Nonlocality activation in a photonic quantum network.

Bell nonlocality refers to correlations between two distant, entangled particles that challenge classical notions of local causality. Beyond its foundational significance, nonlocality is crucial for device-independent technologies like quantum key distribution and randomness generation. Nonlocality quickly deteriorates in the presence of noise, and restoring nonlocal correlations requires additional resources. These often come in the form of many instances of the input state and joint measurements, incurring a significant resource overhead. Here, we experimentally demonstrate that single copies of Bell-local states, incapable of violating any standard Bell inequality, can give rise to nonlocality after being embedded into a quantum network of multiple parties. We subject the initial entangled state to a quantum channel that broadcasts part of the state to two independent receivers and certify the nonlocality in the resulting network by violating a tailored Bell-like inequality. We obtain these results without making any assumptions about the prepared states, the quantum channel, or the validity of quantum theory. Our findings have fundamental implications for nonlocality and enable the practical use of nonlocal correlations in real-world applications, even in scenarios dominated by noise.

Quantum channel correction outperforming direct transmission.

Long-distance optical quantum channels are necessarily lossy, leading to errors in transmitted quantum information, entanglement degradation and, ultimately, poor protocol performance. Quantum states carrying information in the channel can be probabilistically amplified to compensate for loss, but are destroyed when amplification fails. Quantum correction of the channel itself is therefore required, but break-even performance-where arbitrary states can be better transmitted through a corrected channel than an uncorrected one-has so far remained out of reach. Here we perform distillation by heralded amplification to improve a noisy entanglement channel. We subsequently employ entanglement swapping to demonstrate that arbitrary quantum information transmission is unconditionally improved-i.e., without relying on postselection or post-processing of data-compared to the uncorrected channel. In this way, it represents realization of a genuine quantum relay. Our channel correction for single-mode quantum states will find use in quantum repeater, communication and metrology applications.

Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity.

Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication complexity. Recently, a novel quantum resource called the quantum switch-which creates a coherent superposition of the causal order of events, known as quantum causality-has been harnessed theoretically in a new protocol providing provable exponential separation. We experimentally demonstrate such an advantage by realizing a superposition of communication directions for a two-party distributed computation. Our photonic demonstration employs d-dimensional quantum systems, qudits, up to d=2^{13} dimensions and demonstrates a communication complexity advantage, requiring less than (0.696±0.006) times the communication of any causally ordered protocol. These results elucidate the crucial role of the coherence of communication direction in achieving the exponential separation for the one-way processing task, and open a new path for experimentally exploring the fundamentals and applications of advanced features of indefinite causal structures.

Interfering trajectories in experimental quantum-enhanced stochastic simulation.

Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. Recent work has established a quantum advantage in stochastic simulation, leading to quantum devices that execute a simulation using less memory than possible by classical means. To realise this advantage it is essential that the memory register remains coherent, and coherently interacts with the processor, allowing the simulator to operate over many time steps. Here we report a multi-time-step experimental simulation of a stochastic process using less memory than the classical limit. A key feature of the photonic quantum information processor is that it creates a quantum superposition of all possible future trajectories that the system can evolve into. This superposition allows us to introduce, and demonstrate, the idea of comparing statistical futures of two classical processes via quantum interference. We demonstrate interference of two 16-dimensional quantum states, representing statistical futures of our process, with a visibility of 0.96 ± 0.02.

Experimental Validation of Quantum Steering Ellipsoids and Tests of Volume Monogamy Relations.

The set of all qubit states that can be steered to by measurements on a correlated qubit is predicted to form an ellipsoid-called the quantum steering ellipsoid-in the Bloch ball. This ellipsoid provides a simple visual characterization of the initial two-qubit state, and various aspects of entanglement are reflected in its geometric properties. We experimentally verify these properties via measurements on many different polarization-entangled photonic qubit states. Moreover, for pure three-qubit states, the volumes of the two quantum steering ellipsoids generated by measurements on the first qubit are predicted to satisfy a tight monogamy relation, which is strictly stronger than the well-known monogamy of entanglement for concurrence. We experimentally verify these predictions, using polarization and path entanglement. We also show experimentally that this monogamy relation can be violated by a mixed entangled state, which nevertheless satisfies a weaker monogamy relation.

Experimental Realization of a Quantum Autoencoder: The Compression of Qutrits via Machine Learning.

With quantum resources a precious commodity, their efficient use is highly desirable. Quantum autoencoders have been proposed as a way to reduce quantum memory requirements. Generally, an autoencoder is a device that uses machine learning to compress inputs, that is, to represent the input data in a lower-dimensional space. Here, we experimentally realize a quantum autoencoder, which learns how to compress quantum data using a classical optimization routine. We demonstrate that when the inherent structure of the dataset allows lossless compression, our autoencoder reduces qutrits to qubits with low error levels. We also show that the device is able to perform with minimal prior information about the quantum data or physical system and is robust to perturbations during its optimization routine.

