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One of the most sought-after goals in experimental quantum communication is the implementation of a quantum repeater. The performance of quantum repeaters can be assessed by comparing the attained rate with the quantum and private capacity of direct transmission, assisted by unlimited classical two-way communication. However, these quantities are hard to compute, motivating the search for upper bounds. Takeoka, Guha and Wilde found the squashed entanglement of a quantum channel to be an upper bound on both these capacities. In general it is still hard to find the exact value of the squashed entanglement of a quantum channel, but clever sub-optimal squashing channels allow one to upper bound this quantity, and thus also the corresponding capacities. Here, we exploit this idea to obtain bounds for any phase-insensitive Gaussian bosonic channel. This bound allows one to benchmark the implementation of quantum repeaters for a large class of channels used to model communication across fibers. In particular, our bound is applicable to the realistic scenario when there is a restriction on the mean photon number on the input. Furthermore, we show that the squashed entanglement of a channel is convex in the set of channels, and we use a connection between the squashed entanglement of a quantum channel and its entanglement assisted classical capacity. Building on this connection, we obtain the exact squashed entanglement and two-way assisted capacities of the d-dimensional erasure channel and bounds on the amplitude-damping channel and all qubit Pauli channels. In particular, our bound improves on the previous best known squashed entanglement upper bound of the depolarizing channel.

Quantum thermodynamics is a research field that aims at fleshing out the ultimate limits of thermodynamic processes in the deep quantum regime. A complete picture of thermodynamical processes naturally allows for auxiliary systems dubbed 'catalysts', i.e., any physical systems facilitating state transformations while remaining essentially intact in their state, like an auxiliary system, a clock, or an actual catalyst. In this work, we present a comprehensive analysis of the power and limitation of such thermal catalysis. Specifically, we provide a family of optimal catalysts that can be returned with minimal trace distance error after facilitating a state transformation process. To incorporate the genuine physical role of a catalyst, we identify very significant restrictions on arbitrary state transformations under dimension or mean energy bounds, using methods of convex relaxations. We discuss the implication of these findings on possible thermodynamic state transformations in the quantum regime.

A Bell experiment that is ‘loophole’ free—leaving no room for explanations based on experimental imperfections—reveals a statistically significant conflict with local realism A new test of the Bell inequality The celebrated Bell inequality, a theorem published by John Bell in 1964, has long served as a basis for experimentally testing whether nature satisfies local realism. All experiments conducted to date have implied rejection of local-realist hypotheses. But because of experimental limitations all those tests suffered from loopholes — either the locality or the detection loophole. Here, Ronald Hanson and colleagues perform a Bell test that closes these loopholes. Their results are consistent with a violation of the inequality, although the authors reject local-realist hypotheses by two standard deviations only. The experimental setup allows for improvements in the statistics that may consolidate the result. In addition to its fundamental importance, a loophole-free Bell test is an important building block in quantum information processing. More than 50 years ago 1 , John Bell proved that no theory of nature that obeys locality and realism 2 can reproduce all the predictions of quantum theory: in any local-realist theory, the correlations between outcomes of measurements on distant particles satisfy an inequality that can be violated if the particles are entangled. Numerous Bell inequality tests have been reported 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ; however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in ‘loopholes’ 13 , 14 , 15 , 16 . Here we report a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell’s inequality. We use an event-ready scheme 17 , 18 , 19 that enables the generation of robust entanglement between distant electron spins (estimated state fidelity of 0.92 ± 0.03). Efficient spin read-out avoids the fair-sampling assumption (detection loophole 14 , 15 ), while the use of fast random-basis selection and spin read-out combined with a spatial separation of 1.3 kilometres ensure the required locality conditions 13 . We performed 245 trials that tested the CHSH–Bell inequality 20 S ≤ 2 and found S = 2.42 ± 0.20 (where S quantifies the correlation between measurement outcomes). A null-hypothesis test yields a probability of at most P = 0.039 that a local-realist model for space-like separated sites could produce data with a violation at least as large as we observe, even when allowing for memory 16 , 21 in the devices. Our data hence imply statistically significant rejection of the local-realist null hypothesis. This conclusion may be further consolidated in future experiments; for instance, reaching a value of P = 0.001 would require approximately 700 trials for an observed S = 2.4. With improvements, our experiment could be used for testing less-conventional theories, and for implementing device-independent quantum-secure communication 22 and randomness certification 23 , 24 .

Scaling current quantum communication demonstrations to a large-scale quantum network will require not only advancements in quantum hardware capabilities, but also robust control of such devices to bridge the gap in user demand. Moreover, the abstraction of tasks and services offered by the quantum network should enable platform-independent applications to be executed without the knowledge of the underlying physical implementation. Here we experimentally demonstrate, using remote solid-state quantum network nodes, a link layer, and a physical layer protocol for entanglement-based quantum networks. The link layer abstracts the physical-layer entanglement attempts into a robust, platform-independent entanglement delivery service. The system is used to run full state tomography of the delivered entangled states, as well as preparation of a remote qubit state on a server by its client. Our results mark a clear transition from physics experiments to quantum communication systems, which will enable the development and testing of components of future quantum networks.

