A nonlocal subspace $\mathcal{H}_{NS}$ is a subspace within the Hilbert space $\mathcal{H}_n$ of a multi-particle system such that every state $\psi \in \mathcal{H}_{NS}$ violates a given Bell inequality $\mathcal{B}$. Subspace $\mathcal{H}_{NS}$ is maximally nonlocal if each such state $\psi$ violates $\mathcal{B}$ to its algebraic maximum. We propose ways by which states with a stabilizer structure can be used to construct maximally nonlocal subspaces, essentially as a degenerate eigenspace of Bell operators derived from the stabilizer generators. Applications to two tasks in quantum cryptography, namely quantum secret sharing and certification of graph states, are discussed.

We show that allowing magnetic fields to be complex-valued leads to an improvement in the magnetic Hardy-type inequality due to Laptev and Weidl. The proof is based on the study of momenta on the circle with complex magnetic fields, which is of independent interest in the context of PT-symmetric and quasi-Hermitian quantum mechanics. We study basis properties of the non-self-adjoint momenta and derive closed formulae for the similarity transforms relating them to self-adjoint operators.

We describe the design of an artificial `free space' 1D-atom for quantum optics, where we implement an effective two-level atom in a 3D optical environment with a chiral light-atom interface, i.e. absorption and spontaneous emission of light is essentially unidirectional. This is achieved by coupling the atom of interest in a laser-assisted process to a `few-atom' array of emitters with subwavelength spacing, which acts as a phased-array optical antenna. We develop a general quantum optical model based on Wigner-Weisskopf theory, and quantify the directionality of spontaneous emission in terms of a Purcell $\beta$-factor for a given Gaussian (paraxial) mode of the radiation field, predicting values rapidly approaching unity for `few-atom' antennas in bi- and multilayer configurations. Our setup has for neutral atoms a natural implementation with laser-assisted Rydberg interactions, and we present a study of directionality of emission from a string of trapped ions with superwavelength spacing.

In [arXiv:1712.03219] the existence of a strongly (pointwise) converging sequence of quantum channels that can not be represented as a reduction of a sequence of unitary channels strongly converging to a unitary channel is shown. In this work we give a simple characterization of sequences of quantum channels that have the above representation. The corresponding convergence is called the $*$-strong convergence, since it relates to the convergence of selective Stinespring isometries of quantum channels in the $*$-strong operator topology.

Some properties of the $*$-strong convergence of quantum channels are considered.

In this paper, we introduce quantum fidelity based measurement induced nonlocality for the bipartite state over two-sided von Neumann projective measurements. While all the properties of this quantity are reflected from that of one-sided measurement, the latter one is shown to set an upper bound for arbitrary bipartite state. As an illustration, we have studied the nonlocality of Bell diagonal state.

The core problem in optimal control theory applied to quantum systems is to determine the temporal shape of an applied field in order to maximize the expectation of value of some physical observable. The functional which maps the control field into a given value of the observable defines a Quantum Control Landscape (QCL). Studying the topological and structural features of these landscapes is of critical importance for understanding the process of finding the optimal fields required to effectively control the system, specially when external constraints are placed on both the field $\epsilon(t)$ and the available control duration $T$. In this work we analyze the rich structure of the $QCL$ of the paradigmatic Landau-Zener two-level model, studying several features of the optimized solutions, such as their abundance, spatial distribution and fidelities. We also inspect the optimization trajectories in parameter space. We are able rationalize several geometrical and topological aspects of the QCL of this simple model and the effects produced by the constraints. Our study opens the door for a deeper understanding of the QCL of general quantum systems.

The 1-D Anderson model possesses a completely localized spectrum of eigenstates for all values of the disorder. We consider the effect of projecting the Hamiltonian to a truncated Hilbert space, destroying time reversal symmetry. We analyze the ensuing eigenstates using different measures such as inverse participation ratio and sample-averaged moments of the position operator. In addition, we examine amplitude fluctuations in detail to detect the possibility of multifractal behavior (characteristic of mobility edges) that may arise as a result of the truncation procedure.

