At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for example, is characterised by the ensemble of system trajectories in phase space and, by including the probabilities for various trajectories to occur, a work distribution can be constructed. However, without phase space trajectories, the task of constructing a work probability distribution in the quantum regime has proven elusive. Indeed, the existence of such a distribution based on generalised measurements has recently been ruled out [Phys. Rev. Lett. 118, 070601 (2017)]. Here we use quantum trajectories in phase space and define fluctuating work as power integrated along the trajectories, in complete analogy to classical statistical physics. The resulting work probability distribution is valid for any quantum evolution, including cases with coherences in the energy basis. We demonstrate the quantum work probability distribution and its properties with the example of a driven quantum harmonic oscillator. An important feature of the work distribution is its dependence on the initial statistical mixture of pure states and it thus goes beyond the framework of generalised measurements. The proposed approach allows the full thermodynamic characterisation of the dynamics of quantum systems, including the measurement process.

Bohmian trajectories are considered for a particle that is free (i.e. the potential energy is zero), except for a half-line barrier. On the barrier, both Dirichlet and Neumann boundary conditions are considered. The half-line barrier yields one of the simplest cases of diffraction. Using the exact time-dependent propagator found by Schulman, the trajectories are numerically computed for different initial Gaussian wave packets. In particular, it is found that different boundary condition may lead to qualitatively different sets of trajectories. In the Dirichlet case, the particles tend to be more strongly repelled. The case of an incoming plane wave is also considered. The corresponding Bohmian trajectories are compared with the trajectories of an oil drop hopping at the surface of a vibrating bath.

We introduce a game related to the $I_{3322}$ game and analyze the value of this game over various families of synchronous quantum probability densities.

Scalability and foundry compatibility (as for example in conventional silicon based integrated computer processors) in developing quantum technologies are exceptional challenges facing current research. Here we introduce a quantum photonic technology potentially enabling large scale fabrication of semiconductor-based, site-controlled, scalable arrays of electrically driven sources of polarization-entangled photons, with the potential to encode quantum information. The design of the sources is based on quantum dots grown in micron-sized pyramidal recesses along the crystallographic direction (111)B theoretically ensuring high symmetry of the quantum dots - the condition for actual bright entangled photon emission. A selective electric injection scheme in these non-planar structures allows obtaining a high density of light-emitting diodes, with some producing entangled photon pairs also violating Bell's inequality. Compatibility with semiconductor fabrication technology, good reproducibility and control of the position make these devices attractive candidates for integrated photonic circuits for quantum information processing.

A nonlocal game with a synchronous correlation is a natural generalization of a function between two finite sets, and has frequently appeared in the context of graph homomorphisms. In this work we examine analogues of Bell's inequalities for synchronous correlations. We show that unlike in the general case with the CHSH inequality there can be no quantum Bell violation among synchronous correlations with two measurement settings. However we exhibit explicit analogues of Bell's inequalities for synchronous correlation with three measurement settings and two outputs that do admit quantum violations.

In this paper the relations between the asymptotic velocity operators of a quantum system and the asymptotic velocities of the associated Bohmian trajectories are studied. In particular it is proved that, under suitable conditions of asymptotic regularity, the probability distribution of the asymptotic velocities of the Bohmian trajectories is equal to the one derived from the asymptotic velocity operators of the associated quantum system. It is also shown that in the relativistic case the distribution of the asymptotic velocities of the Bohmian trajectories is covariant, or equivalently, it does not depend on a preferred foliation (it is well known that this is not the case for the structure of the Bohmian trajectories or for their spatial distribution at a finite time). This result allows us to develop a covariant formulation of relativistic Bohmian mechanics; such a formulation is proposed here merely as a mathematical possibility, while its empirical adequacy will be discussed elsewhere.

Progress in quantum computing hardware raises questions about how these devices can be controlled, programmed, and integrated with existing computational workflows. We briefly describe several prominent quantum computational models, their associated quantum processing units (QPUs), and the adoption of these devices as accelerators within high-performance computing systems. Emphasizing the interface to the QPU, we analyze instruction set architectures based on reduced and complex instruction sets, i.e., RISC and CISC architectures. We clarify the role of conventional constraints on memory addressing and instruction widths within the quantum computing context. Finally, we examine existing quantum computing platforms, including the D-Wave 2000Q and IBM Quantum Experience, within the context of future ISA development and HPC needs.

