A pump carrier wave in a nonlinear dispersive system may decay by giving birth to blue- and redshifted satellite waves due to modulation or four-wave mixing instability. We analyze situations where the satellites are so different from the carrier wave, that the redshifted satellite either changes its propagation direction $(k<0,$ $\omega >0)$ or even gets a negative frequency $(k,\omega <0)$. Both situations are beyond the envelope approach and require application of the Maxwell equations.

Optical phenomena like nonlinear absorption and nonlinear refraction are often determined through light transmittance techniques. However, in turbid or resonant media, scattering may also significantly attenuate the laser beam, such that absorptive losses may be overestimated. Thus, while transmittance techniques are suitable to determine the power extinction, it is often difficult to characterize the contribution of nonlinear scattering in a sample. In this work we applied the scattered-light imaging method to discriminate the nonlinear extinction due to nonlinear absorption and nonlinear scattering contributions in a turbid medium constituted of ${\mathrm{TiO}}_2$ nanoparticles suspended in acetone. The single-shot method collects an image of the beam transverse profile evolution along the propagation axis inside the sample. It was observed that while the results obtained by the transmittance technique indicate the extinction coefficient (including scattering and absorption contributions), the results obtained with the scattered-light imaging method discriminate the contribution of each phenomenon. Therefore, the results of both approaches are complementary and allow a more complete characterization of turbid media.

We analyze nonclassical correlations between outcomes of measurements conducted on two spatial radiation modes. These correlations cannot be simulated with statistical mixtures of coherent states or, more generally, with non-negative phase-space functions of quantum states and measurements. We argue that nonclassical correlations are naturally related to Bell nonlocality, the former being a more general class of quantum correlations. Indeed, it is known that local realistic as well as noncontextual models correspond to non-negative solutions to a system of linear equations for the joint probability distributions of all observables. We demonstrate that nonclassical correlations correspond to a particular solution to this system, which may have negative values even if local realism is not violated. A modification of Bell inequalities enables us to test such correlations. At the same time, our approach leads to a formulation of Bell inequalities applicable also to continuous variables. The results are illustrated with two-mode squeezed vacuum states and with hybrid entangled states (Schrödinger-Cat states), one mode being analyzed by balanced and the other one by unbalanced homodyne detection.

In this paper, we extend the fluctuation theorems used for quantum channels to multitime processes. The fluctuation theorems for quantum channels are less restrictive. We show that the given entropy production can be equal to the result of a closed system environment. The assumption that the system evolves under a completely positive and trace-preserving map is quite general, but it is more specific for cases in which the system is initially correlated with the environment. System-environment correlations arise naturally in multitime processes with which we can give clear and physical interpretations regarding the effects of correlations. Multitime processes can provide many-body channels. The Choi state of such a many-body channel is called a process tensor. One can derive channels by executing the process tensor on a set of operations. We establish a general quantum fluctuation theorem framework for a many-body channel and its derived channels. In this framework, the effects of correlations are reflected in a Markovian property. For Markovian processes, we can extend the two-point measurement to a three-point measurement and obtain that the fluctuation theorems contain complete information about the intermediate state. For non-Markovian processes, the complete measurement of the intermediate state leads to conflicts. Therefore, we use a general measurement, which only provides partial information, for the intermediate state. The corresponding fluctuation theorems show that memory effects can reduce these fluctuations. This is consistent with the fact that system states can be recovered under non-Markovian processes.

The progress in building quantum computers to execute quantum algorithms has recently been remarkable. Grover's search algorithm in a binary quantum system provides a considerable speed-up over the classical paradigm. It can be extended to a $d$-ary (qudit) quantum system also for utilizing the advantage of larger state space, which helps to reduce the runtime of the algorithm as compared to the traditional binary quantum systems. In a qudit quantum system, an $n$-qudit Toffoli gate plays a significant role in the accurate implementation of Grover's algorithm. In this article, a generalized $n$-qudit Toffoli gate is realized using higher-dimensional qudits to attain a logarithmic depth decomposition without ancilla qudit. The circuit for Grover's algorithm has then been designed for any $d$-ary quantum system, where $d\ge 2$, with the proposed $n$-qudit Toffoli gate to obtain optimized depth compared to earlier approaches. The technique for decomposing an $n$-qudit Toffoli gate requires access to two immediately higher-energy levels, making the design susceptible to errors. Nevertheless, we show that the percentage decrease in the probability of error is significant with both gate count and circuit depth reduced as compared to that in state-of-the-art works.