An experimental quantum Bernoulli factory.

There has been a concerted effort to identify problems computable with quantum technology, which are intractable with classical technology or require far fewer resources to compute. Recently, randomness processing in a Bernoulli factory has been identified as one such task. Here, we report two quantum photonic implementations of a Bernoulli factory, one using quantum coherence and single-qubit measurements and the other one using quantum coherence and entangling measurements of two qubits. We show that the former consumes three orders of magnitude fewer resources than the best-known classical method, while entanglement offers a further fivefold reduction. These concepts may provide a means for quantum-enhanced performance in the simulation of stochastic processes and sampling tasks.

Experimental optical phase measurement approaching the exact Heisenberg limit.

The use of quantum resources can provide measurement precision beyond the shot-noise limit (SNL). The task of ab initio optical phase measurement-the estimation of a completely unknown phase-has been experimentally demonstrated with precision beyond the SNL, and even scaling like the ultimate bound, the Heisenberg limit (HL), but with an overhead factor. However, existing approaches have not been able-even in principle-to achieve the best possible precision, saturating the HL exactly. Here we demonstrate a scheme to achieve true HL phase measurement, using a combination of three techniques: entanglement, multiple samplings of the phase shift, and adaptive measurement. Our experimental demonstration of the scheme uses two photonic qubits, one double passed, so that, for a successful coincidence detection, the number of photon-passes is N = 3. We achieve a precision that is within 4% of the HL. This scheme can be extended to higher N and other physical systems.

Conclusive Experimental Demonstration of One-Way Einstein-Podolsky-Rosen Steering.

Einstein-Podolsky-Rosen steering is a quantum phenomenon wherein one party influences, or steers, the state of a distant party's particle beyond what could be achieved with a separable state, by making measurements on one-half of an entangled state. This type of quantum nonlocality stands out through its asymmetric setting and even allows for cases where one party can steer the other but where the reverse is not true. A series of experiments have demonstrated one-way steering in the past, but all were based on significant limiting assumptions. These consisted either of restrictions on the type of allowed measurements or of assumptions about the quantum state at hand, by mapping to a specific family of states and analyzing the ideal target state rather than the real experimental state. Here, we present the first experimental demonstration of one-way steering free of such assumptions. We achieve this using a new sufficient condition for nonsteerability and, although not required by our analysis, using a novel source of extremely high-quality photonic Werner states.

Strong Unitary and Overlap Uncertainty Relations: Theory and Experiment.

We derive and experimentally investigate a strong uncertainty relation valid for any n unitary operators, which implies the standard uncertainty relation and others as special cases, and which can be written in terms of geometric phases. It is saturated by every pure state of any n-dimensional quantum system, generates a tight overlap uncertainty relation for the transition probabilities of any n+1 pure states, and gives an upper bound for the out-of-time-order correlation function. We test these uncertainty relations experimentally for photonic polarization qubits, including the minimum uncertainty states of the overlap uncertainty relation, via interferometric measurements of generalized geometric phases.

Heralded quantum steering over a high-loss channel.

Entanglement is the key resource for many long-range quantum information tasks, including secure communication and fundamental tests of quantum physics. These tasks require robust verification of shared entanglement, but performing it over long distances is presently technologically intractable because the loss through an optical fiber or free-space channel opens up a detection loophole. We design and experimentally demonstrate a scheme that verifies entanglement in the presence of at least 14.8 ± 0.1 dB of added loss, equivalent to approximately 80 km of telecommunication fiber. Our protocol relies on entanglement swapping to herald the presence of a photon after the lossy channel, enabling event-ready implementation of quantum steering. This result overcomes the key barrier in device-independent communication under realistic high-loss scenarios and in the realization of a quantum repeater.

Erratum: Quantum State Discrimination Using the Minimum Average Number of Copies [Phys. Rev. Lett. 118, 030502 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.118.030502.

Experimental demonstration of nonbilocal quantum correlations.

Quantum mechanics admits correlations that cannot be explained by local realistic models. The most studied models are the standard local hidden variable models, which satisfy the well-known Bell inequalities. To date, most works have focused on bipartite entangled systems. We consider correlations between three parties connected via two independent entangled states. We investigate the new type of so-called "bilocal" models, which correspondingly involve two independent hidden variables. These models describe scenarios that naturally arise in quantum networks, where several independent entanglement sources are used. Using photonic qubits, we build such a linear three-node quantum network and demonstrate nonbilocal correlations by violating a Bell-like inequality tailored for bilocal models. Furthermore, we show that the demonstration of nonbilocality is more noise-tolerant than that of standard Bell nonlocality in our three-party quantum network.

