Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of states violate this principle and display eigenstate localization, a counter-intuitive feature known to arise due to purely quantum or semiclassical effects. In the spectrum of chaotic systems, the localized and random states interact with one another and modifies the spectral statistics. In this work, a $3 \times 3$ random matrix model is used to obtain exact result for the ratio of spacing between a generic and localized state. We consider time-reversal-invariant as well as non-invariant scenarios. These results agree with the spectra computed from realistic physical systems that display localized eigenmodes.

We present an axiomatic framework for thermodynamics that incorporates information as a fundamental concept. The axioms describe both ordinary thermodynamic processes and those in which information is acquired, used and erased, as in the operation of Maxwell's demon. This system, like previous axiomatic systems for thermodynamics, supports the construction of conserved quantities and an entropy function governing state changes. Here, however, the entropy exhibits both information and thermodynamic aspects. Although our axioms are not based upon probabilistic concepts, a natural and highly useful concept of probability emerges from the entropy function itself. Our abstract system has many models, including both classical and quantum examples.

The ingredients normally required to achieve topological superconductivity (TSC) are Cooper pairing, broken inversion symmetry, and broken time-reversal symmetry. We present a theoretical exploration of the possibility of using ultra-thin films of superconducting metals as a platform for TSC. Because they necessarily break inversion symmetry when prepared on a substrate and have intrinsic Cooper pairing, they can be TSCs when time-reversal symmetry is broken by an external magnetic field. Using microscopic density functional theory calculations we show that for ultrathin Pb and $\beta$-Sn superconductors the position of the Fermi level can be tuned to quasi-2D band extrema energies using strain, and that the $g$-factors of these Bloch states can be extremely large enhancing the influence of external magnetic fields.

We introduce an exactly solvable model of two-dimensional Dirac fermion in presence of an asymmetric vector potential. Fundamental solutions of its stationary equation are represented by an irreducible combination of two Gauss hypergeometric functions. Peculiar spectral properties of the system are analyzed.

We present a simple protocol for certifying graph states in quantum networks using stabiliser measurements. The certification statements can easily be applied to different protocols using graph states. We see for example how it can be used to for measurement based verified quantum compu- tation, certified sampling of random unitaries and quantum metrology and sharing quantum secrets over untrusted channels.

The use of imaginary numbers in modelling quantum mechanical systems encompasses the wave-like nature of quantum states. Here we introduce a resource theoretic framework for imaginarity, where the free states are taken to be those with density matrices that are real with respect to a fixed basis. This theory is closely related to the resource theory of coherence, as it is basis dependent, and the imaginary numbers appear in the off-diagonal elements of the density matrix. Unlike coherence however, the set of physically realizable free operations is identical to both completely resource non-generating operations, and stochastically resource non-generating operations. Moreover, the resource theory of imaginarity does not have a self-adjoint resource destroying map. After introducing and characterizing the free operations, we provide several measures of imaginarity, and give necessary and sufficient conditions for pure state transformations via physically consistent free operations in the single shot regime.

Analyzing weak microwave signals in the GHz regime is a challenging task if the signal level is very low and the photon energy widely undefined. Due to its discrete level structure, a superconducting qubit is only sensitive to photons of certain energies. With a multi-level quantum system (qudit) in contrast, the unknown photon frequency can be deduced from the higher level AC Stark shift. The measurement accuracy is given by the signal amplitude, its detuning from the discrete qudit energy level structure and the anharmonicity. We demonstrate an energy sensitivity in the order of $10^{-4}$ with a measurement range of 1 GHz. Here, using a transmon qubit, we experimentally observe shifts in the transition frequencies involving up to three excited levels. These shifts are in good agreement with an analytic circuit model and master equation simulations. For large detunings, we find the shifts to scale linearly with the power of the applied microwave drive.

We derive the theory of open quantum system dynamics intervened by a series of nonselective measurements. We analyze the cases of time independent and time dependent Hamiltonian dynamics in between the measurements and find the approximate master equation in the stroboscopic limit. We also consider a situation, in which the measurement basis changes in time, and illustrate it by nonselective measurements in the basis of diabatic states of the Landau-Zener model.

