Related papers: Orbit dimensions in linear and Gaussian quantum op…
Light-matter interactions that are nonlinear with respect to the photon number reveal the true quantum nature of coherent states. We characterize how coherent states depart from Gaussian by the emergence of negative values in their Wigner…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
We study quantum vortex states of strongly interacting bosons in a two-dimensional rotating optical lattice. The system is modeled by Bose-Hubbard Hamiltonian with rotation. We consider lattices of different geometries, such as square,…
The measurement of a quantum state poses a unique challenge for experimentalists. Recently, the technique of "direct measurement" was proposed for characterizing a quantum state in-situ through sequential weak and strong measurements. While…
Gaussian states, operations, and measurements are central building blocks for continuous-variable quantum information processing which paves the way for abundant applications, especially including network-based quantum computation and…
We show how a quantum optical measurement scheme based on heterodyne detection can be used to explore geometrical and topological properties of condensed matter systems. Considering a 2D material placed in a cavity with a coupling to the…
Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view…
The mean-field approach to two-site Bose-Hubbard systems is well established and leads to nonlinear classical equations of motion for the population imbalance and the phase difference. It can, e.g., be based on the representation of the…
The geometric measure of entanglement $E$ of an $m$ qubit quantum state takes maximal possible value $m$. In previous work of Gross, Flammia, and Eisert, it was shown that $E \ge m-O(\log m)$ with high probability as $m\to\infty$. They…
We present a review of theories of states of quantum matter without quasiparticle excitations. Solvable examples of such states are provided through a holographic duality with gravitational theories in an emergent spatial dimension. We…
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
Complete characterization of states and processes that occur within quantum devices is crucial for understanding and testing their potential to outperform classical technologies for communications and computing. However, solving this task…
Fuzzy geometry considered as the possible mathematical framework for reformulation of quantum-mechanical formalism in geometric terms. In this approach the states of massive particle m correspond to elements of fuzzy manifold called fuzzy…
An octant representation of higher-order optical modes that includes Laguerre-Gaussian and Hermite-Gaussian modes is presented. The octant picture captures the high-dimensional nature of three-state optical systems and beyond, with standard…
We consider the action of the group of local unitary transformations, U(m) x U(n), on the set of (mixed) states W of the bipartite m x n quantum system. We prove that the generic U(m) x U(n)--orbits in W have dimension m^2+n^2-2. This…
An arbitrary quantum-optical process (channel) can be completely characterized by probing it with coherent states using the recently developed coherent-state quantum process tomography (QPT) [Lobino et al., Science 322, 563 (2008)]. In…
Different constructions for Hilbert state space for constrained systems are investigated. Properties of Gaussian states analogous to quantum mechanical Gaussian wave functions are studied. Their evolution for quadratic Hamiltonian case are…
Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal.…
We propose a protocol for coherently transferring non-Gaussian quantum states from optical field to a mechanical oscillator. The open quantum dynamics and continuous-measurement process, which can not be treated by the…
It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive…