Minimum-Consumption Discrimination of Quantum States via Globally Optimal Adaptive Measurements.

Reducing the average resource consumption is the central quest in discriminating non-orthogonal quantum states for a fixed admissible error rate ϵ. The globally optimal fixed local projective measurement for this task is found to be different from that for previous minimum-error discrimination tasks [S. Slussarenko et al., Phys. Rev. Lett. 118, 030502 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.030502]. To achieve the ultimate minimum average consumption, here we develop a general globally optimal adaptive strategy (GOA) by subtly using the updated posterior probability, which works under any error rate requirements and any one-way measurement restrictions, and can be solved by a convergent iterative relation. First, under the local measurement restrictions, our GOA is solved to serve as the local bound, which saves 16.6 copies (24%) compared with the previously best globally optimal fixed local projective measurement. When the more powerful two-copy collective measurements are allowed, our GOA is experimentally demonstrated to beat the local bound by 3.9 copies (6.0%). By exploiting both adaptivity and collective measurements, our Letter marks an important step toward minimum-consumption quantum state discrimination.

Experimental Demonstration of Inequivalent Mutually Unbiased Bases.

Quantum measurements based on mutually unbiased bases (MUBs) play crucial roles in foundational studies and quantum information processing. It is known that there exist inequivalent MUBs, but little is known about their operational distinctions, not to say experimental demonstration. In this Letter, by virtue of a simple estimation problem, we experimentally demonstrate the operational distinctions between inequivalent triples of MUBs in dimension 4 based on high-precision photonic systems. The experimental estimation fidelities coincide well with the theoretical predictions with only 0.16% average deviation, which is 25 times less than the difference (4.1%) between the maximum estimation fidelity and the minimum estimation fidelity. Our experiments clearly demonstrate that inequivalent MUBs have different information extraction capabilities and different merits for quantum information processing.

Implementing quantum dimensionality reduction for non-Markovian stochastic simulation.

Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly non-Markovian processes - where the future behaviour depends on events that happened far in the past - must track copious amounts of information about past observations, requiring high-dimensional memories. Quantum technologies can ameliorate this cost, allowing models of the same processes with lower memory dimension than corresponding classical models. Here we implement such memory-efficient quantum models for a family of non-Markovian processes using a photonic setup. We show that with a single qubit of memory our implemented quantum models can attain higher precision than possible with any classical model of the same memory dimension. This heralds a key step towards applying quantum technologies in complex systems modelling.

Experimental quantification of dynamical coherence via entangling two qubits.

Coherence and entanglement are both the fundamental properties which quantify the degree of nonclassicality possessed in a quantum state. Recently coherence and entanglement are considered as a dynamical resource where the nonclassicality is strongly related to the amount of the static resources which can be generated in a quantum process. In [Phys. Rev. Lett.125, 130401 (2020)10.1103/PhysRevLett.125.130401], for the first time, the authors study the interconvertability of these two kinds of dynamical resources. Here, we demonstrate this resource conversion in an all optical setup, and successfully observe the dynamical resource conversion. The experimental observation prove the ability of manipulating dynamical resource within current quantum photonic technologies.

Efficient Experimental Verification of Quantum Gates with Local Operations.

Verifying the correct functioning of quantum gates is a crucial step toward reliable quantum information processing, but it becomes an overwhelming challenge as the system size grows due to the dimensionality curse. Recent theoretical breakthroughs show that it is possible to verify various important quantum gates with the optimal sample complexity of O(1/ε) using local operations only, where ε is the estimation precision. In this Letter, we propose a variant of quantum gate verification (QGV) that is robust to practical gate imperfections and experimentally realize efficient QGV on a 2-qubit controlled-not gate and a 3-qubit Toffoli gate using only local state preparations and measurements. The experimental results show that, by using only 1600 and 2600 measurements on average, we can verify with 95% confidence level that the implemented controlled-not gate and Toffoli gate have fidelities of at least 99% and 97%, respectively. Demonstrating the superior low sample complexity and experimental feasibility of QGV, our work promises a solution to the dimensionality curse in verifying large quantum devices in the quantum era.