Shannon entropy ($S$), R{\'e}nyi entropy ($R$), Tsallis entropy ($T$), Fisher information ($I$) and Onicescu energy ($E$) have been explored extensively in both \emph{free} H atom (FHA) and \emph{confined} H atom (CHA). For a given quantum state, accurate results are presented by employing respective \emph{exact} analytical wave functions in $r$ space. The $p$-space wave functions are generated from respective Fourier transforms$-$for FHA these can be expressed analytically in terms of Gegenbauer polynomials, whereas in CHA these are computed numerically. \emph{Exact} mathematical expressions of $R_r^{\alpha}, R_p^{\beta}$, $T_r^{\alpha}, T_p^{\beta}, E_r, E_p$ are derived for \emph{circular} states of a FHA. Pilot calculations are done taking order of entropic moments ($\alpha, \beta$) as $(\frac{3}{5}, 3)$ in $r$ and $p$ spaces. A detailed, systematic analysis is performed for both FHA and CHA with respect to state indices $n,l$, and with confinement radius ($r_c$) for the latter. In a CHA, at small $r_{c}$, kinetic energy increases, whereas $S_{\rvec}, R^{\alpha}_{\rvec}$ decrease with growth of $n$, signifying greater localization in high-lying states. At moderate $r_{c}$, there exists an interplay between two mutually opposing factors: (i) radial confinement (localization) and (ii) accumulation of radial nodes with growth of $n$ (delocalization). Most of these results are reported here for the first time, revealing many new interesting features. Comparison with literature results, wherever possible, offers excellent agreement.

The accessible information and the informational power quantify the maximum amount of information that can be extracted from a quantum ensemble and by a quantum measurement, respectively. Here, we investigate the tradeoff between the accessible information (informational power, respectively) and the purity of the states of the ensemble (the elements of the measurement, respectively). Under any given lower bound on the purity, i) we compute the minimum informational power and show that it is attained by the depolarized uniformly-distributed measurement; ii) we give a lower bound on the accessible information. Under any given upper bound on the purity, i) we compute the maximum accessible information and show that it is attained by an ensemble of pairwise commuting states with at most two distinct non-null eigenvalues; ii) we give a lower bound on the maximum informational power. The present results provide, as a corollary, novel sufficient conditions for the tightness of the Jozsa-Robb-Wootters lower bound to the accessible information.

Clausius inequality has deep implications for reversibility and the arrow of time. Quantum theory is able to extend this result for closed systems by inspecting the trajectory of the density matrix on its manifold. Here we show that this approach can provide an upper and lower bound to the irreversible entropy production for open quantum systems as well. These provide insights on the thermodynamics of the information erasure. Limits of the applicability of our bounds are discussed, and demonstrated in a quantum photonic simulator.

This paper provides, firstly, a succinct mathematical derivation of Bose-Einstein condensation (BEC) of photons elaborating on previous results [M\"uller, E.E., Annals of Phys. 184, 219-230 (1988); M\"uller, E.E. Physica 139A, 165-174 (1986)] including new results on the condensate function, and, secondly, applies this framework to consistently explain experimental findings reported in Klaers J., Schmitt, J., Vewinger, F & Weitz, M., Nature 468, 545-548 (2010). The theoretical approach presented here invites to significantly widen the experimental framework for BEC of photons including three-dimensional photon resonators and thermalization mechanisms different from a dye medium in the cavity.

We experimentally demonstrate an original method to measure very accurately the density of a frozen Rydberg gas. It is based on the use of adiabatic transitions induced by the long-range dipole-dipole interaction in pairs of nearest neighbor Rydberg atoms by sweeping an electric field with time. The efficiency of this two-body process is experimentally tunable, depends strongly on the density of the gas and can be accurately calculated. The analysis of this efficiency leads to an accurate determination of the Rydberg gas density, and to a calibration of the Rydberg detection. Our method does not require any prior knowledge or estimation of the volume occupied by the Rydberg gas, or of the efficiency of the detection.