We study a one-dimensional system of strongly-correlated bosons interacting with a dynamical lattice. A minimal model describing the latter is provided by extending the standard Bose-Hubbard Hamiltonian to include extra degrees of freedom on the bonds of the lattice. We show that this model is capable of reproducing phenomena similar to those present in usual fermion-phonon models. In particular, we discover a bosonic analog of the Peierls transition, where the translational symmetry of the underlying lattice is spontaneously broken. The latter provides a dynamical mechanism to obtain a topological insulator in the presence of interactions, analogous to the Su-Schrieffer-Heeger (SSH) model for electrons. We numerically characterize the phase diagram of the model, which includes different types of bond order waves and topological solitons. Finally, we study the possibility of implementing the model experimentally using atomic systems.

We show that DNF formulae can be quantum PAC-learned in polynomial time under product distributions using a quantum example oracle. The best classical algorithm (without access to membership queries) runs in superpolynomial time. Our result extends the work by Bshouty and Jackson (1998) that proved that DNF formulae are efficiently learnable under the uniform distribution using a quantum example oracle. Our proof is based on a new quantum algorithm that efficiently samples the coefficients of a {\mu}-biased Fourier transform.

We analyze the tailored coupled-cluster (TCC) method, which is a multi-reference formalism that combines the single-reference coupled-cluster (CC) approach with a full configuration interaction (FCI) solution covering the static correlation. This covers in particular the high efficiency coupled-cluster method tailored by tensor-network states (TNS-TCC). For statically correlated systems, we introduce the conceptually new CAS-ext-gap assumption for multi-reference problems which replaces the unreasonable HOMO-LUMO gap. We characterize the TCC function and show local strong monotonicity and Lipschitz continuity such that Zarantonello's Theorem yields locally unique solutions fulfilling a quasi-optimal error bound for the TCC method. We perform an energy error analysis revealing the mathematical complexity of the TCC-method. Due to the basis-splitting nature of the TCC formalism, the error decomposes into several parts. Using the Aubin-Nitsche-duality method we derive a quadratic (Newton type) error bound valid for the linear-tensor-network TCC scheme DMRG-TCC and other TNS-TCC methods.

Optical cavities are one of the best ways to increase atom-light coupling and will be a key ingredient for future quantum technologies that rely on light-matter interfaces. We demonstrate that traveling-wave "ring" cavities can achieve a greatly reduced mode waist $w$, leading to larger atom-cavity coupling strength, relative to conventional standing-wave cavities for given mirror separation and stability. Additionally, ring cavities can achieve arbitrary transverse-mode spacing simultaneously with the large mode-waist reductions. Following these principles, we build a parabolic atom-ring cavity system that achieves strong collective coupling $NC = 15(1)$ between $N=10^3$ Rb atoms and a ring cavity with a single-atom cooperativity $C$ that is a factor of $35(5)$ times greater than what could be achieved with a near-confocal standing-wave cavity with the same mirror separation and finesse. By using parabolic mirrors, we eliminate astigmatism--which can otherwise preclude stable operation--and increase optical access to the atoms. Cavities based on these principles, with enhanced coupling and large mirror separation, will be particularly useful for achieving strong coupling with ions, Rydberg atoms, or other strongly interacting particles, which often have undesirable interactions with nearby surfaces.

One of the peculiar features in quantum mechanics is that a superposition of macroscopically distinct states can exits. In optical system, this is highlighted by a superposition of coherent states (SCS), i.e. a superposition of classical states. Recently this highly nontrivial quantum state and its variant have been demonstrated experimentally. Here we demonstrate the superposition of coherent states in quantum measurement which is also a key concept in quantum mechanics. More precisely, we propose and implement a projection measurement onto the arbitrary superposition of the SCS bases in optical system. The measurement operators are reconstructed experimentally by a novel quantum detector tomography protocol. Our device is realized by combining the displacement operation and photon counting, well established technologies, and thus has implications in various optical quantum information processing applications.

We demonstrate a different scheme to perform optical sectioning of a sample based on the concept of induced coherence [Zou et al., Phys. Rev. Lett. 67, 318 (1991)]. This can be viewed as a different type of optical coherence tomography scheme where the varying reflectivity of the sample along the direction of propagation of an optical beam translates into changes of the degree of first-order coherence between two beams. As a practical advantage the scheme allows probing the sample with one wavelength and measuring photons with another wavelength. In a bio-imaging scenario, this would result in a deeper penetration into the sample because of probing with longer wavelengths, while still using the optimum wavelength for detection. The scheme proposed here could achieve submicron axial resolution by making use of nonlinear parametric sources with broad spectral bandwidth emission.