We introduce a generalization of the communication of partial ignorance where both parties of a prepare-and-measure setup receive inputs from a third party before a success metric is maximized over the measurements and preparations. We call these communication scenarios partial ignorance communication tasks of type $T_{n,m}$, where $n$ indicates the number of possible correct answers in the communication task and $m$ loosely represents the information about the correct answer that is revealed to the party preparing states. Various methods are used to obtain bounds on the success metrics, including semidefinite programs, ultraweak monotones for communication matrices, and frame theory for quantum states. The simplest scenarios in this alternative generalized prepare-and-measure setting, partial-ignorance communication tasks of types $T_{3,1}$, $T_{4,1}$, and $T_{4,2}$, are analyzed exhaustively for bits and qudits. Finally, this generalized setting allows the introduction of operational equivalences to the preparations and measurements, allowing us to analyze and observe a contextual advantage for quantum theory in the partial ignorance communication task of type $T_{4,1}$.

The $R\left(1\right)$, $R\left(3\right)$, and $P\left(3\right)$ rovibrational transitions in the (2-0) overtone band of the HD molecule are measured in Doppler-free saturation using the technique of NICE-OHMS spectroscopy. For the $P\left(3\right)$ line, hitherto not observed in saturation, we report a frequency of $203821936805\left(60\right)$ kHz. The dispersive line shapes observed in the three spectra show strong correlations, allowing for extraction of accurate information on rotational level spacings. This leads to level spacings of ${\mathrm{\Delta }}_{(J=3)-(J=1)}=13283245098\left(30\right)$ kHz in the $v=0$ ground state and ${\mathrm{\Delta }}_{(J=4)-(J=2)}=16882368179\left(20\right)$ kHz in the $v=2$ excited vibration in HD. These results show that experimental values for the rotational spacings are consistently larger than those obtained with advanced ab initio theoretical calculations at $1.5\sigma$, where the uncertainty is determined by theory. The same holds for the vibrational transitions where systematic deviations of 1.7–1.9$\sigma$ are consistently found for the five lines accurately measured in the (2-0) band.

Quasibound states of the nitrogen molecular anion are studied by electron scattering from ${\mathrm{N}}_2$ using ab initio $R$-matrix theory and a close-coupling model. Scattering calculations are performed using both cc-pVTZ and cc-pVQZ target basis sets involving up to 26 low-lying target states in a complete active space configuration-interaction representation. Complex resonance potential energy curves are characterized as a function of internuclear separation for all eight ${{\mathrm{N}}_2}^{-}$ states identified, including the well-known $X{}^2{\mathrm{\Pi }}_g$ shape resonance, one $1{}^2{\mathrm{\Sigma }}_g^{+}$ Feshbach resonance, as well as six core-excited resonances involving 1 ${}^2{\mathrm{\Delta }}_g$, 1 ${}^2{\mathrm{\Pi }}_u$, 2 ${}^2{\mathrm{\Pi }}_u$, 3 ${}^2{\mathrm{\Pi }}_u$, 1 ${}^2{\mathrm{\Sigma }}_u^{+}$, and 1 ${}^2{\mathrm{\Sigma }}_u^{-}$. The ${}^2{\mathrm{\Delta }}_g$ and ${}^2{\mathrm{\Sigma }}_u^{-}$ resonant states are identified and characterized. Comparisons are made with the very different resonance structure in the isoelectronic ${\mathrm{CO}}^{-}$ anion. The present resonance analysis provides a starting point for studies of the vibrational excitation, electron-impact dissociation, and other resonance-driven phenomena in ${\mathrm{N}}_2$.

