One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators, because of quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak value measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. In this Letter, we show how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them.

The physical impact and the testability of the Kochen-Specker (KS) theorem is debated because of the fact that perfect compatibility in a single quantum system cannot be achieved in practical experiments with finite precision. Here, we follow the proposal of A. Cabello and M. T. Cunha [Phys. Rev. Lett. 106, 190401 (2011)], and present a compatibility-loophole-free experimental violation of an inequality of noncontextual theories by two spatially separated entangled qutrits. A maximally entangled qutrit-qutrit state with a fidelity as high as $0.975\pm 0.001$ is prepared and distributed to separated spaces, and these two photons are then measured locally, providing the compatibility requirement. The results show that the inequality for noncontextual theory is violated by 31 standard deviations. Our experiments pave the way to close the debate about the testability of the KS theorem. In addition, the method to generate high-fidelity and high-dimension entangled states will provide significant advantages in high-dimension quantum encoding and quantum communication.

We use trapped atomic ions forming a hybrid Coulomb crystal and exploit its phonons to study an isolated quantum system composed of a single spin coupled to an engineered bosonic environment. We increase the complexity of the system by adding ions and controlling coherent couplings and, thereby, we observe the emergence of thermalization: Time averages of spin observables approach microcanonical averages while related fluctuations decay. Our platform features precise control of system size, coupling strength, and isolation from the external world to explore the dynamics of equilibration and thermalization.

The ability to live in coherent superpositions is a signature trait of quantum systems and constitutes an irreplaceable resource for quantum-enhanced technologies. However, decoherence effects usually destroy quantum superpositions. It was recently predicted that, in a composite quantum system exposed to dephasing noise, quantum coherence in a transversal reference basis can stay protected for an indefinite time. This can occur for a class of quantum states independently of the measure used to quantify coherence, and it requires no control on the system during the dynamics. Here, such an invariant coherence phenomenon is observed experimentally in two different setups based on nuclear magnetic resonance at room temperature, realizing an effective quantum simulator of two- and four-qubit spin systems. Our study further reveals a novel interplay between coherence and various forms of correlations, and it highlights the natural resilience of quantum effects in complex systems.

Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find the highest achievable precision with the given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in the quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter, we show that the sequential feedback scheme has a threefold improvement over the parallel scheme for Hamiltonian parameter estimations on two-dimensional systems, and an order of $O(d+1)$ improvement for Hamiltonian parameter estimation on $d$-dimensional systems. We also show that, contrary to the conventional belief, it is possible to simultaneously achieve the highest precision for estimating all three components of a magnetic field, which sets a benchmark on the local precision limit for the estimation of a magnetic field.

We show that it is possible to significantly reduce rank 2 tensor shifts of a clock transition by operating at a judiciously chosen magnetic-field-insensitive point. In some cases shifts are almost completely eliminated making the transition an effective $J=0$ to $J=0$ candidate. This significantly improves the feasibility of a recent proposal for clock operation with large ion crystals. For such multi-ion clocks, geometric constraints and selection rules naturally divide clock operation into two categories based on the orientation of the magnetic field. We discuss the limitations imposed on each type and how calibrations might be carried out for clock operation.

The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered systems in the many-body localized phase have power-law entanglement spectra, arising from the presence of extensively many local integrals of motion. The power-law entanglement spectrum distinguishes many-body localized systems from ergodic systems, as well as from ground states of gapped integrable models or free systems in the vicinity of scale-invariant critical points. We confirm our results using large-scale exact diagonalization. In addition, we develop a matrix-product state algorithm which allows us to access the eigenstates of large systems close to the localization transition, and discuss general implications of our results for variational studies of highly excited eigenstates in many-body localized systems.

We show that, for any $n$, there are $m$-outcome quantum correlations, with $m>n$, which are stronger than any nonsignaling correlation produced from selecting among $n$-outcome measurements. As a consequence, for any $n$, there are $m$-outcome quantum measurements that cannot be constructed by selecting locally from the set of $n$-outcome measurements. This is a property of the set of measurements in quantum theory that is not mandatory for general probabilistic theories. We also show that this prediction can be tested through high-precision Bell-type experiments and identify past experiments providing evidence that some of these strong correlations exist in nature. Finally, we provide a modified version of quantum theory restricted to having at most $n$-outcome quantum measurements.

