Activation of indistinguishability-based quantum coherence for enhanced metrological applications with particle statistics imprint.

SignificanceQuantum coherence has a fundamentally different origin for nonidentical and identical particles since for the latter a unique contribution exists due to indistinguishability. Here we experimentally show how to exploit, in a controllable fashion, the contribution to quantum coherence stemming from spatial indistinguishability. Our experiment also directly proves, on the same footing, the different role of particle statistics (bosons or fermions) in supplying coherence-enabled advantage for quantum metrology. Ultimately, our results provide insights toward viable quantum-enhanced technologies based on tunable indistinguishability of identical building blocks.

Experimental optimal generation of hybrid entangled states in photonic quantum walks.

While the existence of disorders is commonly believed to weaken the unique properties of quantum systems, recent progress has predicted that it can exhibit a counterintuitive enhanced effect on the behavior of entanglement generation, which is even independent of the chosen initial conditions and physical platforms. However, to achieve a maximally entangled state in such disordered quantum systems, the key limitation of this is the scarcity of an infinite coherence time, which makes its experimental realization challenging. Here, we experimentally investigate the entanglement entropy dynamics in a photonic quantum walk with disorders in time. Through the incorporation of a classic optimization algorithm, we experimentally demonstrate that such disordered systems can relax to a high-entanglement hybrid state at any given time step. Moreover, this prominent entangling ability is universal for a wide variety of initial conditions. Our results may inspire achieving a well-controlled entanglement generator for quantum computation and information tasks.

Extracting information from single qubits among multiple observers with optimal weak measurements.

In the context of quantum information, major efforts have been made to maximize the mutual information by measuring single copies of signal states. In general, one execution of optimal projective measurement extracts all the accessible mutual information. However, in some scenarios, weak measurements are preferred because of kinds of specific requirements, e.g., to distribute secret keys to multi-observers. In this study, we propose a method to construct optimal weak measurements for multi-party quantum communications. Utilizing the method in [Physical Review Letters 120, 160501 (2018)] to classify the mutual information, the theoretical study shows that by successively performing this optimal weak measurement, all accessible information can be obtained by multiple observers. This conclusion is experimentally verified by a cascaded measurement apparatus that can perform six successive weak measurements on heralded single photons. The experimental results clearly indicate that almost all accessible mutual information is extracted by this sequence of optimal weak measurements; meanwhile, none of the information is destroyed or residual. Thus, this optimal weak measurement is an efficient and reliable tool for performing quantum communication tasks. The consistence between the experimental and theoretical results verifies that the classifying method in [Phys. Rev. Lett.120, 160501 (2018)] can be applied to characterize realistic quantum measurements.

Experimental quantum entanglement and teleportation by tuning remote spatial indistinguishability of independent photons.

Quantitative control of spatial indistinguishability of identical subsystems as a direct quantum resource at distant sites has not yet been experimentally proven. We design a setup capable of tuning remote spatial indistinguishability of two independent photons by individually adjusting their spatial distribution in two distant regions, leading to polarization entanglement from uncorrelated photons. This is achieved by spatially localized operations and classical communication on photons that meet only at the detectors. The amount of entanglement depends uniquely on the degree of spatial indistinguishability, quantified by an entropic measure I, which enables teleportation with fidelities above the classical threshold. The results open the way to viable indistinguishability-enhanced quantum information processing.

Experimental extraction of nonlocal weak values for demonstrating the failure of a product rule.

We experimentally demonstrate an alternative method for measuring nonlocal weak values in linear optics, avoiding the use of second-order interaction. The method is based on the concept of modular values. The paths of two photons, initialized in hyperentangled states, are adopted as the meter with the polarization acting as the system. The modular values are read out through the reconstructed final states of the meter. The weak value of nonlocal observables is given through its connection to the modular value. Comparing the weak values of local and nonlocal observables, we demonstrate the failure of product rules for an entangled system. Our results significantly simplify the task of measuring nonlocal weak values and will play an important role in the application of weak measurement.

Experimental Optimal Verification of Entangled States Using Local Measurements.

