almost the same as W state’s. It is demonstrated that the structure of qudit state is important for the weak measurement in a step. This work is meaningful for the quantum information process.

Nonclassical Correlations in a Three-Mode Continuous-Variable System

We investigate a standard measure of quantum discord for tripartite coherent states of the Greenberger–Horne–Zeilinger (GHZ) type. Furthermore, we check the monotonicity of a superquantum discord according to weak quantum measurements. We accomplish our study by manipulating the amount of quantum information lost during the perturbation of the quantum system and controlling the measurement strength. In addition, we calculate the entanglement of the system under study. Finally we compare the behavior of the three correlations.

Anomalous time delays and quantum weak measurements in optical micro-resonators.

Quantum weak measurements, wavepacket shifts and optical vortices are universal wave phenomena, which originate from fine interference of multiple plane waves. These effects have attracted considerable attention in both classical and quantum wave systems. Here we report on a phenomenon that brings together all the above topics in a simple one-dimensional scalar wave system. We consider inelastic scattering of Gaussian wave packets with parameters close to a zero of the complex scattering coefficient. We demonstrate that the scattered wave packets experience anomalously large time and frequency shifts in such near-zero scattering. These shifts reveal close analogies with the Goos–Hänchen beam shifts and quantum weak measurements of the momentum in a vortex wavefunction. We verify our general theory by an optical experiment using the near-zero transmission (near-critical coupling) of Gaussian pulses propagating through a nano-fibre with a side-coupled toroidal micro-resonator. Measurements demonstrate the amplification of the time delays from the typical inverse-resonator-linewidth scale to the pulse-duration scale.

Amplifying and freezing of quantum coherence using weak measurement and quantum measurement reversal**Project supported by the National Natural Science Foundation of China (Grant Nos. 11204156, 61178012, 11304179, and 11247240) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20133705110001).

We analyze universal conditions where the l1 norm and relative entropy of coherence are amplified and frozen under identical bit-flip channels; that is, using pre-measurements (quantum weak measurements or quantum measurement reversals) on the systems before undergoing local bit-flip channels. With the option of quantum weak measurements or quantum measurement reversals, the measurement strength and the success probability are all determined by the initial state of the quantum system.

Quantum measurement-induced antiferromagnetic order and density modulations in ultracold Fermi gases in optical lattices.

Ultracold atomic systems offer a unique tool for understanding behavior of matter in the quantum degenerate regime, promising studies of a vast range of phenomena covering many disciplines from condensed matter to quantum information and particle physics. Coupling these systems to quantized light fields opens further possibilities of observing delicate effects typical of quantum optics in the context of strongly correlated systems. Measurement backaction is one of the most funda- mental manifestations of quantum mechanics and it is at the core of many famous quantum optics experiments. Here we show that quantum backaction of weak measurement can be used for tailoring long-range correlations of ultracold fermions, realizing quantum states with spatial modulations of the density and magnetization, thus overcoming usual requirement for a strong interatomic interactions. We propose detection schemes for implementing antiferromagnetic states and density waves. We demonstrate that such long-range correlations cannot be realized with local addressing, and they are a consequence of the competition between global but spatially structured backaction of weak quantum measurement and unitary dynamics of fermions.

Collective dynamics of multimode bosonic systems induced by weak quantum measurement

In contrast to the fully projective limit of strong quantum measurement, where the evolution is locked to a small subspace (quantum Zeno dynamics), or even frozen completely (quantum Zeno effect), the weak non-projective measurement can effectively compete with standard unitary dynamics leading to nontrivial effects. Here we consider global weak measurement addressing collective variables, thus preserving quantum superpositions due to the lack of which path information. While for certainty we focus on ultracold atoms, the idea can be generalized to other multimode quantum systems, including various quantum emitters, optomechanical arrays, and purely photonic systems with multiple-path interferometers (photonic circuits). We show that light scattering from ultracold bosons in optical lattices can be used for defining macroscopically occupied spatial modes that exhibit long-range coherent dynamics. Even if the measurement strength remains constant, the quantum measurement backaction acts on the atomic ensemble quasi-periodically and induces collective oscillatory dynamics of all the atoms. We introduce an effective model for the evolution of the spatial modes and present an analytic solution showing that the quantum jumps drive the system away from its stable point. We confirm our finding describing the atomic observables in terms of stochastic differential equations.

Entropic Uncertainty Relation Under Dissipative Environments and Its Steering by Local Non-unitary Operations

Entropic uncertainty relation (EUR) quantifies the precision of measurements for arbitrary two non-commuting observables within a specified system. Due to exposure in a noisy environment, a practical system unavoidably suffers from decay by interacting with the environment. Inthis paper, we investigate the dynamic behaviors of EUR for a pair of non-commuting observables under two typical dissipative environments. Specifically, we study the dynamics features of EUR in a single-qubit system under the degradation induced by amplitude damping (AD) and depolarizing noises, respectively. It has been found that AD and depolarizing noises do not always cause the increase of the uncertainty, and can reduce the amount in a relative long-time regime. Remarkably, it has been shown that there exists a critical phenomenon that AD noise can always lead to the reducing of the uncertainty when the ratio of ground state and excited state is beyond a threshold in the system. Furthermore, we propose a general and effective approach to steer EUR by means of a kind of non-unitary operations, namely, quantum weak measurements. It is verified that quantum weak measurements can effectively reduce the entropic uncertainty in the dissipative environment.