Sudden changes are ubiquitous in nature. Identifying them is crucial for a number of applications in biology, medicine, and social sciences. Here we take the problem of detecting sudden changes to the quantum domain. We consider a source that emits quantum particles in a default state, until a point where a mutation occurs that causes the source to switch to another state. The problem is then to find out where the change occurred. We determine the maximum probability of correctly identifying the change point, allowing for collective measurements on the whole sequence of particles emitted by the source. Then, we devise online strategies where the particles are measured individually and an answer is provided as soon as a new particle is received. We show that these online strategies substantially underperform the optimal quantum measurement, indicating that quantum sudden changes, although happening locally, are better detected globally.

We analyze doubly magic trapping of Cs hyperfine transitions including previously neglected contributions from the ground state hyperpolarizability and the interaction of the laser light and a static magnetic field. Extensive numerical searches do not reveal any doubly magic trapping conditions for any pair of hyperfine states. However, including the hyperpolarizability reveals light intensity insensitive traps for a wide range of wavelengths at specific intensities. We then investigate the use of bichromatic trapping light fields. Deploying a bichromatic scheme, we demonstrate doubly magic red and blue detuned traps for pairs of states separated by one or two single photon transitions.

Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.

We apply laser fields to trapped atomic ions to constrain the quantum dynamics from a simultaneously applied global microwave field to an initial product state and a target entangled state. This approach comes under what has become known in the literature as “quantum Zeno dynamics” and we use it to prepare entangled states of two and three ions. With two trapped ${{}^9\mathrm{Be}}^{+}$ ions, we obtain Bell state fidelities up to $0.990_{-5}^{+2}$; with three ions, a $W$-state fidelity of $0.910_{-7}^{+4}$ is obtained. Compared to other methods of producing entanglement in trapped ions, this procedure can be relatively insensitive to certain imperfections such as fluctuations in laser intensity.

We propose a microwave frequency single-photon transistor which can operate under continuous wave probing and represents an efficient single microwave photon detector. It can be realized using an impedance matched system of a three level artificial ladder-type atom coupled to two microwave cavities connected to input-output waveguides. Using a classical drive on the upper transition, we find parameter space where a single photon control pulse incident on one of the cavities can be fully absorbed into hybridized excited states. This subsequently leads to series of quantum jumps in the upper manifold and the appearance of a photon flux leaving the second cavity through a separate input-output port. The proposal does not require time variation of the probe signals, thus corresponding to a passive version of a single-photon transistor. The resulting device is robust to qubit dephasing processes, possesses low dark count rate for large anharmonicity, and can be readily implemented using current technology.

We present two results which combined enable one to reliably detect multimode, multipartite entanglement in the presence of measurement errors. The first result leads to a method to compute the best (approximated) physical covariance matrix given a measured nonphysical one assuming that no additional information about the measurement is available except the standard deviations from the mean values. The other result states that a widely used entanglement condition is a consequence of negativity of partial transposition. Our approach can quickly verify the entanglement of experimentally obtained multipartite states, which is demonstrated on several realistic examples. Compared to existing detection schemes, ours is very simple and efficient. In particular, it does not require any complicated optimizations.

Boson sampling, the task of sampling the probability distribution of photons at the output of a photonic network, is believed to be hard for any classical device. Unlike other models of quantum computation that require thousands of qubits to outperform classical computers, boson sampling requires only a handful of single photons. However, a scalable implementation of boson sampling is missing. Here, we show how superconducting circuits provide such platform. Our proposal differs radically from traditional quantum-optical implementations: rather than injecting photons in waveguides, making them pass through optical elements like phase shifters and beam splitters, and finally detecting their output mode, we prepare the required multiphoton input state in a superconducting resonator array, control its dynamics via tunable and dispersive interactions, and measure it with nondemolition techniques.

The indeterminacy inherent in quantum measurements is an outstanding character of quantum theory, which manifests itself typically in the uncertainty principle. In the last decade, several universally valid forms of error-disturbance uncertainty relations were derived for completely general quantum measurements for arbitrary states. Subsequently, Branciard established a form that is optimal for spin measurements for some pure states. However, the bound in his inequality is not stringent for mixed states. One of the present authors recently derived a new bound tight in the corresponding mixed state case. Here, a neutron-optical experiment is carried out to investigate this new relation: it is tested whether error and disturbance of quantum measurements disappear or persist in mixing up the measured ensemble. The attainability of the new bound is experimentally observed, falsifying the tightness of Branciard’s bound for mixed spin states.