The initialization of a quantum system into a certain state is a crucial aspect of quantum information science. While a variety of measurement strategies have been developed to characterize how well the system is initialized, for a given one, there is in general a trade-off between its efficiency and the accessible information of the quantum state. Conventional quantum state tomography can characterize unknown states while requiring exponentially expensive time-consuming postprocessing. Alternatively, recent theoretical breakthroughs show that quantum state verification provides a technique to quantify the prepared state with significantly fewer samples, especially for multipartite entangled states. In this Letter, we modify the original proposal to be robust to practical imperfections, and experimentally implement a scalable quantum state verification on two-qubit and four-qubit entangled states with nonadaptive local measurements. For all the tested states, the estimated infidelity is inversely proportional to the number of samples, which illustrates the power to characterize a quantum state with a small number of samples. Compared to the globally optimal strategy which requires nonlocal measurements, the efficiency in our experiment is only worse by a small constant factor (<2.5). We compare the performance difference between quantum state verification and quantum state tomography in an experiment to characterize a four-photon Greenberger-Horne-Zeilinger state, and the results indicate the advantage of quantum state verification in both the achieved efficiency and precision.

Experimental Investigation of Quantum PT-Enhanced Sensor.

PT-symmetric theory is developed to extend quantum mechanics to a complex region, but it wins its great success first in classical systems, for example, optical waveguides and electric circuits, etc., because there are so many counterintuitive phenomena and striking applications, including unidirectional light transport, PT-enhanced sensors (one kind of exceptional-point-based sensor), and wireless power transfer. However, these phenomena and applications are mostly based on the ability to approach a PT-symmetric broken region, which makes it difficult to transfer them to the quantum regime, since the broken quantum PT-symmetric system has not been constructed effectively, until recently several methods have been raised. Here, we construct a quantum PT-symmetric system assisted by weak measurement, which can effectively transit from the unbroken region to the broken region. The full energy spectrum including the real and imaginary parts is directly measured using weak values. Furthermore, based on the ability of approaching a broken region, we for the first time translate the previously mentioned PT-enhanced sensor into the quantum version, and investigate its various features that are associated to the optimal conditions for sensitivity enhancement. In this experiment, we obtain an enhancement of 8.856 times over the conventional Hermitian sensor. Moreover, by separately detecting the real and imaginary parts of energy splitting, we can derive the additional information of the direction of perturbations. Our work paves the way of leading classical interesting PT phenomena and applications to their quantum counterparts. More generally, since the PT system is a subset of non-Hermitian systems, our work will be also helpful in the studies of general exception point in the quantum regime.

Coherent Control of Nitrogen-Vacancy Center Spins in Silicon Carbide at Room Temperature.

Solid-state color centers with manipulatable spin qubits and telecom-ranged fluorescence are ideal platforms for quantum communications and distributed quantum computations. In this work, we coherently control the nitrogen-vacancy (NV) center spins in silicon carbide at room temperature, in which telecom-wavelength emission is detected. We increase the NV concentration sixfold through optimization of implantation conditions. Hence, coherent control of NV center spins is achieved at room temperature, and the coherence time T_{2} can be reached to around 17.1 µs. Furthermore, an investigation of fluorescence properties of single NV centers shows that they are room-temperature photostable single-photon sources at telecom range. Taking advantage of technologically mature materials, the experiment demonstrates that the NV centers in silicon carbide are promising platforms for large-scale integrated quantum photonics and long-distance quantum networks.

Direct Measurement of a Nonlocal Entangled Quantum State.

Entanglement and the wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using weak values, was demonstrated by Lundeen et al. [Nature 474, 188 (2011)]. However, it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element, since that requires obtaining weak values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using modular values. The method is experimentally implemented for a photon pair in a hyperentangled state, i.e., entangled both in polarization and momentum degrees of freedom.

Experimental Realization of Robust Self-Testing of Bell State Measurements.

Bell state measurements, of which the eigenvectors are in an entangled form, are crucial resources in the construction of quantum networks. Therefore, device-independent certification of a Bell state measurement has significance in the quantum information process because it satisfies the exact demand on security. In this study, we implement a proof-of-concept experiment to certify a Bell state measurement device independently in an entanglement swapping process, namely, self-testing. Instead of preparing a tensor product of two singlets with four photons, multiplex encoding in polarization and spatial modes is utilized to produce two pairs of entangled qubits. As a result, we implement a full Bell state measurement and achieve a high degree of Bell violation on the remaining two qubits, which are required for nontrivial self-testing of a Bell state measurement. Furthermore, our results combine the correlations before and after the swapping; thus, the quality of the performed Bell state measurement can be precisely inferred.

Measurements of Nonlocal Variables and Demonstration of the Failure of the Product Rule for a Pre- and Postselected Pair of Photons.

