Quantum Physics (quant-ph)

Abstract: We address the use of a calcite crystal-based local detector to the discrimination of orbital angular momentum of quantum radiation produced by parametric down conversion. We demonstrate that a discrimination can be obtained exploiting the introduction of a fine and controlled spatial shift between two replicas of the state in the crystals. We believe that this technology could be used for future development of long-distance quantum communication techniques, where information encoding is based on orbital angular momentum.

Abstract: As an important tomography technique in quantum computing, Hamiltonian Learning (HL) provides a significant method for verifying the accuracy of a quantum system. Often, learning a certain Hamiltonian requires the measurements from its steady states. However, not all the Hamiltonian can be uniquely determined from the steady state. It has been revealed that the success of HL depends on the Hamiltonian model and the rank of the state. Here, we analyze the HL with respect to a specific type of steady state that is decomposed by eigenstates with degeneracy, making the Hamiltonian's eigenstate unknown. To overcome this challenge, we extract information from the orthogonality relationship between the eigenstate space and its complement space, constructing the orthogonal space equation (OSE). The equation number of OSE can be utilized to determine whether a Hamiltonian can be recovered from a certain steady state. Finally, we investigate how symmetries in the Hamiltonian affect the feasibility of the HL method.

Abstract: We present a simple proof of a sufficient condition for the uniqueness of non-equilibrium steady states of Gorini-Kossakowski-Sudarshan-Lindblad equations. We demonstrate the applications of the sufficient condition using examples of the transverse-field Ising model, the XYZ model, and the tight-binding model with dephasing.

Abstract: The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth of the required number of measurements. The conceptual solution for this dimensionality curse relies on a simple idea - a complete description of a quantum state is excessive and can be discarded in favor of experimentally accessible information about the system. The probably approximately correct (PAC) learning theory has been recently successfully applied to a problem of building accurate predictors for the measurement outcomes using a dataset which scales only linearly with the number of qubits. Here we present a constructive and numerically efficient protocol which learns a tensor network model of an unknown quantum system. We discuss the limitations and the scalability of the proposed method.

Abstract: There are bipartite quantum nonlocal correlations requiring very low detection efficiency to reach the loophole-free regime but that need too many measurement settings to be practical for actual experiments. This leads to the general problem of what can be concluded about loophole-free Bell nonlocality if only a random subset of these settings is tested. Here we develop a method to address this problem. We show that, in some cases, it is possible to detect loophole-free Bell nonlocality testing only a small random fraction of the settings. The prize to pay is a higher detection efficiency. The method allows for a novel approach to the design of loophole-free Bell tests in which, given the dimension of the local system, the visibility, and the detection efficiency available, one can calculate the fraction of the contexts needed to reach the detection-loophole-free regime. The results also enforce a different way of thinking about the costs of classically simulating quantum nonlocality, as it shows that the amount of resources that are needed can be made arbitrarily large simply by considering more contexts.

Abstract: The Casimir-Polder force between atoms or nanoparticles and graphene-coated dielectric substrates is investigated in the region of large separations. Graphene coating with any value of the energy gap and chemical potential is described in the framework of the Dirac model using the formalism of the polarization tensor. It is shown that the Casimir-Polder force from a graphene-coated substrate reaches the limit of large separations at approximately 5.6 $\mu$m distance between an atom or a nanoparticle and graphene coating independently of the values of the energy gap and chemical potential. According to our results, however, the classical limit, where the Casimir-Polder force no longer depends on the Planck constant and the speed of light, may be attained at much larger separations depending on the values of the energy gap and chemical potential. In addition, we have found a simple analytic expression for the Casimir-Polder force from a graphene-coated substrate at large separations and determined the region of its applicability. It is demonstrated that the asymptotic results for the large-separation Casimir-Polder force from a graphene-coated substrate are in better agreement with the results of numerical computations for the graphene sheets with larger chemical potential and smaller energy gap. Possible applications of the obtained results in nanotechnology and bioelectronics are discussed.

Abstract: In a previous paper, the distribution of resonance poles in the complex plane of the wavenumber $k$ associated to the multiple scattering of a quantum particle in a random point field was numerically discovered. This distribution presented two distinctive structures: a set of peaks at small $k$ when the wavelength is larger than the interscatterer distance, and a band almost parallel to the real axis at larger $k$. In this paper, a detailed theoretical study based on wave transport theory is proposed to explain the origin of these structures and to predict their location in the complex $k$ plane. First, it is shown that the peaks at small $k$ can be understood using an effective wave equation for the average wave function over the disorder. Then, that the band at large $k$ can be described by the Bethe-Salpeter equation for the square modulus of the wavefunction, which is derived from the diagrammatic method. This study is supported by careful comparisons with numerical simulations. The largest simulations revealed the presence of quantum scars in the bulk of the disordered medium.

Abstract: In this paper, we study the tunable quantum neural network architecture in the quantum exact learning framework with access to a uniform quantum example oracle. We present an approach that uses amplitude amplification to correctly tune the network to the target concept. We applied our approach to the class of positive $k$-juntas and found that $O(n^22^k)$ quantum examples are sufficient with experimental results seemingly showing that a tighter upper bound is possible.

Abstract: Fast quantum gates are of paramount importance for enabling efficient and error-resilient quantum computations. In the present work we analyze Landau-Zener-St\"uckelberg-Majorana (LSZM) strong driving protocols, tailored to implement fast gates with particular emphasis on small gap qubits. We derive analytical equations to determine the specific set of driving parameters for the implementation of single qubit and two qubit gates employing single period sinusoidal pulses. Our approach circumvents the need to scan experimentally a wide range of parameters and instead it allows to focus in fine-tuning the device near the analytically predicted values. We analyze the dependence of relaxation and decoherence on the amplitude and frequency of the pulses, obtaining the optimal regime of driving parameters to mitigate the effects of the environment. Our results focus on the study of the single qubit $X_{\frac{\pi}{2}}$, $Y_{\frac{\pi}{2}}$ and identity gates. Also, we propose the $\sqrt{\rm{bSWAP}}$ as the simplest two-qubit gate attainable through a robust LZSM driving protocol.