Nonlocality, Steering, and Quantum State Tomography in a Single Experiment.

We investigate whether paradigmatic measurements for quantum state tomography, namely mutually unbiased bases and symmetric informationally complete measurements, can be employed to certify quantum correlations. For this purpose, we identify a simple and noise-robust correlation witness for entanglement detection, steering, and nonlocality that can be evaluated based on the outcome statistics obtained in the tomography experiment. This allows us to perform state tomography on entangled qutrits, a test of Einstein-Podolsky-Rosen steering and a Bell inequality test, all within a single experiment. We also investigate the trade-off between quantum correlations and subsets of tomographically complete measurements as well as the quantification of entanglement in the different scenarios. Finally, we perform a photonics experiment in which we demonstrate quantum correlations under these flexible assumptions, namely with both parties trusted, one party untrusted and both parties untrusted.

"Super-Heisenberg" and Heisenberg Scalings Achieved Simultaneously in the Estimation of a Rotating Field.

The Heisenberg scaling, which scales as N^{-1} in terms of the number of particles or T^{-1} in terms of the evolution time, serves as a fundamental limit in quantum metrology. Better scalings, dubbed as "super-Heisenberg scaling," however, can also arise when the generator of the parameter involves many-body interactions or when it is time dependent. All these different scalings can actually be seen as manifestations of the Heisenberg uncertainty relations. While there is only one best scaling in the single-parameter quantum metrology, different scalings can coexist for the estimation of multiple parameters, which can be characterized by multiple Heisenberg uncertainty relations. We demonstrate the coexistence of two different scalings via the simultaneous estimation of the magnitude and frequency of a field where the best precisions, characterized by two Heisenberg uncertainty relations, scale as T^{-1} and T^{-2}, respectively (in terms of the standard deviation). We show that the simultaneous saturation of two Heisenberg uncertainty relations can be achieved by the optimal protocol, which prepares the optimal probe state, implements the optimal control, and performs the optimal measurement. The optimal protocol is experimentally implemented on an optical platform that demonstrates the saturation of the two Heisenberg uncertainty relations simultaneously, with up to five controls. As the first demonstration of simultaneously achieving two different Heisenberg scalings, our study deepens the understanding on the connection between the precision limit and the uncertainty relations, which has wide implications in practical applications of multiparameter quantum estimation.

Operational Resource Theory of Imaginarity.

Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems and their dynamics and interaction. Since the inception of quantum theory, it has been debated whether complex numbers are essential or whether an alternative consistent formulation is possible using real numbers only. Here, we attack this long-standing problem theoretically and experimentally, using the powerful tools of quantum resource theories. We show that, under reasonable assumptions, quantum states are easier to create and manipulate if they only have real elements. This gives an operational meaning to the resource theory of imaginarity. We identify and answer several important questions, which include the state-conversion problem for all qubit states and all pure states of any dimension and the approximate imaginarity distillation for all quantum states. As an application, we show that imaginarity plays a crucial role in state discrimination, that is, there exist real quantum states that can be perfectly distinguished via local operations and classical communication but that cannot be distinguished with any nonzero probability if one of the parties has no access to imaginarity. We confirm this phenomenon experimentally with linear optics, discriminating different two-photon quantum states by local projective measurements. Our results prove that complex numbers are an indispensable part of quantum mechanics.

Zero-trade-off multiparameter quantum estimation via simultaneously saturating multiple Heisenberg uncertainty relations.

Quantum estimation of a single parameter has been studied extensively. Practical applications, however, typically involve multiple parameters, for which the ultimate precision is much less understood. Here, by relating the precision limit directly to the Heisenberg uncertainty relation, we show that to achieve the highest precisions for multiple parameters at the same time requires the saturation of multiple Heisenberg uncertainty relations simultaneously. Guided by this insight, we experimentally demonstrate an optimally controlled multipass scheme, which saturates three Heisenberg uncertainty relations simultaneously and achieves the highest precisions for the estimation of all three parameters in SU(2) operators. With eight controls, we achieve a 13.27-dB improvement in terms of the variance (6.63 dB for the SD) over the classical scheme with the same loss. As an experiment demonstrating the simultaneous achievement of the ultimate precisions for multiple parameters, our work marks an important step in multiparameter quantum metrology with wide implications.