Several well-known statistical measures similar to \emph{LMC} and \emph{Fisher-Shannon} complexity have been computed for confined hydrogen atom in both position ($r$) and momentum ($p$) spaces. Further, a more generalized form of these quantities with R\'enyi entropy ($R$) is explored here. The role of scaling parameter in the exponential part is also pursued. $R$ is evaluated taking order of entropic moments $\alpha, \beta$ as $(\frac{2}{3},3)$ in $r$ and $p$ spaces. Detailed systematic results of these measures with respect to variation of confinement radius $r_c$ is presented for low-lying states such as, $1s$-$3d,~4f$ and $5g$. For \emph{nodal} states, such as $2s,~3s$ and $3p$, as $r_c$ progresses there appears a maximum followed by a minimum in $r$ space, having certain values of the scaling parameter. However, the corresponding $p$-space results lack such distinct patterns. This study reveals many other interesting features.

The so-called information-thermodynamics link has been created in a series of works starting from Maxwell demon and established by the idea of transforming information into work in the though experiment of Szilard which then evolved into the vast field of research. The aim of this note is firstly to present two new models of the Szilard engine containing arbitrary number of molecules which show irrelevance of acquiring information for work extraction. Secondly, the difference between the definition of entropy for ergodic systems and systems with ergodicity breaking constraints is emphasized. The role of nonergodic systems as information carriers and the thermodynamic cost of stability and accuracy of information encoding and processing is briefly discussed.

We introduce a general framework for de Finetti reduction results, applicable to various notions of partially exchangeable probability distributions. Explicit statements are derived for the cases of exchangeability, Markov exchangeability, and some generalizations of these. Our techniques are combinatorial and rely on the "BEST" theorem, enumerating the Eulerian cycles of a multigraph.

A quantum computer has the potential to effciently solve problems that are intractable for classical computers. Constructing a large-scale quantum processor, however, is challenging due to errors and noise inherent in real-world quantum systems. One approach to this challenge is to utilize modularity--a pervasive strategy found throughout nature and engineering--to build complex systems robustly. Such an approach manages complexity and uncertainty by assembling small, specialized components into a larger architecture. These considerations motivate the development of a quantum modular architecture, where separate quantum systems are combined via communication channels into a quantum network. In this architecture, an essential tool for universal quantum computation is the teleportation of an entangling quantum gate, a technique originally proposed in 1999 which, until now, has not been realized deterministically. Here, we experimentally demonstrate a teleported controlled-NOT (CNOT) operation made deterministic by utilizing real-time adaptive control. Additionally, we take a crucial step towards implementing robust, error-correctable modules by enacting the gate between logical qubits, encoding quantum information redundantly in the states of superconducting cavities. Such teleported operations have significant implications for fault-tolerant quantum computation, and when realized within a network can have broad applications in quantum communication, metrology, and simulations. Our results illustrate a compelling approach for implementing multi-qubit operations on logical qubits within an error-protected quantum modular architecture.

This paper reviews the structure of standard quantum mechanics, introducing the basics of the von Neumann-Dirac axiomatic formulation as well as the well-known Copenhagen interpretation. We review also the major conceptual difficulties arising from this theory, first and foremost, the well-known measurement problem. The main aim of this essay is to show the possibility to solve the conundrums affecting quantum mechanics via the methodology provided by the primitive ontology approach. Using Bohmian mechanics as an example, the paper argues for a realist attitude towards quantum theory. In the second place, it discusses the Quinean criterion for ontology and its limits when it comes to quantum physics, arguing that the primitive ontology programme should be considered as an improvement on Quine's method in determining the ontological commitments of a theory.

Quantum mechanics, devoid of any additional assumption, does not give any theoretical constraint on the projection basis to be used for the measurement process. It is shown in this paper that it does neither allow any physical means for an experimenter to determine which measurement bases have been used by another experimenter. As a consequence, quantum mechanics allows a situation in which two experimenters witness incoherent stories without being able to detect such incoherence, even if they are allowed to communicate freely by exchanging iterative and bilateral messages.

The classical Lippmann-Schwinger equation plays an important role in the scattering theory (non-relativistic case, Schr\"odinger equation). In the present paper we consider the relativistic analogue of the Lippmann-Schwinger equation. We represent the corresponding equation in the integral form. Using this integral equation we investigate the stationary scattering problems (relativistic case, Dirac equation). We consider the dynamical scattering problems (relativistic case, Dirac equation) as well.