We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of contextuality across measurement scenarios; it bears a precise relationship to violations of Bell inequalities; its value, and a witnessing inequality, can be computed using linear programming; it is monotone with respect to the "free" operations of a resource theory for contextuality; and it measures quantifiable advantages in informatic tasks, such as games and a form of measurement based quantum computing.

We report on the alteration of photon emission properties of a single trapped ion coupled to a high finesse optical fiber cavity. We show that the vacuum field of the cavity can simultaneously affect the emissions in both the infrared (IR) and ultraviolet (UV) branches of the $\Lambda-$type level system of $^{40}\mathrm{Ca}^+$ despite the cavity coupling only to the IR transition. The cavity induces strong emission in the IR transition through the Purcell effect resulting in a simultaneous suppression of the UV fluorescence. The measured suppression of this fluorescence is as large as 66% compared with the case without the cavity. Through analysis of the measurement results, we have obtained an ion-cavity coupling of $\bar{g}_0 = 2\pi\cdot (5.3 \pm 0.1)$ MHz, the largest ever reported so far for a single ion in the IR domain.

We use the Holevo information to estimate distinguishability of microstates of a black hole in anti-de Sitter space by measurements one can perform on a subregion of a Cauchy surface of the dual conformal field theory. We find that microstates are not distinguishable at all until the subregion reaches a certain size and that perfect distinguishability can be achieved before the subregion covers the entire Cauchy surface. We will compare our results with expectations from the entanglement wedge reconstruction, tensor network models, and the bit threads interpretation of the Ryu-Takayanagi formula.

We calculate the gauge invariant cumulants (and moments) associated with the Zak phase in the Rice-Mele model. We reconstruct the underlying probability distribution by maximizing the information entropy and applying the moments as constraints. When the Wannier functions are localized within one unit cell, the probability distribution so obtained corresponds to that of the Wannier function. We show that in the fully dimerized limit the magnitude of the moments are all equal. In this limit, if the on-site interaction is decreased towards zero, the distribution shifts towards the midpoint of the unit cell, but the overall shape of the distribution remains the same. Away from this limit, if alternate hoppings are finite, and the on-site interaction is decreased, the distribution also shifts towards the midpoint of the unit cell, but it does this by changing shape, by becoming asymmetric around the maximum, as well as by shifting. We also follow the probability distribution of the polarization in cycles around the topologically non-trivial point of the model. The distribution moves across to the next unit cell, its shape distorting considerably in the process. If the radius of the cycle is large, the shift of the distribution is accompanied by large variations in the maximum.

We investigate the application of amplitude-shaped control pulses for enhancing the time and frequency resolution of multipulse quantum sensing sequences. Using the electronic spin of a single nitrogen vacancy center in diamond and up to 10,000 coherent microwave pulses with a cosine square envelope, we demonstrate 0.6 ps timing resolution for the interpulse delay. This represents a refinement by over 3 orders of magnitude compared to the 2 ns hardware sampling. We apply the method for the detection of external AC magnetic fields and nuclear magnetic resonance signals of carbon-13 spins with high spectral resolution. Our method is simple to implement and especially useful for quantum applications that require fast phase gates, many control pulses, and high fidelity.

The aim of this contribution is to discuss relations between non-classical features, such as entanglement, incompatibility of measurements, steering and non-locality, in general probabilistic theories. We show that all these features are particular forms of entanglement, which leads to close relations between their quantifications. For this, we study the structure of the tensor products of a compact convex set with a semiclassical state space.

One of the most widely known building blocks of modern physics is Heisenberg's indeterminacy principle. Among the different statements of this fundamental property of the full quantum mechanical nature of physical reality, the uncertainty relation for energy and time has a special place. Its interpretation and its consequences have inspired continued research efforts for almost a century. In its modern formulation, the uncertainty relation is understood as setting a fundamental bound on how fast any quantum system can evolve. In this Topical Review we describe important milestones, such as the Mandelstam-Tamm and the Margolus-Levitin bounds on the quantum speed limit, and summarise recent applications in a variety of current research fields -- including quantum information theory, quantum computing, and quantum thermodynamics amongst several others. To bring order and to provide an access point into the many different notions and concepts, we have grouped the various approaches into the minimal time approach and the geometric approach, where the former relies on quantum control theory, and the latter arises from measuring the distinguishability of quantum states. Due to the volume of the literature, this Topical Review can only present a snapshot of the current state-of-the-art and can never be fully comprehensive. Therefore, we highlight but a few works hoping that our selection can serve as a representative starting point for the interested reader.

One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance". These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? One important feature of quantum theory is that it has a classical limit, recovering classical theory through the process of decoherence. We show that any theory with a classical limit must contain entangled states, thus establishing entanglement as an inevitable feature of any theory superseding classical theory.