We report the first implementation of the von Neumann instantaneous measurements of nonlocal variables, which becomes possible due to technological achievements in creating hyperentangled photons. Tests of reliability and of the nondemolition property of the measurements have been performed with high precision, showing the suitability of the scheme as a basic ingredient of numerous quantum information protocols. The method allows us to demonstrate for the first time with strong measurements a special feature of pre- and postselected quantum systems: the failure of the product rule. It has been verified experimentally that for a particular pre- and postselected pair of particles, a single measurement on particle A yields with certainty σ_{x}^{A}=-1, a single measurement on particle B yields with certainty σ_{y}^{B}=-1, and a single nonlocal measurement on particles A and B yields with certainty σ_{x}^{A}σ_{y}^{B}=-1.

Measuring the Winding Number in a Large-Scale Chiral Quantum Walk.

We report the experimental measurement of the winding number in an unitary chiral quantum walk. Fundamentally, the spin-orbit coupling in discrete time quantum walks is implemented via a birefringent crystal collinearly cut based on a time-multiplexing scheme. Our protocol is compact and avoids extra loss, making it suitable for realizing genuine single-photon quantum walks at a large scale. By adopting a heralded single photon as the walker and with a high time resolution technology in single-photon detection, we carry out a 50-step Hadamard discrete-time quantum walk with high fidelity up to 0.948±0.007. Particularly, we can reconstruct the complete wave function of the walker that starts the walk in a single lattice site through the local tomography of each site. Through a Fourier transform, the wave function in quasimomentum space can be obtained. With this ability, we propose and report a method to reconstruct the eigenvectors of the system Hamiltonian in quasimomentum space and directly read out the winding numbers in different topological phases (trivial and nontrivial) in the presence of chiral symmetry. By introducing nonequivalent time frames, we show that whole topological phases in a periodically driven system can also be characterized by two different winding numbers. Our method can also be extended to the high winding number situation.

Achieving Heisenberg-Scaling Precision with Projective Measurement on Single Photons.

It has been suggested that both quantum superpositions and nonlinear interactions are important resources for quantum metrology. However, to date the different roles that these two resources play in the precision enhancement are not well understood. Here, we experimentally demonstrate a Heisenberg-scaling metrology to measure the parameter governing the nonlinear coupling between two different optical modes. The intense mode with n (more than 10^{6} in our work) photons manifests its effect through the nonlinear interaction strength which is proportional to its average photon number. The superposition state of the weak mode, which contains only a single photon, is responsible for both the linear Hamiltonian and the scaling of the measurement precision. By properly preparing the initial state of single photon and making projective photon-counting measurements, the extracted classical Fisher information (FI) can saturate the quantum FI embedded in the combined state after coupling, which is ∼n^{2} and leads to a practical precision ≃1.2/n. Free from the utilization of entanglement, our work paves a way to realize Heisenberg-scaling precision when only a linear Hamiltonian is involved.

Directly Measuring the Degree of Quantum Coherence using Interference Fringes.

Quantum coherence is the most distinguished feature of quantum mechanics. It lies at the heart of the quantum-information technologies as the fundamental resource and is also related to other quantum resources, including entanglement. It plays a critical role in various fields, even in biology. Nevertheless, the rigorous and systematic resource-theoretic framework of coherence has just been developed recently, and several coherence measures are proposed. Experimentally, the usual method to measure coherence is to perform state tomography and use mathematical expressions. Here, we alternatively develop a method to measure coherence directly using its most essential behavior-the interference fringes. The ancilla states are mixed into the target state with various ratios, and the minimal ratio that makes the interference fringes of the "mixed state" vanish is taken as the quantity of coherence. We also use the witness observable to witness coherence, and the optimal witness constitutes another direct method to measure coherence. For comparison, we perform tomography and calculate l_{1} norm of coherence, which coincides with the results of the other two methods in our situation. Our methods are explicit and robust, providing a nice alternative to the tomographic technique.

Experimental Quantification of Asymmetric Einstein-Podolsky-Rosen Steering.

Einstein-Podolsky-Rosen (EPR) steering describes the ability of one observer to nonlocally "steer" the other observer's state through local measurements. EPR steering exhibits a unique asymmetric property; i.e., the steerability can differ between observers, which can lead to one-way EPR steering in which only one observer obtains steerability in the steering process. This property is inherently different from the symmetric concepts of entanglement and Bell nonlocality, and it has attracted increasing interest. Here, we experimentally demonstrate asymmetric EPR steering for a class of two-qubit states in the case of two measurement settings. We propose a practical method to quantify the steerability. We then provide a necessary and sufficient condition for EPR steering and clearly demonstrate one-way EPR steering. Our work provides new insight into the fundamental asymmetry of quantum nonlocality and has potential applications in asymmetric quantum information processing.