We derived stochastic master equation for a system interacting with the environment prepared in a superposition of coherent states. We use the model of repeating interactions and measurements with the environment given by an infinite chain of identical and not interacting between themselves quantum systems. Elements of the environment chain interact with the quantum system in turn one by one and they are subsequently measured. We determined the conditional evolution of the quantum system for the continuous in time observations as a limit of discrete recurrence equations.

We consider a simple (1+1)-dimensional model for the Casimir-Polder interaction consisting of two oscillators coupled to a scalar field. We include dissipation in a first principles approach by allowing the oscillators to interact with heat baths. For this system, we derive an expression for the free energy in terms of real frequencies. From this representation, we derive the Matsubara representation for the case with dissipation. Further we consider the case of vanishing intrinsic frequencies of the oscillators. We show that in this case the contribution from the zeroth Matsubara frequency gets modified and no problems with the laws of thermodynamics appear.

We consider the out-of-equilibrium dynamics generated by joining two domains with arbitrary opposite magnetisations. We study the stationary state which emerges by the unitary evolution via the spin $1/2$ XXZ Hamiltonian, in the gapless regime, where the system develops a stationary spin current. Using the generalized hydrodynamic approach, we present a simple formula for the space-time profile of the spin current and the magnetisation exact in the limit of large times. As a remarkable effect, we show that the stationary state has a strongly discontinuous dependence on the strength of interaction. This feature allows us to give a qualitative estimation for the transient behavior of the current which is compared with numerical simulations. Moreover, we analyse the behavior around the edge of the magnetisation profile and we argue that, unlike the XX free-fermionic point, interactions always prevent the emergence of a Tracy-Widom scaling.

Blackbody radiation contains (on average) an entropy of 3.9+/-2.5 bits per photon. This applies also to the Hawking radiation from both analogue black holes and general relativistic black holes. The flip side of this observation is the information budget: If the emission process is unitary, then this entropy is exactly compensated by "hidden information" in photon-photon correlations. Herein we extend this argument to the Hawking radiation from general relativistic black holes, demonstrating that unitarity (when placed in a proper physical context) leads to a perfectly reasonable entropy/information budget without any pressing need for new physics. Unitarity instead has a different implication --- the horizon (if present) cannot be an event horizon, it must be an apparent/trapping horizon, or some variant thereof. The key technical aspect of our calculation is a variant of the "average subsystem" approach developed by Page. We shall demonstrate that the Page curve, which is extracted from a bipartite pure system consisting of (black hole)+(Hawking radiation), misses crucial aspects of the relevant physics; thereby giving rise to paradoxes that need new physics to be resolved. In contrast the "average subsystem" approach gives much better results when applied to a tripartite pure system consisting of the (black hole)+(Hawking radiation)+(rest of universe).

In this paper we investigate measures of chaos and entanglement in rational conformal field theories in 1+1 dimensions. First, we derive a universal formula for the late time value of the out-of-time-ordered correlators for this class of theories. Our universal result can be expressed as a particular combination of the modular S-matrix elements known as the anyon monodromy scalar. Next, in the explicit setup of a $SU(N)_k$ Wess-Zumino-Witten model, we compare the late time behavior of the out-of-time-ordered correlators and the purity. Interestingly, in the large-c limit, the purity grows logarithmically as in holographic theories; in contrast, the out-of-time-ordered correlators remain, in general, non-vanishing.

The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the latter solution is reported for the first time. Applications of these solutions include angular momenta, a quantitative calculation of the absorption spectrum and accurate plots of surfaces of amplitude functions. The shape of an amplitude function, and even the quantum numbers in a particular set to specify such an individual function, depend on the coordinates in a particular chosen system, and are therefore artefacts of that particular coordinate representation within wave mechanics. All discussion of atomic or molecular properties based on such shapes or quantum numbers therefore lacks general significance

We investigate the relation between the classical ergodicity and the quantum eigenstate thermalization in the fully connected Ising ferromagnets. In the case of spin-1/2, an expectation value of an observable in a single energy eigenstate coincides with the long-time average in the underlying classical dynamics, which is a consequence of the Wentzel-Kramers-Brillouin approximation. In the case of spin-1, the underlying classical dynamics is not necessarily ergodic. In that case, it turns out that, in the thermodynamic limit, the statistics of the expectation values of an observable in the energy eigenstates coincides with the statistics of the long-time averages in the underlying classical dynamics starting from random initial states sampled uniformly from the classical phase space. This feature seems to be a general property in semiclassical systems, and the result presented here is crucial in discussing equilibration, thermalization, and dynamical transitions of such systems.