The eigenstates of Maxwell's monochromatic equations in a multiconstituent composite medium are developed and used to expand a physical field that is created either by an externally given current density or by an incident external field. The local electric permittivity $\kappa \left(\mathbf{r}\right)$, as well as the local magnetic permeability $\mu \left(\mathbf{r}\right)$, are assumed to have uniform values in each constituent, but to differ in the different constituents.

Dynamically encircling an exceptional point in non-Hermitian systems shows a chiral state switching behavior as a result of the nonadiabatic transition between nonorthogonal eigenstates. It has been revealed that the chiral dynamics is protected by the topological structure of eigenvalue sheets where only one lowest-loss sheet exists. This raises the question on what the dynamics would be in non-Hermitian systems possessing multiple degenerate lowest-loss energy levels. Here, we address this question by studying a photonic-waveguide-array non-Hermitian system where two exceptional points are encircled dynamically. The system possesses four quasidegenerate lowest-loss eigenvalue sheets and such topological structure results in an exotic nonchiral behavior for switching eigenstates such that the final state is always a superposition of the four lowest-loss eigenstates. We find that this intriguing phenomenon is robust to a certain perturbation of the system parameters. Our findings enrich the understanding of exceptional point-encirclement physics and may inspire potential non-Hermitian applications for manipulating waves.

The general form of the coincidence Bell inequalities for an arbitrary $(n,2,3)$ scenario [i.e., an $n$-party, two-setting, and three-dimensional system (qutrit) scenario] is presented. To detect the nonlocal properties of the noisy $n$-qutrit Greenberger-Horne-Zeilinger states, in this work we investigate the most robust (4,2,3)-scenario and (5,2,3)-scenario coincidence Bell inequalities. By deriving the most robust $(n-1)$-party coincidence inequalities, we have established two tight and inequivalent $(n,2,3)$ coincidence Bell inequalities with a visibility of 0.5 for $n=4$ and, similarly, two tight and inequivalent $(n,2,3)$ coincidence Bell inequalities with a visibility of 0.488785 for $n=5$. These inequalities are all tight. To our knowledge, up to now these inequalities have been the most robust Bell inequalities for the corresponding scenarios. Our results are useful for building the iteration formula of $(n,2,3)$-scenario coincidence Bell inequalities with the lowest critical visibility.

Treating the time of an event as a quantum variable, we derive a scheme in which superpositions in time are used to perform operations in an indefinite causal order. We use some aspects of a recently developed space-time-symmetric formalism of events. We propose a specific implementation of the scheme and recover the quantum switch, where quantum operations are performed in an order which is entangled with the state of a control qubit. Our scheme does not rely on any exotic quantum gravitational effect, but instead on phenomena which are naturally fuzzy in time, such as the decay of an excited atom.

In the context of quantum technologies over continuous variables, Gaussian states and operations are typically regarded as freely available, as they are relatively easily accessible experimentally. In contrast, the generation of non-Gaussian states, as well as the implementation of non-Gaussian operations, pose significant challenges. This divide has motivated the introduction of resource theories of non-Gaussianity. As for any resource theory, it is of practical relevance to identify free conversion protocols between resources, namely, Gaussian conversion protocols between non-Gaussian states. Via systematic numerical investigations, we address the approximate conversion between experimentally relevant single-mode non-Gaussian states via arbitrary deterministic one-to-one mode Gaussian maps. First we show that cat and binomial states are approximately equivalent for finite energy, while this equivalence was previously known only in the infinite-energy limit. Then we consider the generation of cat states from photon-added and photon-subtracted squeezed states, improving over known schemes by introducing additional squeezing operations. The numerical tools that we develop also allow one to devise conversions of trisqueezed into cubic-phase states beyond previously reported performances. Finally, we identify various other conversions which instead are not viable.

We consider measurement disturbance tradeoffs in quantum machine learning protocols which seek to learn about quantum data. We study the simplest example of a binary classification task in the unsupervised regime. Specifically, we investigate how a classification of two qubits, that can each be in one of two unknown states, affects our ability to perform a subsequent classification on three qubits when a third is added. Surprisingly, we find a range of strategies in which a nontrivial first classification does not affect the success rate of the second classification. There is, however, a nontrivial measurement disturbance tradeoff between the success rate of the first and second classifications, and we fully characterize this tradeoff analytically.