We report the first complete characterization of single-qubit and two-qubit gate fidelities in silicon-based spin qubits, including cross talk and error correlations between the two qubits. To do so, we use a combination of standard randomized benchmarking and a recently introduced method called character randomized benchmarking, which allows for more reliable estimates of the two-qubit fidelity in this system, here giving a 92% fidelity estimate for the controlled-Zgate. Interestingly, with character randomized benchmarking, the two-qubit gate fidelity can be obtained by studying the additional decay induced by interleaving the two-qubit gate in a reference sequence of single-qubit gates only. This work sets the stage for further improvements in all the relevant gate fidelities in silicon spin qubits beyond the error threshold for fault-tolerant quantum computation.

The recently reported violation of a Bell inequality using entangled electronic spins in diamonds (Hensen et al ., Nature 526, 682–686) provided the first loophole-free evidence against local-realist theories of nature. Here we report on data from a second Bell experiment using the same experimental setup with minor modifications. We find a violation of the CHSH-Bell inequality of 2.35 ± 0.18, in agreement with the first run, yielding an overall value of S  = 2.38 ± 0.14. We calculate the resulting P -values of the second experiment and of the combined Bell tests. We provide an additional analysis of the distribution of settings choices recorded during the two tests, finding that the observed distributions are consistent with uniform settings for both tests. Finally, we analytically study the effect of particular models of random number generator (RNG) imperfection on our hypothesis test. We find that the winning probability per trial in the CHSH game can be bounded knowing only the mean of the RNG bias. This implies that our experimental result is robust for any model underlying the estimated average RNG bias, for random bits produced up to 690 ns too early by the random number generator.

Quantum mechanics and the theory of gravity are presently not compatible. A particular question is whether gravity causes decoherence. Several models for gravitational decoherence have been proposed, not all of which can be described quantum mechanically. Since quantum mechanics may need to be modified, one may question the use of quantum mechanics as a calculational tool to draw conclusions from the data of experiments concerning gravity. Here we propose a general method to estimate gravitational decoherence in an experiment that allows us to draw conclusions in any physical theory where the no-signalling principle holds, even if quantum mechanics needs to be modified. As an example, we propose a concrete experiment using optomechanics. Our work raises the interesting question whether other properties of nature could similarly be established from experimental observations alone—that is, without already having a rather well-formed theory of nature to make sense of experimental data. Whether gravity causes decoherence is a natural question on the way of making quantum physics compatible with the theory of gravity. Here the authors devise a general method to estimate gravitational decoherence in any no-signalling physical theory, which holds even if quantum mechanics would be modified.

The goal of future quantum networks is to enable new internet applications that are impossible to achieve using only classical communication 1 , 2 – 3 . Up to now, demonstrations of quantum network applications 4 , 5 – 6 and functionalities 7 , 8 , 9 , 10 , 11 – 12 on quantum processors have been performed in ad hoc software that was specific to the experimental setup, programmed to perform one single task (the application experiment) directly into low-level control devices using expertise in experimental physics. Here we report on the design and implementation of an architecture capable of executing quantum network applications on quantum processors in platform-independent high-level software. We demonstrate the capability of the architecture to execute applications in high-level software by implementing it as a quantum network operating system—QNodeOS—and executing test programs, including a delegated computation from a client to a server 13 on two quantum network nodes based on nitrogen-vacancy (NV) centres in diamond 14 , 15 . We show how our architecture allows us to maximize the use of quantum network hardware by multitasking different applications. Our architecture can be used to execute programs on any quantum processor platform corresponding to our system model, which we illustrate by demonstrating an extra driver for QNodeOS for a trapped-ion quantum network node based on a single 40 Ca + atom 16 . Our architecture lays the groundwork for computer science research in quantum network programming and paves the way for the development of software that can bring quantum network technology to society. A new quantum operating system architecture is described that is capable of executing applications on quantum networks in high-level software, which is a step towards bringing quantum network technology to society.

Cryptography’s importance in our everyday lives continues to grow in our increasingly digital world. Oblivious transfer has long been a fundamental and important cryptographic primitive, as it is known that general two-party cryptographic tasks can be built from this basic building block. Here we show the experimental implementation of a 1-2 random oblivious transfer protocol by performing measurements on polarization-entangled photon pairs in a modified entangled quantum key distribution system, followed by all of the necessary classical postprocessing including one-way error correction. We successfully exchange a 1,366 bit random oblivious transfer string in ~3 min and include a full security analysis under the noisy storage model, accounting for all experimental error rates and finite size effects. This demonstrates the feasibility of using today’s quantum technologies to implement secure two-party protocols. The oblivious transfer protocol is a cryptographic primitive used to create many different secure two-party schemes. Here, Erven et al . provide the first implementation of the oblivious transfer protocol using entangled photons, within the noisy storage model.