Quantum two-level systems interacting with the surroundings are ubiquitous in nature. The interaction suppresses quantum coherence and forces the system towards a steady state. Such dissipative processes are captured by the paradigmatic spin-boson model, describing a two-state particle, the "spin", interacting with an environment formed by harmonic oscillators. A fundamental question to date is to what extent intense coherent driving impacts a strongly dissipative system. Here we investigate experimentally and theoretically a superconducting qubit strongly coupled to an electromagnetic environment and subjected to a coherent drive. This setup realizes the driven Ohmic spin-boson model. We show that the drive reinforces environmental suppression of quantum coherence, and that a coherent-to-incoherent transition can be achieved by tuning the drive amplitude. An out-of-equilibrium detailed balance relation is demonstrated. These results advance fundamental understanding of open quantum systems and bear potential for the design of entangled light-matter states.

In the paper, it is argued that the phenomenon known as the quantum pigeonhole principle (namely, three quantum particles are put in two boxes, yet no two particles are in the same box) can be explained not as a violation of Dirichlet's box principle in the case of quantum particles but as a nonvalidness of a bivalent logic for describing not-yet verified propositions relating to quantum mechanical experiments.

Superposition of two or more states is one of the fundamental concepts of quantum mechanics and provides the basis for several advantages quantum information processing offers. In this work, we experimentally demonstrate that quantum superposition permits two-way communication between two distant parties that can exchange only one particle once, an impossible task in classical physics. This is achieved by preparing a single photon in a coherent superposition of the two parties' locations. Furthermore, we show that this concept allows the parties to perform secure quantum communication, where the transmitted bits and even the direction of communication remain private. These important features can lead to the development of new quantum communication schemes, which are simultaneously secure and resource-efficient.

We study the localization and oscillation properties of the Majorana fermions that arise in a two-dimensional electron gas (2DEG) with spin-orbit coupling (SOC) and a Zeeman field coupled with a d-wave superconductor. Despite the angular dependence of the d-wave pairing, localization and oscillation properties are found to be similar to the ones seen in conventional s-wave superconductors. In addition, we study a microscopic lattice version of the previous system that can be characterized by a topological invariant. We derive its real space representation that involves nearest and next-to-nearest-neighbors pairing. Finally, we show that the emerging chiral Majorana fermions are indeed robust against static disorder. This analysis has potential applications to quantum simulations and experiments in high-$T_c$ superconductors.

Quantum illumination is a technique for detecting the presence of a target in a noisy environment by means of a quantum probe. We prove that the two-mode squeezed vacuum state is the optimal probe for quantum illumination in the scenario of asymmetric discrimination, where the goal is minimizing the probability of a false positive with a given probability of a false negative. Quantum illumination with two-mode squeezed vacuum states offers a 6 dB advantage in the error probability exponent compared to illumination with coherent states. Whether more advanced quantum illumination strategies may offer further improvements had been a longstanding open question. Our fundamental result proves that nothing can be gained by considering more exotic quantum states, such as e.g. multi-mode entangled states. Our proof is based on a new fundamental entropic inequality for the noisy quantum Gaussian attenuators. We also prove that without access to a quantum memory, the optimal probes for quantum illumination are the coherent states.

A central task in quantum information processing is to characterize quantum processes. In the realm of optical quantum information processing, this amounts to characterizing the transformations of the mode creation and annihilation operators. This transformation is unitary for linear optical systems, whereas these yield the well-known Bogoliubov transformations for systems with Hamiltonians that are quadratic in the mode operators. In this paper, we show that a modified Mach-Zehnder interferometer can characterize both these kinds of evolutions for multimode systems. While it suffices to use coherent states for the characterization of linear optical systems, we additionally require single photons to characterize quadratically nonlinear optical systems.

It is first shown that the homogeneous and massless Klein-Gordon equation for a complex scalar wave function of frequency $\nu$ can be written as a Lorentz invariant Schr\"{o}dinger equation for a free particle of `effective mass' $\frac{1}{2}(h\nu/c^2)$. It is then shown that this Schr\"{o}dinger equation is the basis of a unified operator theory of free and monochromatic classical and quantum light. It strengthens the theoretical foundation of entanglement in classical optics.