The continuous-time quantum walk denotes the evolution of a particle on a given graph governed by Schrödinger's equation. For different applications, the corresponding Hamiltonian is proportional to either the Laplacian or the adjacency matrix of the graph. The two quantum walks are equivalent on regular graphs, since each vertex has the same degree. However, for irregular graphs, the evolutions of the two quantum walks are generally different. In this paper, we report an experimental investigation of the two quantum walks on irregular graphs with single photons and interferometric networks. We demonstrate that it is possible to obtain equivalent probability distributions with the two quantum walks on specific irregular graphs, where the particle is initially localized at a vertex or uniformly distributed at multiple vertices. Our results not only deepen the understanding of the equivalence between the two quantum walks, but also extend the application of the continuous-time quantum walk.

The performance of beyond mean-field methods in solving the quantum many-body problem for fermions is usually characterized by the correlation energy measured with respect to the underlying mean-field value. In this paper we address the issue of characterizing the amount of correlations associated to different approximations from a quantum information perspective. With this goal in mind, we analyze the traditional Hartree-Fock (HF) method with spontaneous symmetry breaking, the HF with symmetry restoration and the generator coordinate method in an exactly solvable fermion model known as the three-level Lipkin model. To characterize correlations including entanglement and beyond we use the quantum discord between different partition orbitals. We find that for physically motivated partitions, the quantum discord of the exact ground state is reasonably well reproduced by the different approximations. However, other partitions create “fake quantum correlations” in order to capture quantum correlations corresponding to partitions for which the Hartree-Fock solution fails. Those are removed and redistributed through a symmetry restoration process.

We investigate the entanglement features in the interacting system of a quantized optical field and a two-level system which is statically driven, known as the asymmetric quantum Rabi model (AsymQRM). Intriguing entanglement resonance valleys with the increase of the photon-atom coupling strength and peaks with the increase of the driving amplitude are found. It is revealed that both of these two kinds of entanglement resonance are caused by the avoided level crossing of the associated eigenenergies. In sharp contrast to the quantum Rabi model, the entanglement of the AsymQRM collapses to zero in the strong coupling regime except when the driving amplitude is equal to $m\omega /2$, with $m$ being an integer and $\omega$ being the photon frequency. Our analysis demonstrates that such entanglement reappearance is induced by the hidden symmetry of the AsymQRM. Supplying an insightful understanding of the AsymQRM, our results will be helpful in exploring the hidden symmetry and in preparing photon-atom entanglement in light-matter coupled systems.

Quantum cost is a key ingredient in evaluating the quality of quantum protocols from a practical viewpoint. We show that the quantum cost of a $d$-dimensional dense coding protocol is equal to $d+3$ when transmitting the classical message (0,0) and $d+4$ when transmitting another classical message. It appears as linear growth with the dimension and thus makes sense for implementation. In contrast, the quantum cost of high-dimensional teleportation protocols is equal to 13, which is the maximum value of the cost for the two-dimensional case. As an application, we establish the relation between the quantum cost and fidelity of dense coding protocols in terms of four typical noise scenarios.

The exact evaluation of the molecular ground state in quantum chemistry requires an exponentially increasing computational cost. Quantum computation is a promising way to overcome the exponential problem using polynomial-time quantum algorithms. A quantum-classical hybrid optimization scheme known as the variational quantum eigensolver is preferred for noisy intermediate-scale quantum devices. However, the circuit depth becomes one of the bottlenecks of its application to large molecules of more than 20 qubits. In this work, we employ point-group symmetry to reduce the number of operators in constructing ansatz so as to achieve a more compact quantum circuit. We illustrate this methodology with a series of molecules ranging from LiH (12 qubits) to ${\mathrm{C}}_2{\mathrm{H}}_4$ (28 qubits). A significant reduction of up to 82% of the operator numbers is reached on ${\mathrm{C}}_2{\mathrm{H}}_4$. This also sheds light onto further work in this direction to construct even shallower ansatz with enough expressive power and simulate even larger scale systems.