Quantum simulation of Landau-Zener model dynamics supporting the Kibble-Zurek mechanism.

The Kibble-Zurek mechanism (KZM) captures the key physics of nonequilibrium dynamics in second order phase transitions, and accurately predicts the density of topological defects formed in such processes. However, the central prediction of KZM--i.e., the scaling of the density of defects with the quench rate--still needs further experimental confirmation, particularly for quantum transitions. Here, we perform a quantum simulation of the nonequilibrium dynamics of the Landau-Zener model based on a nine-stage optical interferometer with an overall visibility of 0.975±0.008. The results support the adiabatic-impulse approximation, which is the core of Kibble-Zurek theory. Moreover, the developed high-fidelity multistage optical interferometer can support more complex linear optical quantum simulations.

Efficient learning of mixed-state tomography for photonic quantum walk.

Noise-enhanced applications in open quantum walk (QW) has recently seen a surge due to their ability to improve performance. However, verifying the success of open QW is challenging, as mixed-state tomography is a resource-intensive process, and implementing all required measurements is almost impossible due to various physical constraints. To address this challenge, we present a neural-network-based method for reconstructing mixed states with a high fidelity (∼97.5%) while costing only 50% of the number of measurements typically required for open discrete-time QW in one dimension. Our method uses a neural density operator that models the system and environment, followed by a generalized natural gradient descent procedure that significantly speeds up the training process. Moreover, we introduce a compact interferometric measurement device, improving the scalability of our photonic QW setup that enables experimental learning of mixed states. Our results demonstrate that highly expressive neural networks can serve as powerful alternatives to traditional state tomography.

Phase estimation with weak measurement using a white light source.

We report results of a high precision phase estimation based on a weak measurement scheme using a commercial light-emitting diode. The method is based on a measurement of the imaginary part of the weak value of a polarization operator. The imaginary part of the weak value appeared due to the measurement interaction itself. The sensitivity of our method is equivalent to resolving light pulses of the order of a attosecond and it is robust against chromatic dispersion.

Optical demonstration of quantum fault-tolerant threshold.

A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable to the output of a higher probability of correct logical qubits under the presence of errors. However, strict requirements to encode qubits and operators render the implementation of a full fault-tolerant computation challenging even for the achievable noisy intermediate-scale quantum technology. Especially the threshold for fault-tolerant computation still lacks experimental verification. Here, based on an all-optical setup, we experimentally demonstrate the existence of the threshold for the fault-tolerant protocol. Four physical qubits are represented as the spatial modes of two entangled photons, which are used to encode two logical qubits. The experimental results clearly show that when the error rate is below the threshold, the probability of correct output in the circuit, formed with fault-tolerant gates, is higher than that in the corresponding non-encoded circuit. In contrast, when the error rate is above the threshold, no advantage is observed in the fault-tolerant implementation. The developed high-accuracy optical system may provide a reliable platform to investigate error propagation in more complex circuits with fault-tolerant gates.

Experimental verification of generalized eigenstate thermalization hypothesis in an integrable system.

Identifying the general mechanics behind the equilibration of a complex isolated quantum system towards a state described by only a few parameters has been the focus of attention in non-equilibrium thermodynamics. And several experimentally unproven conjectures are proposed for the statistical description of quantum (non-)integrable models. The plausible eigenstate thermalization hypothesis (ETH), which suggests that each energy eigenstate itself is thermal, plays a crucial role in understanding the quantum thermalization in non-integrable systems; it is commonly believed that it does not exist in integrable systems. Nevertheless, integrable systems can still relax to the generalized Gibbs ensemble. From a microscopic perspective, understanding the origin of this generalized thermalization that occurs in an isolated integrable system is a fundamental open question lacking experimental investigations. Herein, we experimentally investigated the spin subsystem relaxation in an isolated spin-orbit coupling quantum system. By applying the quantum state engineering technique, we initialized the system with various distribution widths in the mutual eigenbasis of the conserved quantities. Then, we compared the steady state of the spin subsystem reached in a long-time coherent dynamics to the prediction of a generalized version of ETH and the underlying mechanism of the generalized thermalization is experimentally verified for the first time. Our results facilitate understanding the origin of quantum statistical mechanics.