Quantum teleportation establishes a correspondence between an entangled state shared by two separate par- ties that can communicate classically and the presence of a quantum channel connecting the two parties. The standard benchmark for quantum teleportation, based on the average fidelity between the input and output states, indicates that some entangled states do not lead to channels which can be certified to be quantum. It was re- cently shown that if one considers a finer-tuned witness, then all entangled states can be certified to produce a non-classical teleportation channel. Here we experimentally demonstrate a complete characterization of a new family of such witnesses, of the type proposed in Phys. Rev. Lett. 119, 110501 (2017) under different con- ditions of noise. Furthermore, we show non-classical teleportation using quantum states that can not achieve average teleportation fidelity above the classical limit. Our results have fundamental implications in quantum information protocols and may also lead to new applications and quality certification of quantum technologies.

We report on the broadband measurement of quantum radiation pressure noise (QRPN) in an optomechanical cavity at room temperature over a broad range of frequencies relevant to gravitational-wave detectors. We show that QRPN drives the motion of a high-reflectivity single-crystal microresonator, which serves as one mirror of a Fabry-Perot cavity. In our measurements QRPN dominates over all other noise between 10 kHz and 50 kHz and scales as expected with the circulating power inside the cavity. The thermal noise of the microresonator, the largest noise source next to the QRPN, is measured and shown to agree with a structural damping model from 200 Hz to 30 kHz. By observing the effects of QRPN in the audio-band, we now have a testbed for studying techniques to mitigate back-action, such as variational readout and squeezed light injection, that could be used to improve the sensitivity of gravitational-wave detectors.

Second-order optical processes lead to a host of applications in classical and quantum optics. With the enhancement of parametric interactions that arise due to light confinement, on-chip implementations promise very-large-scale photonic integration. But as yet there is no route to a device that acts at the single photon level. Here we exploit the $\chi^{(3)}$ nonlinear response of a Si$_{3}$N$_{4}$ microring resonator to induce a large effective $\chi^{(2)}$. Effective second-order upconversion (ESUP) of a seed to an idler can be achieved with 74,000 %/W efficiency, indicating that single photon nonlinearity is within reach of current technology. Moreover, we show a nonlinear coupling rate of seed and idler larger than the energy dissipation rate in the resonator, indicating a strong coupling regime. Consequently we observe a Rabi-like splitting, for which we provide a detailed theoretical description. This yields new insight into the dynamics of ultrastrong effective nonlinear interactions in microresonators, and access to novel phenomena and applications in classical and quantum nonlinear optics.

In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually $1/2 + \xi$ where the bias $\xi$ vanishes when a security parameter m defined by the protocol increases, the task realised is a (non exact) coin tossing. It is found here that exact coin tossing is impossible. At the same time, an unconditionally secure quantum protocol that realises a (non exact) coin tossing is proposed. The protocol executes m biased quantum coin tossing procedures at the same time. It executes the first round in each of these m procedures sequentially, then the second rounds are executed, and so on until the end of the n procedures. Each procedure requires 4n particles where $n \in O(\lg m)$. The final bit x is the parity of the m random bits. The information about each of these m bits is announced a little bit at a time which implies that the principle used against bit commitment does not apply. The bias on x is smaller than $1/m$. The result is discussed in the light of the impossibility result for exact coin tossing.

The experimental demonstration that neutrons can reside in gravitational quantum stationary states formed in the gravitational field of the Earth indicates a need to examine in more detail the general theoretical properties of gravitational eigenstates. Despite the almost universal study of quantum theory applied to atomic and molecular states very little work has been done to investigate the properties of the hypothetical stationary states that should exist in similar types of gravitational central potential wells, particularly those with large quantum numbers. In this first of a series of papers, we attempt to address this shortfall by developing analytic, non-integral expressions for the electromagnetic dipole state-to-state transition rates of charged particles for any given initial and final gravitational quantum states. The expressions are non-relativistic and hence valid provided the eigenstate wavefunctions do not extend significantly into regions of strong gravity. The formulae may be used to obtain tractable approximations to the transition rates that can be used to give general trends associated with certain types of transitions. Surprisingly, we find that some of the high angular momentum eigenstates have extremely long lifetimes and a resulting stability that belies the multitude of channels available for state decay.