Protecting entanglement from correlated amplitude damping channel using weak measurement and quantum measurement reversal

Based on the quantum technique of weak measurement, we propose a scheme to protect the entanglement from correlated amplitude damping decoherence. In contrast to the results of memoryless amplitude damping channel, we show that the memory effects play a significant role in the suppression of entanglement sudden death and protection of entanglement under severe decoherence. Moreover, we find that the initial entanglement could be drastically amplified by the combination of weak measurement and quantum measurement reversal even under the correlated amplitude damping channel. The underlying mechanism can be attributed to the probabilistic nature of weak measurements.

Proposal for reversing the weak measurement with arbitrary maximum photon number

We present a proposal for reversing the weak (partial-collapse) quantum measurement on a cavity field with arbitrary maximum photon number. We start by putting forth a protocol to realize quantum phase gates between the cavity field and an ancilla qubit. Afterward, adopting these phase gates and some other quantum gates, we can determine the reversal of the cavity state just by observing the ancilla qubit. Compared to previous proposals, our proposal does not need any other weak measurement and can save reversal time, which is significantly important in quantum informatics and quantum computation.

Application of quantum weak measurement for glucose concentration detection.

A quantum weak measurement scheme based on a Mach-Zehnder interferometer is proposed to detect the concentration of glucose, bringing this mechanism into the field of biomedical sensing for the first time, to the best of our knowledge. With a Mach-Zehnder interferometer system, we can analyze tiny phase differences between the two paths by measuring spectrum shift. We measured the concentration of glucose with weak measurement to achieve a concentration resolution of 8.98×10⁻⁵ g/L corresponding to a volume refractive index of 1.39×10⁻⁸ RIU, which was more than five times higher than the resolution achieved by conventional interference, 4.99×10⁻⁴ g/L. In the detection of glucose concentration in the blood serum of mice, a resolution of 1.0136×10⁻⁷ g/L for weak measurement was obtained.

Application of quantum weak measurement for glucose concentration detection

Application of quantum weak measurement for glucose concentration detection

Weak values are quantum: you can bet on it

The outcome of a weak quantum measurement conditioned to a subsequent postselection (a weak value protocol) can assume peculiar values. These results cannot be explained in terms of conditional probabilistic outcomes of projective measurements. However, a classical model has been recently put forward that can reproduce peculiar expectation values, reminiscent of weak values. This led the authors of that work to claim that weak values have an entirely classical explanation. Here we discuss what is quantum about weak values with the help of a simple model based on basic quantum mechanics. We first demonstrate how a classical theory can indeed give rise to non-trivial conditional values, and explain what features of weak values are genuinely quantum. We finally use our model to outline some main issues under current research.

Dynamics and improvement of quantum correlations in the triple Jaynes–Cummings model

We investigate the dynamics and improvement of tripartite quantum correlations in three atoms interacting with the independent cavities, in terms of genuinely multipartite concurrence, lower bound of concurrence and tripartite geometric quantum discord. By choosing the GHZ and W states as atomic initial states, we study the relationship between the initial state and entanglement transfer, and the robustness of different correlation measures. The results show that the different initial states can control entanglement transfer between the subsystems, and the tripartite geometric quantum discord is more robust than tripartite entanglement in the evolution process. Then, we propose the optimal scheme to improve tripartite entanglement in certain conditions via the weak measurement and quantum measurement reversal. In addition, we find that our study also works for the N-qubit GHZ state by using genuinely multipartite concurrence.

Entanglement Protection for Two-Qubit in a Non-Markovian Common Bath

In this paper, we propose a scheme to protect quantum entanglement and coherence from a non-Markovian noisy environment. 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 thus suffer less decoherence in the time evolution. After the time evolution the second weak measurement can partially retrieve the original information encoded in the quantum system. Our study is based on a non-Markovian dynamic equation which allows us to investigate the impact of the memory effect on the performance of the protection scheme. We analyze several factors that may affect the protection efficiency. The results suggest that two measurement strengths should be chosen in a linear relation but the ratio is not one. Besides, we also show the memory effect can drastically improve the protection efficiency.

Protection of quantum correlations against decoherence

The protection of different quantum correlations, such as Bell nonlocality, quantum discord, and geometric quantum discord as trace distance against noise, is explored. By weak measurement and quantum measurement reversal, we show that the mentioned quantum correlations can be effectively preserved probabilistically from the decoherence due to amplitude damping. The results will play an important role in the experiments using the quantum correlations as resource.