Related papers: Lie algebraic invariants in quantum linear optics

State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on…

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic non-perturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field…

Spontaneous parametric down-conversion in quantum optics is an invaluable resource for the realization of high-dimensional qudits with spatial modes of light. One of the main open challenges is how to directly generate a desirable qudit…

Inherent binary or collective interactions in ensembles of quantum emitters induce a spread in the energy and lifetime of their eigenstates. While this typically causes fast decay and dephasing, in many cases certain special entangled…

A symmetry-preserving, reduced-order state observer is presented for the unmeasured part of a system's state, where the nonlinear system dynamics exhibit symmetry under the action of a Lie group. Leveraging this symmetry with a moving…

Quantum metrology employs quantum resources to enhance the measurement sensitivity beyond that can be achieved classically. While multi-photon entangled NOON states can in principle beat the shot-noise limit and reach the Heisenberg limit,…

We derive an analytical description for the quantum state preparation using systems of on-off detectors. Our method will apply the true click statistics of such detector systems. In particular, we consider heralded quantum state preparation…

We propose a linear optical quantum computation scheme using time-frequency degree of freedom. In this scheme, a qubit is encoded in single-photon frequency combs, and manipulation of the qubits is performed using time-resolving detectors,…

Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example: they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom…

We show that Hall conductance and its non-abelian and higher-dimensional analogs are obstructions to promoting a symmetry of a state to a gauge symmetry. To do this, we define a local Lie algebra over a Grothendieck site as a pre-cosheaf of…

Performing interferometry in an optical lattice formed by standing waves of light offers potential advantages over its free-space equivalents since the atoms can be confined and manipulated by the optical potential. We demonstrate such an…

We propose and experimentally verify a scheme to engineer arbitrary states of traveling light field up to the two-photon level. The desired state is remotely prepared in the signal channel of spontaneous parametric down-conversion by means…

This paper studies the Kalman decomposition for linear quantum systems. Contrary to the classical case, the coordinate transformation used for the decomposition must belong to a specific class of transformations as a consequence of the laws…

We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…

A novel scheme is presented for generation of a multipartite W state for arbitrary number of qubits. Based on a recent proposal of entanglement without touching, it serves to demonstrate the potential of particle indistinguishability as a…

Fock states are quantized states of electromagnetic waves with diverse applications in quantum optics and quantum communication. However, generation of arbitrary optical Fock states still remains elusive. Majority of Fock state generation…

We study dissipative translationally invariant free-fermionic theories with quadratic Liouvillians. Using a Lie-algebraic approach, we solve the Lindblad equation and find the density matrix at all times for arbitrary time dependence of the…

Invariants are a set of properties over program attributes that are expected to be true during the execution of a program. Since developing those invariants manually can be costly and challenging, there are a myriad of approaches that…

For linear time-invariant systems, a separation principle holds: stable observer and stable state feedback can be designed for the time-invariant system, and the combined observer and feedback will be stable. For non-linear systems, a local…

Conditional quantum optical processes enable a wide range of technologies from generation of highly non-classical states to implementation of quantum logic operations. The process fidelity that can be achieved in a realistic implementation…