Experimentally modeling stochastic processes with less memory by the use of a quantum processor.

Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. However, the most interesting systems are often so complex that simulating their future behavior demands storing immense amounts of information regarding how they have behaved in the past. For increasingly complex systems, simulation becomes increasingly difficult and is ultimately constrained by resources such as computer memory. Recent theoretical work shows that quantum theory can reduce this memory requirement beyond ultimate classical limits, as measured by a process' statistical complexity, C. We experimentally demonstrate this quantum advantage in simulating stochastic processes. Our quantum implementation observes a memory requirement of Cq = 0.05 ± 0.01, far below the ultimate classical limit of C = 1. Scaling up this technique would substantially reduce the memory required in simulations of more complex systems.

Quantum State Discrimination Using the Minimum Average Number of Copies.

In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the average error probability for fixed resources. Here we introduce a new state discrimination task: minimizing the average resources for a fixed admissible error probability. We show that this new task is not performed optimally by previously known strategies, and derive and experimentally test a detection scheme that performs better.

Efficient and pure femtosecond-pulse-length source of polarization-entangled photons.

We present a source of polarization entangled photon pairs based on spontaneous parametric downconversion engineered for frequency uncorrelated telecom photon generation. Our source provides photon pairs that display, simultaneously, the key properties for high-performance quantum information and fundamental quantum science tasks. Specifically, the source provides for high heralding efficiency, high quantum state purity and high entangled state fidelity at the same time. Among different tests we apply to our source we observe almost perfect non-classical interference between photons from independent sources with a visibility of (100 ± 5)%.

Observation of Genuine One-Way Einstein-Podolsky-Rosen Steering.

Within the hierarchy of inseparable quantum correlations, Einstein-Podolsky-Rosen steering is distinguished from both entanglement and Bell nonlocality by its asymmetry-there exist conditions where the steering phenomenon changes from being observable to not observable, simply by exchanging the role of the two measuring parties. While this one-way steering feature has been previously demonstrated for the restricted class of Gaussian measurements, for the general case of positive-operator-valued measures even its theoretical existence has only recently been settled. Here, we prove, and then experimentally observe, the one-way steerability of an experimentally practical class of entangled states in this general setting. As well as its foundational significance, the demonstration of fundamentally asymmetric nonlocality also has practical implications for the distribution of the trust in quantum communication networks.

A quantum Fredkin gate.

Minimizing the resources required to build logic gates into useful processing circuits is key to realizing quantum computers. Although the salient features of a quantum computer have been shown in proof-of-principle experiments, difficulties in scaling quantum systems have made more complex operations intractable. This is exemplified in the classical Fredkin (controlled-SWAP) gate for which, despite theoretical proposals, no quantum analog has been realized. By adding control to the SWAP unitary, we use photonic qubit logic to demonstrate the first quantum Fredkin gate, which promises many applications in quantum information and measurement. We implement example algorithms and generate the highest-fidelity three-photon Greenberger-Horne-Zeilinger states to date. The technique we use allows one to add a control operation to a black-box unitary, something that is impossible in the standard circuit model. Our experiment represents the first use of this technique to control a two-qubit operation and paves the way for larger controlled circuits to be realized efficiently.

Experimental measurement-device-independent verification of quantum steering.

Bell non-locality between distant quantum systems--that is, joint correlations which violate a Bell inequality--can be verified without trusting the measurement devices used, nor those performing the measurements. This leads to unconditionally secure protocols for quantum information tasks such as cryptographic key distribution. However, complete verification of Bell non-locality requires high detection efficiencies, and is not robust to typical transmission losses over long distances. In contrast, quantum or Einstein-Podolsky-Rosen steering, a weaker form of quantum correlation, can be verified for arbitrarily low detection efficiencies and high losses. The cost is that current steering-verification protocols require complete trust in one of the measurement devices and its operator, allowing only one-sided secure key distribution. Here we present measurement-device-independent steering protocols that remove this need for trust, even when Bell non-locality is not present. We experimentally demonstrate this principle for singlet states and states that do not violate a Bell inequality.

Experimental test of universal complementarity relations.

Complementarity restricts the accuracy with which incompatible quantum observables can be jointly measured. Despite popular conception, the Heisenberg uncertainty relation does not quantify this principle. We report the experimental verification of universally valid complementarity relations, including an improved relation derived here. We exploit Einstein-Poldolsky-Rosen correlations between two photonic qubits to jointly measure incompatible observables of one. The product of our measurement inaccuracies is low enough to violate the widely used, but not universally valid, Arthurs-Kelly relation.