A gated quantum dot strongly coupled to an optical microcavity.

The strong-coupling regime of cavity quantum electrodynamics (QED) represents the light-matter interaction at the fully quantum level. Adding a single photon shifts the resonance frequencies-a profound nonlinearity. Cavity QED is a test bed for quantum optics1-3 and the basis of photon-photon and atom-atom entangling gates4,5. At microwave frequencies, cavity QED has had a transformative effect6, enabling qubit readout and qubit couplings in superconducting circuits. At optical frequencies, the gates are potentially much faster; the photons can propagate over long distances and can be easily detected. Following pioneering work on single atoms1-3,7, solid-state implementations using semiconductor quantum dots are emerging8-15. However, miniaturizing semiconductor cavities without introducing charge noise and scattering losses remains a challenge. Here we present a gated, ultralow-loss, frequency-tunable microcavity device. The gates allow both the quantum dot charge and its resonance frequency to be controlled electrically. Furthermore, cavity feeding10,11,13-17, the observation of the bare-cavity mode even at the quantum dot-cavity resonance, is eliminated. Even inside the microcavity, the quantum dot has a linewidth close to the radiative limit. In addition to a very pronounced avoided crossing in the spectral domain, we observe a clear coherent exchange of a single energy quantum between the 'atom' (the quantum dot) and the cavity in the time domain (vacuum Rabi oscillations), whereas decoherence arises mainly via the atom and photon loss channels. This coherence is exploited to probe the transitions between the singly and doubly excited photon-atom system using photon-statistics spectroscopy18. The work establishes a route to the development of semiconductor-based quantum photonics, such as single-photon sources and photon-photon gates.

Partial Self-Testing and Randomness Certification in the Triangle Network.

Quantum nonlocality can be demonstrated without inputs (i.e., each party using a fixed measurement setting) in a network with independent sources. Here we consider this effect on ring networks, and show that the underlying quantum strategy can be partially characterized, or self-tested, from observed correlations. Applying these results to the triangle network allows us to show that the nonlocal distribution of Renou et al. [Phys. Rev. Lett. 123, 140401 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.140401] requires that (i) all sources produce a minimal amount of entanglement, (ii) all local measurements are entangled, and (iii) each local outcome features a minimal entropy. Hence we show that the triangle network allows for genuine network quantum nonlocality and certifiable randomness.

Unlimited One-Way Steering.

This work explores the asymmetry of quantum steering in a setup using high-dimensional entanglement. We construct entangled states with the following properties: (i) one party (Bob) can never steer the state of the other party (Alice), considering the most general measurements, and (ii) Alice can strongly steer the state of Bob, in the sense of demonstrating genuine high-dimensional steering. In other words, Alice can convince Bob that they share an entangled state of arbitrarily high Schmidt number, while Bob can never convince Alice that the state is even simply entangled. In this sense, one-way steering can become unlimited. A key result for our construction is a condition for the joint measurability of all high-dimensional measurements subjected to the combined effect of noise and loss, which is of independent interest.

Toward the Device-Independent Certification of a Quantum Memory.

Quantum memories represent one of the main ingredients of future quantum communication networks. Their certification is therefore a key challenge. Here we develop efficient certification methods for quantum memories. Considering a device-independent approach, where no a priori characterization of sources or measurement devices is required, we develop a robust self-testing method for quantum memories. We then illustrate the practical relevance of our technique in a relaxed scenario by certifying a fidelity of 0.87 in a recent solid-state ensemble quantum memory experiment. More generally, our methods apply for the characterization of any device implementing a qubit identity quantum channel.

Simulability of High-Dimensional Quantum Measurements.

We investigate the compression of quantum information with respect to a given set M of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from M and an arbitrary quantum state ρ are recovered exactly by first compressing ρ into a lower-dimensional space, followed by some quantum measurements. A full quantum compression is possible, i.e., leaving only classical information, if and only if the set M is jointly measurable. Our notion of simulability can thus be seen as a quantification of measurement incompatibility in terms of dimension. After defining these concepts, we provide an illustrative example involving mutually unbiased bases, and develop a method based on semidefinite programming for constructing simulation models. In turn we analytically construct optimal simulation models for all projective measurements subjected to white noise or losses. Finally, we discuss how our approach connects with other concepts introduced in the context of quantum channels and quantum correlations.

Certification of Genuine Multipartite Entanglement with General and Robust Device-Independent Witnesses.

Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.

Setting Up Experimental Bell Tests with Reinforcement Learning.

Finding optical setups producing measurement results with a targeted probability distribution is hard, as a priori the number of possible experimental implementations grows exponentially with the number of modes and the number of devices. To tackle this complexity, we introduce a method combining reinforcement learning and simulated annealing enabling the automated design of optical experiments producing results with the desired probability distributions. We illustrate the relevance of our method by applying it to a probability distribution favouring high violations of the Bell-Clauser-Horne-Shimony-Holt (CHSH) inequality. As a result, we propose new unintuitive experiments leading to higher Bell-CHSH inequality violations than the best currently known setups. Our method might positively impact the usefulness of photonic experiments for device-independent quantum information processing.