Testing a quantum error-correcting code on various platforms.

Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high fidelity. Here we propose a simple quantum error-correcting code for the detected amplitude damping channel. The code requires only two qubits. We implement the encoding, the channel, and the recovery on an optical platform, the IBM Q System, and a nuclear magnetic resonance system. For all of these systems, the error correction advantage appears when the damping rate exceeds some threshold. We compare the features of these quantum information processing systems used and demonstrate the advantage of quantum error correction on current quantum computing platforms.

Minimizing Backaction through Entangled Measurements.

When an observable is measured on an evolving coherent quantum system twice, the first measurement generally alters the statistics of the second one, which is known as measurement backaction. We introduce, and push to its theoretical and experimental limits, a novel method of backaction evasion, whereby entangled collective measurements are performed on several copies of the system. This method is inspired by a similar idea designed for the problem of measuring quantum work [Perarnau-Llobet et al., Phys. Rev. Lett. 118, 070601 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.070601]. By using entanglement as a resource, we show that the backaction can be extremely suppressed compared to all previous schemes. Importantly, the backaction can be eliminated in highly coherent processes.

Minimal Tradeoff and Ultimate Precision Limit of Multiparameter Quantum Magnetometry under the Parallel Scheme.

The precise measurement of a magnetic field is one of the most fundamental and important tasks in quantum metrology. Although extensive studies on quantum magnetometry have been carried out over past decades, the ultimate precision that can be achieved for the estimation of all three components of a magnetic field under the parallel scheme remains unknown. This is largely due to the lack of understandings on the incompatibility of the optimal probe states for the estimation of the three components. Here we provide an approach to characterize the minimal tradeoff among the precisions of multiple parameters that arise from the incompatibility of the optimal probe states, which leads to the identification of the ultimate precision limit for the estimation of all three components of a magnetic field under the parallel scheme. The optimal probe state that achieves the ultimate precision is also explicitly constructed. The obtained precision sets a benchmark on the precision of the multiparameter quantum magnetometry under the parallel scheme, which is of fundamental interest and importance in quantum metrology.

Experimental Optimal Orienteering via Parallel and Antiparallel Spins.

Antiparallel spins are superior in orienteering to parallel spins. This intriguing phenomenon is tied to entanglement associated with quantum measurements rather than quantum states. Using photonic systems, we experimentally realize the optimal orienteering protocols based on parallel spins and antiparallel spins, respectively. The optimal entangling measurements for decoding the direction information from parallel spins and antiparallel spins are realized using photonic quantum walks, which is a useful idea that is of wide interest in quantum information processing and foundational studies. Our experiments clearly demonstrate the advantage of antiparallel spins over parallel spins in orienteering. In addition, entangling measurements can extract more information than local measurements even if no entanglement is present in the quantum states.

Control-Enhanced Sequential Scheme for General Quantum Parameter Estimation at the Heisenberg Limit.

The advantage of quantum metrology has been experimentally demonstrated for phase estimations where the dynamics are commuting. General noncommuting dynamics, however, can have distinct features. For example, the direct sequential scheme, which can achieve the Heisenberg scaling for the phase estimation under commuting dynamics, can have even worse performances than the classical scheme when the dynamics are noncommuting. Here we realize a scalable optimally controlled sequential scheme, which can achieve the Heisenberg precision under general noncommuting dynamics. We also present an intuitive geometrical framework for the controlled scheme and identify sweet spots in time at which the optimal controls used in the scheme can be prefixed without adaptation, which simplifies the experimental protocols significantly. We successfully implement the scheme up to eight controls in an optical platform and demonstrate a precision near the Heisenberg limit. Our work opens the avenue for harvesting the power of quantum control in quantum metrology, and provides a control-enhanced recipe to achieve the Heisenberg precision under general noncommuting dynamics.

Entanglement Detection by Violations of Noisy Uncertainty Relations: A Proof of Principle.