We study the matrix elements of few-body observables, focusing on the off-diagonal ones, in the eigenstates of the two-dimensional transverse field Ising model. By resolving all possible symmetries, we relate the onset of quantum chaos to the structure of the matrix elements. In particular, we show that a general result of the theory of random matrices, namely, the value 2 of the ratio of variances (diagonal to off-diagonal) of the matrix elements of Hermitian operators, occurs in the quantum chaotic regime. Furthermore, we explore the behavior of the off-diagonal matrix elements of observables as a function of the eigenstate energy differences, and show that it is in accordance with the eigenstate thermalization hypothesis ansatz.

Coherent interactions between electromagnetic and matter waves lie at the heart of quantum science and technology. However, the diffraction nature of light has limited the scalability of many atom-light based quantum systems. Here, we use the optical fields in a hollow-core photonic crystal fiber to spatially split, reflect, and recombine a coherent superposition state of free-falling 85Rb atoms to realize an inertia-sensitive atom interferometer. The interferometer operates over a diffraction-free distance, and the contrasts and phase shifts at different distances agree within one standard error. The integration of phase coherent photonic and quantum systems here shows great promise to advance the capability of atom interferometers in the field of precision measurement and quantum sensing with miniature design of apparatus and high efficiency of laser power consumption.

We develop a systematic study of Jahn-Teller (JT) models with continuous symmetries by exploring their algebraic properties. The compact symmetric spaces corresponding to JT models carrying a Lie group symmetry are identified, and their invariance properties applied to reduce their multi-branched adiabatic potential energy surface into an orbit space. Each orbit consists of a set of JT distorted molecular structures with equal adiabatic electronic spectrum. Molecular motion may be decomposed into pseudorotational motion and radial. The former preserves the orbit, while the latter maps an orbit into another. The internal space of each orbit may have different dimensionality, depending on the number of degenerate states in their adiabatic electronic spectra. Qualitatively different pseudorotational modes occur in orbits of different types. The general theory is illustrated with a diverse set of examples. Aspects of the abelian and non-abelian Berry phases of JT models with continuous symmetries are also investigated. The relevance of our study for the more common case of JT systems with only discrete point group symmetry, and for generic asymmetric molecular systems with conical intersections involving more than two states is likewise discussed.

What are the conditions for adiabatic quantum computation (AQC) to outperform classical computation? We consider the strong quantum speedup: scaling advantage in computational time over the best classical algorithms. Although there exist several quantum adiabatic algorithms achieving the strong quantum speedup, the essential keys to their speedups are still unclear. Here, we propose a necessary condition for the quantum speedup in AQC. This is a conjecture that a superposition of macroscopically distinct states appears during AQC if it achieves the quantum speedup. This is a natural extension of the conjecture in circuit-based quantum computation [A. Shimizu et al., J. Phys. Soc. Jpn. 82, 054801 (2013)]. To describe the statement of the conjecture, we introduce an index $p$ that quantifies a superposition of macroscopically distinct states---macroscopic entanglement---from the asymptotic behaviors of fluctuations of additive observables. We theoretically test the conjecture by investigating five quantum adiabatic algorithms. All the results show that the conjecture is correct for these algorithms. We therefore expect that a superposition of macroscopically distinct states is an appropriate indicator of entanglement crucial to the strong quantum speedup in AQC.

We analyze the disorder-perturbed transport of quantum states in the absence of backscattering. This comprises, for instance, the propagation of edge-mode wave packets in topological insulators, or the propagation of photons in inhomogeneous media. We quantify the disorder-induced dephasing, which we show to be bound. Moreover, we identify a gap condition to remain in the backscattering-free regime despite of disorder-induced momentum broadening. Our analysis comprises the full disorder-averaged quantum state, on the level of both populations and coherences, appreciating states as potential carriers of quantum information. The well-definedness of states is guaranteed by our treatment of the nonequilibrium dynamics with Lindblad master equations.

We have examined both single and entangled two-mode multiphoton coherent states and shown how the `Janus-faced' properties between two partner states are mirrored in appropriate tomograms. Entropic squeezing, quadrature squeezing and higher-order squeezing properties for a wide range of nonclassical states are estimated directly from tomograms. We have demonstrated how squeezing properties of two-mode entangled states produced at the output port of a quantum beamsplitter are sensitive to the relative phase between the reflected and transmitted fields. This feature allows for the possibility of tuning the relative phase to enhance squeezing properties of the state. Finally we have examined the manner in which decoherence affects squeezing and the changes in the optical tomogram of the state due to interaction with the environment.