We describe how an ensemble of four-level atoms in the diamond-type configuration can be applied to create a fully controllable effective coupling between two cavity modes. The diamond-type configuration allows one to use a bimodal cavity, which supports modes of different frequencies or circular polarizations, because each mode is coupled to different atomic transition. This system can be used for mapping a quantum state of one cavity mode onto the other mode on demand. Additionally, it can serve as a fast opening high-Q cavity system that can be easily and coherently controlled with laser fields.

We present protocols for the generation of high-dimensional entangled states of anharmonic oscillators by means of coherent manipulation of light-matter systems in the ultrastrong coupling regime. Our protocols consider a pair of ultrastrong coupled qubit-cavity systems, each coupled to an ancilla qubit, and combine classical pulses plus the selection rules imposed by the parity symmetry. We study the robustness of the entangling protocols under dissipative effects. This proposal may have applications within state-of-art circuit quantum electrodynamics.

This paper provides a novel approach to solving the transmission of electrons through large graphene nano-structures, which is shown to be accurate both at high and low speeds. The model for graphene being solved is the continuum model governed by an analogue to the Dirac equation. For a solution, the Dirac equation is scalarised using the Foldy-Wouthuysen expansion approximation, to reduce the problem of calculating the electron wave propagation to a scalar differential equation. Also transformed is the exact solution of the Dirac equation in homogeneous space for the calculation of the propagation of electron waves. By analytically calculating the boundary conditions of the transformed wave functions, we have been able to generate transfer matrices for the scalar propagation equations. Furthermore, we have implemented the scattering matrix method upon these transfer matrices. implementing the scattering matrix method makes a numerical stable propagation of the waves through the graphene. Finally we test the convergence and accuracy of the new method against analytic solutions. Also included is a rich appendix detailing the results of our research into relativistic Green's functions.

Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model's microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time $\tau_{bd}$, proportional to the size of the system. This behaviour is explained by noticing that the low-energy modes, responsible for the scaling properties, are resilient to the absorption of energy. Our results suggest that relevant features of the universality do hold also when the system is brought out-of-equilibrium by a periodic driving.

We prove a generalization of the quantum de Finetti theorem when the local space is an infinite-dimensional Fock space. In particular, instead of considering the action of the permutation group on $n$ copies of that space, we consider the action of the unitary group $U(n)$ on the creation operators of the $n$ modes and define a natural generalization of the symmetric subspace as the space of states invariant under unitaries in $U(n)$. Our first result is a complete characterization of this subspace, which turns out to be spanned by a family of generalized coherent states related to the special unitary group $SU(p,q)$ of signature $(p,q)$. More precisely, this construction yields a unitary representation of the noncompact simple real Lie group $SU(p,q)$. We therefore find a dual unitary representation of the pair of groups $U(n)$ and $SU(p,q)$ on an $n(p+q)$-mode Fock space.

The (Gaussian) $SU(p,q)$ coherent states resolve the identity on the symmetric subspace, which implies a Gaussian de Finetti theorem stating that tracing over a few modes of a unitary-invariant state yields a state close to a mixture of Gaussian states. As an application of this de Finetti theorem, we show that the $n\times n$ upper-left submatrix of an $n\times n$ Haar-invariant unitary matrix is close in total variation distance to a matrix of independent normal variables if $n^3 =O(m)$.

We propose an extension of Quantum Mechanics based on the idea that the underlying "quantum noise" has a non-zero, albeit very small, correlation time $\tau_c$. The standard (non-relativistic) Schrodinger equation is recovered to zeroth order in $\tau_c$, and the first correction to energy levels is explicitly computed. Some consequences are discussed, in particular the violation of Heisenberg's uncertainty principle at short times.