Noise-Resistant Device-Independent Certification of Bell State Measurements.

Device-independent certification refers to the characterization of an apparatus without reference to the internal description of other devices. It is a trustworthy certification method, free of assumption on the underlying Hilbert space dimension and on calibration methods. We show how it can be used to quantify the quality of a Bell-state measurement, whether deterministic, partial, or probabilistic. Our certification is noise resistant and opens the way towards the device-independent self-testing of Bell-state measurements in existing experiments.

Certifying the Building Blocks of Quantum Computers from Bell's Theorem.

Bell's theorem has been proposed to certify, in a device-independent and robust way, blocks either producing or measuring quantum states. In this Letter, we provide a method based on Bell's theorem to certify coherent operations for the storage, processing, and transfer of quantum information. This completes the set of tools needed to certify all building blocks of a quantum computer. Our method distinguishes itself by its robustness to experimental imperfections, and so could be used to certify that today's quantum devices are qualified for usage in future quantum computers.

Detecting Large Quantum Fisher Information with Finite Measurement Precision.

We propose an experimentally accessible scheme to determine the lower bounds on the quantum Fisher information (QFI), which ascertains multipartite entanglement or usefulness for quantum metrology. The scheme is based on comparing the measurement statistics of a state before and after a small unitary rotation. We argue that, in general, the limited resolution of collective observables prevents the detection of large QFI. This can be overcome by performing an additional operation prior to the measurement. We illustrate the power of this protocol for present-day spin-squeezing experiments, where the same operation used for the preparation of the initial spin-squeezed state improves also the measurement precision and hence the lower bound on the QFI by 2 orders of magnitude. We also establish a connection to the Leggett-Garg inequalities. We show how to simulate a variant of the inequalities with our protocol and demonstrate that large QFI is necessary for their violation with coarse-grained detectors.

How difficult is it to prove the quantumness of macroscropic states?

General wisdom tells us that if two quantum states are "macroscopically distinguishable" then their superposition should be hard to observe. We make this intuition precise and general by quantifying the difficulty to observe the quantum nature of a superposition of two states that can be distinguished without microscopic accuracy. First, we quantify the distinguishability of any given pair of quantum states with measurement devices lacking microscopic accuracy, i.e., measurements suffering from limited resolution or limited sensitivity. Next, we quantify the required stability that has to be fulfilled by any measurement setup able to distinguish their superposition from a mere mixture. Finally, by establishing a relationship between the stability requirement and the "distinguishability with inaccurate measurements" of the two superposed states, we demonstrate that, indeed, the more distinguishable the states are, the more demanding the stability requirements.

Witnessing trustworthy single-photon entanglement with local homodyne measurements.

Single-photon entangled states, i.e., states describing two optical paths sharing a single photon, constitute the simplest form of entanglement. Yet they provide a valuable resource in quantum information science. Specifically, they lie at the heart of quantum networks, as they can be used for quantum teleportation, swapped, and purified with linear optics. The main drawback of such entanglement is the difficulty in measuring it. Here, we present and experimentally test an entanglement witness allowing one to say whether a given state is path entangled and also that entanglement lies in the subspace, where the optical paths are each filled with one photon at most, i.e., refers to single-photon entanglement. It uses local homodyning only and relies on no assumption about the Hilbert space dimension of the measured system. Our work provides a simple and trustworthy method for verifying the proper functioning of future quantum networks.

Coarse graining makes it hard to see micro-macro entanglement.

Observing quantum effects such as superpositions and entanglement in macroscopic systems requires not only a system that is well protected against environmental decoherence, but also sufficient measurement precision. Motivated by recent experiments, we study the effects of coarse graining in photon number measurements on the observability of micro-macro entanglement that is created by greatly amplifying one photon from an entangled pair. We compare the results obtained for a unitary quantum cloner, which generates micro-macro entanglement, and for a measure-and-prepare cloner, which produces a separable micro-macro state. We show that the distance between the probability distributions of results for the two cloners approaches zero for a fixed moderate amount of coarse graining. Proving the presence of micro-macro entanglement therefore becomes progressively harder as the system size increases.

Quantum cloning for absolute radiometry.

In the quantum regime information can be copied with only a finite fidelity. This fidelity gradually increases to 1 as the system becomes classical. In this Letter we show how this fact can be used to directly measure the amount of radiated power. We demonstrate how these principles can be used to build a practical primary standard.

Towards quantum experiments with human eyes as detectors based on cloning via stimulated emission.

We show theoretically that a large Bell inequality violation can be obtained with human eyes as detectors, in a "micro-macro" experiment where one photon from an entangled pair is greatly amplified via stimulated emission. The violation is robust under photon loss. This leads to an apparent paradox, which we resolve by noting that the violation proves the existence of entanglement before the amplification. The same is true for the micro-macro experiments performed so far with conventional detectors. However, we also prove that there is genuine micro-macro entanglement even for high loss.