The quantum description of an atom with a magnetic quadrupole moment in the presence of a time-dependent magnetic field is analysed. It is shown that the time-dependent magnetic field induces an electric field that interacts with the magnetic quadrupole moment of the atom and gives rise to a Landau-type quantization. It is also shown that a time-independent Schr\"odinger equation can be obtained, i.e., without existing the interaction between the magnetic quadrupole moment of the atom and the time-dependent magnetic field, therefore, the Schr\"odinger equation can be solved exactly. It is also analysed this system subject to scalar potentials.

Even though the evolution of an isolated quantum system is unitary, the complexity of interacting many-body systems prevents the observation of recurrences of quantum states for all but the smallest systems. For large systems one can not access the full complexity of the quantum states and the requirements to observe a recurrence in experiments reduces to being close to the initial state with respect to the employed observable. Selecting an observable connected to the collective excitations in one-dimensional superfluids, we demonstrate recurrences of coherence and long range order in an interacting quantum many-body system containing thousands of particles. This opens up a new window into the dynamics of large quantum systems even after they reached a transient thermal-like state.

Localized-surface plasmon resonance is of importance in both fundamental and applied physics for the subwavelength confinement of optical field, but realization of quantum coherent processes is confronted with challenges due to strong dissipation. Here we propose to engineer the electromagnetic environment of metallic nanoparticles (MNPs) using optical microcavities. An analytical quantum model is built to describe the MNP-microcavity interaction, revealing the significantly enhanced dipolar radiation and consequentially reduced Ohmic dissipation of the plasmonic modes. As a result, when interacting with a quantum emitter, the microcavity-engineered MNP enhances the quantum yield over 40 folds and the radiative power over one order of magnitude. Moreover, the system can enter the strong coupling regime of cavity quantum electrodynamics, providing a promising platform for the study of plasmonic quantum electrodynamics, quantum information processing, precise sensing and spectroscopy.

To realize one desired nonadiabatic holonomic gate, various equivalent evolution paths can be chosen. However, in the presence of errors, these paths become inequivalent. In this paper, we investigate the difference of these evolution paths in the presence of systematic Rabi frequency errors and aim to find paths with optimal robustness to realize one-qubit nonadiabatic holonomic gates. We focus on three types of evolution paths in the $\Lambda$ system: paths belonging to the original two-loop scheme [New J. Phys. {\bf 14}, 103035 (2012)], the single-loop multiple-pulse scheme [Phys. Rev. A {\bf 94}, 052310 (2016)], and the off-resonant single-shot scheme [Phys. Rev. A {\bf 92}, 052302 (2015); Phys. Lett. A {\bf 380}, 65 (2016)]. Whereas both the single-loop multiple-pulse and single-shot schemes aim to improve the robustness of the original two-loop scheme by shortening the exposure to decoherence, we here find that the two-loop scheme is more robust to systematic errors in the Rabi frequencies. More importantly, we derive conditions under which the resilience to this kind of error can be optimized, thereby strengthening the robustness of nonadiabatic holonomic gates.

We analyze Landauer's principle for repeated interaction systems consisting of a reference quantum system $\mathcal{S}$ in contact with a environment $\mathcal{E}$ consisting of a chain of independent quantum probes. The system $\mathcal{S}$ interacts with each probe sequentially, for a given duration, and the Landauer principle relates the energy variation of $\mathcal{E}$ and the decrease of entropy of $\mathcal{S}$ by the entropy production of the dynamical process. We consider refinements of the Landauer bound at the level of the full statistics (FS) associated to a two-time measurement protocol of, essentially, the energy of $\mathcal{E}$. The emphasis is put on the adiabatic regime where the environment, consisting of $T \gg 1$ probes, displays variations of order $T^{-1}$ between the successive probes, and the measurements take place initially and after $T$ interactions. We prove a large deviations principle and a central limit theorem as $T \to \infty$ for the classical random variable describing the entropy production of the process, with respect to the FS measure. In a special case, related to a detailed balance condition, we obtain an explicit limiting distribution of this random variable without rescaling. At the technical level, we generalize the discrete non-unitary adiabatic theorem by the present authors in [Commun. Math. Phys. (2017) 349: 285] and analyze the spectrum of complex deformations of families of irreducible completely positive trace-preserving maps.

I purport to show why old and new claims on the role of counterfactual reasoning for the EPR argument and the Bell theorem are unjustified: once the logical relation between locality and counterfactual reasoning is clarified, the use of the latter does no harm and the nonlocality result can well follow from the EPR premises. To show why, I critically review (i) incompleteness arguments that Einstein developed before the EPR paper, and (ii) more recent claims that equate the use of counterfactual reasoning with the assumption of a strong form of realism.