This paper develops further approximate methods for obtaining the dipole matrix elements and corresponding transition and decay rates of the high-n, high-l gravitational eigenstates. These methods include (1) investigation of the polar spreads of the angular components of the high-n, high-l eigenstates and the effects these have on the limiting values of the angular components of the dipole matrix elements in the case of large l and m and (2) investigation of the rapid cut off and limited width of the low-p, high-n radial eigenfunctions, and the development of an equation to determine the width, position and oscillatory behaviour of those eigenfunctions in cases of arbitrarily large values of n, l and p. The methods have wider applicability than dipole transition rate estimates and may be also used to determine limits on the rates for more general interactions. Combining the methods enables the establishment of upper limits to the total dipole decay rates of many high-n, low-p states on the state diagram to be determined, even those that have many channels available for decay. The results continue to support the hypothetical existence of a specialized set of high-n, low-p gravitational eigenfunctions that are invisible and stable, both with respect to electromagnetic decay and gravitational collapse, making them excellent dark matter candidates.

We present criteria to detect the depth of entanglement in macroscopic ensembles of spin-j particles using the variance and second moments of the collective spin components. The class of states detected goes beyond traditional spin-squeezed states by including Dicke states and other unpolarized states. The criteria derived are easy to evaluate numerically even for systems of very many particles and outperform past approaches, especially in practical situations where noise is present. We also derive analytic lower bounds based on the linearization of our criteria, which make it possible to define spin-squeezing parameters for Dicke states. In addition, we obtain spin squeezing parameters also from the condition derived in [A. S. Sorensen and K. Molmer, Phys. Rev. Lett. 86, 4431 (2001)]. We also extend our results to systems with fluctuating number of particles.

We demonstrate a new scheme of infrared spectroscopy with visible light sources and detectors. The technique relies on the nonlinear interference of correlated photons, produced via spontaneous parametric down conversion in a nonlinear crystal. Visible and infrared photons are split into two paths and the infrared photons interact with the sample under study. The photons are reflected back to the crystal, resembling a conventional Michelson interferometer. Interference of the visible photons is observed and it is dependent on the phases of all three interacting photons: pump, visible and infrared. The transmission coefficient and the refractive index of the sample in the infrared range can be inferred from the interference pattern of visible photons. The method does not require the use of potentially expensive and inefficient infrared detectors and sources, it can be applied to a broad variety of samples, and it does not require a priori knowledge of sample properties in the visible range.

We show that parametric coupling techniques can be used to generate selective entangling interactions for multi-qubit processors. By inducing coherent population exchange between adjacent qubits under frequency modulation, we implement a universal gateset for a linear array of four superconducting qubits. An average process fidelity of $\mathcal{F}=93\%$ is estimated for three two-qubit gates via quantum process tomography. We establish the suitability of these techniques for computation by preparing a four-qubit maximally entangled state and comparing the estimated state fidelity against the expected performance of the individual entangling gates. In addition, we prepare an eight-qubit register in all possible bitstring permutations and monitor the fidelity of a two-qubit gate across one pair of these qubits. Across all such permutations, an average fidelity of $\mathcal{F}=91.6\pm2.6\%$ is observed. These results thus offer a path to a scalable architecture with high selectivity and low crosstalk.

Understanding the properties of novel solid-state quantum emitters is pivotal for a variety of applications in field ranging from quantum optics to biology. Recently discovered defects in hexagonal boron nitride are especially interesting, as they offer much desired characteristics such as narrow emission lines and photostability. Here, we study the dependence of the emission on the excitation wavelength. We find that, in order to achieve bright single photon emission with high quantum efficiency, the excitation wavelength has to be matched to the emitter. This is a strong indication that the emitters possess a complex level scheme and cannot be described by a simple two or three level system. Using this excitation dependence of the emission, we thus gain further insight to the internal level scheme and demonstrate how to distinguish different emitters both spatially as well as in terms of their photon correlations.

In this paper we derive various identities involving the {\it action} functional which enters the path-integral formulation of quantum mechanics. They provide some kind of generalisations of the Ehrenfest theorem giving correlations between powers of the action and its functional derivatives.

One-time programs, computer programs which self-destruct after being run only once, are a powerful building block in cryptography and would allow for new forms of secure software distribution. However, ideal one-time programs have been proved to be unachievable using either classical or quantum resources. Here we relax the definition of one-time programs to allow some probability of error in the output and show that quantum mechanics offers security advantages over purely classical resources. We introduce a scheme for encoding probabilistic one-time programs as quantum states with prescribed measurement settings, explore their security, and experimentally demonstrate various one-time programs using measurements on single-photon states. These include classical logic gates, a program to solve Yao's millionaires problem, and a one-time delegation of a digital signature. By combining quantum and classical technology, we demonstrate that quantum techniques can enhance computing capabilities even before full-scale quantum computers are available.