It is well known that the violation of a local uncertainty relation can be used as an indicator for the presence of entanglement. Unfortunately, the practical use of these nonlinear witnesses has been limited to few special cases in the past. However, new methods for computing uncertainty bounds have become available. Here we report on an experimental implementation of uncertainty-based entanglement witnesses, benchmarked in a regime dominated by strong local noise. We combine the new computational method with a local noise tomography in order to design noise-adapted entanglement witnesses. This proof-of-principle experiment shows that quantum noise can be successfully handled by a fully quantum model in order to enhance the ability to detect entanglement.

Experimentally reducing the quantum measurement back action in work distributions by a collective measurement.

In quantum thermodynamics, the standard approach to estimating work fluctuations in unitary processes is based on two projective measurements, one performed at the beginning of the process and one at the end. The first measurement destroys any initial coherence in the energy basis, thus preventing later interference effects. To decrease this back action, a scheme based on collective measurements has been proposed by Perarnau-Llobet et al. Here, we report its experimental implementation in an optical system. The experiment consists of a deterministic collective measurement on two identically prepared qubit states, encoded in the polarization and path degree of a single photon. The standard two-projective measurement approach is also experimentally realized for comparison. Our results show the potential of collective schemes to decrease the back action of projective measurements, and capture subtle effects arising from quantum coherence.

Experimental Cyclic Interconversion between Coherence and Quantum Correlations.

Quantum resource theories seek to quantify sources of nonclassicality that bestow quantum technologies their operational advantage. Chief among these are studies of quantum correlations and quantum coherence. The former isolates nonclassicality in the correlations between systems, and the latter captures nonclassicality of quantum superpositions within a single physical system. Here, we present a scheme that cyclically interconverts between these resources without loss. The first stage converts coherence present in an input system into correlations with an ancilla. The second stage harnesses these correlations to restore coherence on the input system by measurement of the ancilla. We experimentally demonstrate this interconversion process using linear optics. Our experiment highlights the connection between nonclassicality of correlations and nonclassicality within local quantum systems and provides potential flexibilities in exploiting one resource to perform tasks normally associated with the other.

Observation of Stronger-than-Binary Correlations with Entangled Photonic Qutrits.

We present the first experimental confirmation of the quantum-mechanical prediction of stronger-than-binary correlations. These are correlations that cannot be explained under the assumption that the occurrence of a particular outcome of an n≥3-outcome measurement is due to a two-step process in which, in the first step, some classical mechanism precludes n-2 of the outcomes and, in the second step, a binary measurement generates the outcome. Our experiment uses pairs of photonic qutrits distributed between two laboratories, where randomly chosen three-outcome measurements are performed. We report a violation by 9.3 standard deviations of the optimal inequality for nonsignaling binary correlations.

Deterministic realization of collective measurements via photonic quantum walks.

Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here, we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity 0.9946 without post selection. As an application, we achieve the highest tomographic efficiency in qubit state tomography to date. Our work offers an effective recipe for beating the precision limit of local measurements in quantum state tomography and metrology. In addition, our study opens an avenue for harvesting the power of collective measurements in quantum information-processing and for exploring the intriguing physics behind this power.

Experimental demonstration of wave-particle duality relation based on coherence measure.

Wave-particle duality is a typical example of Bohr's complementarity principle that plays a significant role in quantum mechanics. Previous studies used the visibility of an interference pattern to quantify the wave property and used path information to quantify the particle property. However, coherence is the core and basis of the interference phenomenon. If we could use coherence to characterize the wave property, the understanding of wave-particle duality would be strengthened. A recent theoretical work [ Phys. Rev. Lett.116, 160406 (2016)] found two relations between quantum coherence and path information. Here, we demonstrate the new measure of wave-particle duality based on two kinds of coherence measures quantitatively for the first time. The wave property, quantified by the coherence in the l1-norm measure and the relative entropy measure, can be obtained via tomography of the target state, which is encoded in the path degree of freedom of the photons. The particle property, quantified by the path information, can be obtained via the discrimination of detector states, which is encoded in the polarization degree of freedom of the photons. Our work may deepen people's understanding of coherence and provide a new perspective regarding wave-particle duality.