Quantum key distribution (QKD) provides information-theoretic security based on the laws of quantum mechanics. The desire to reduce costs and increase robustness in real-world applications has motivated the study of coexistence between QKD and intense classical data traffic in a single fiber. Previous works on coexistence in metropolitan areas have used wavelength-division multiplexing, however, coexistence in backbone fiber networks remains a great experimental challenge, as Tbps data of up to 20 dBm optical power is transferred, and much more noise is generated for QKD. Here we present for the first time, to the best of our knowledge, the integration of QKD with a commercial backbone network of 3.6 Tbps classical data at 21 dBm launch power over 66 km fiber. With 20 GHz pass-band filtering and large effective core area fibers, real-time secure key rates can reach 4.5 kbps and 5.1 kbps for co-propagation and counter-propagation at the maximum launch power, respectively. This demonstrates feasibility and represents an important step towards building a quantum network that coexists with the current backbone fiber infrastructure of classical communications.

Where does quantum advantage spring from? Such an investigation necessitates invoking an ontology on which non-classical features of quantum theory are explored. One such non-classical ontic-feature is preparation contextuality (PC) and advantage in oblivious communication tasks is its operational signature. This letter primarily addresses quantum advantage in communication complexity (CC). We demonstrate that quantum advantage in one-way CC operationally reveals PC. Specifically, we construct oblivious communication tasks tailored to given CC problems. The bound on classical success probability in the oblivious communication tasks forms our preparation non-contextual inequalities. We use the same states along with their orthogonal mixtures and the same measurements responsible for advantage in CC problems to orchestrate an advantageous protocol for the oblivious communication tasks and the violation of the associated inequalities. Further, we find a criterion for unbounded violation of these inequalities and demonstrate the same for two widely studied CC problems. Additionally, the tools thus developed enables the complete proof of the fact that (spatial and temporal) Bell-inequality violation implies an advantage in oblivious communication tasks, thereby revealing PC. Along with the implications of this work, we discuss other known indications towards our assertion that PC is the principal non-classical feature underlying quantum advantage.

The density functional theory (DFT)+$U$ method is a pragmatic and effective approach for calculating the ground-state properties of strongly-correlated systems. Linear response calculations have become a widespread technique for determining Hubbard parameters from first principles. We provide a detailed treatment of spin in the context of linear response calculations. We construct alternative definitions for Hubbard and Hund's parameters that are consistent with the contemporary DFT+$U$ functional, but which yield lower values for $U$ than the standard, spin-independent approach. We have tested these on a complete series of transition-metal complexes [M(H2O)6]n+ (for M = Ti to Zn), calculating Hubbard $U$ and Hund's $J$ values for both transition metal and oxygen subspaces. We demonstrate that the conventional Hubbard $U$ formula, unlike the conventional DFT+$U$ method, incorporates interactions that are off-diagonal in the spin indices and places greater weight on one spin channel over the other. We employ and expand upon the minimum-tracking linear response method, which is shown to be numerically well-behaved even for closed-shell and near-filled subspaces such as in zinc. In such cases the $U$ value may become highly sensitive to the details of the subspace. We find that a Hubbard correction on the oxygen atoms is required in order to preserve bond lengths in these systems, while predicting spectroscopic properties appears beyond the reach of standard DFT+$U$ functionals. Finally, we demonstrate that the random-phase approximation does not accurately describe screening effects among different spins.

Michael Baer is known for his many achievements in the field of non-adiabatic quantum dynamics and the theory of reaction dynamics. Among his main tools of inquiry is the study of two state quantum systems. I was fortunate enough to collaborate with him on such models in the first part of the previous decade and the last years of the previous century. Here I return to the original two state system, that is Pauli's electron with a spin. And show how this system can be interpreted as a vortical fluid. The similarities and difference between spin flows and classical ideal flows are elucidated.

The Stern-Gerlach (SG) effect, discovered almost a century ago, has become a paradigm of quantum mechanics. Surprisingly there is little evidence that the original scheme with freely propagating atoms exposed to gradients from macroscopic magnets is a fully coherent quantum process. Specifically, no high-visibility spatial interference pattern has been observed with such a scheme, and furthermore no full-loop SG interferometer has been realized with the scheme as envisioned decades ago. On the contrary, numerous theoretical studies explained why it is a near impossible endeavor. Here we demonstrate for the first time both a high-visibility spatial SG interference pattern and a full-loop SG interferometer, based on an accurate magnetic field, originating from an atom chip, that ensures coherent operation within strict constraints described by previous theoretical analyses. This also allows us to observe the gradual emergence of time-irreversibility as the splitting is increased. Finally, achieving this high level of control over magnetic gradients may facilitate technological applications such as large-momentum-transfer beam splitting for metrology with atom interferometry, ultra-sensitive probing of electron transport down to shot-noise and squeezed currents, as well as nuclear magnetic resonance and compact accelerators.