Extracting as much information as possible about an object when probing with

a limited number of photons is an important goal with applications from biology

and security to metrology. Imaging with a few photons is a challenging task as

the detector noise and stray light are then predominant, which precludes the

use of conventional imaging methods. Quantum correlations between photon pairs

has been exploited in a so called 'heralded imaging scheme' to eliminate this

# All

The method of many body Green's functions is used to describe an arbitrary

system of electrons and nuclei in a rigorous manner given the Hamiltonian of

Coulombic interactions and kinetic energies. The theory given resolves the

problem arising from the translational and rotational invariance of the

Hamiltonian afflicting the existing theory based on the same technique. As a

result, we derive a coupled set of exact equations for the electron and nuclei

Green's functions giving a systematic way to potentially compute various

Recently, the study of non-Hermitian physics has attracted considerable

attention. The modified bulk-boundary correspondence has been proposed to

understand topological edge states in non-Hermitian static systems. Here we

report a new experimental observation of edge states in non-Hermitian

periodically driven systems. Some unconventional edge states are found not to

be satisfied with the bulk-boundary correspondence when the system belongs to

the broken parity-time (PT) symmetric phase. The experiments are performed in

In practical implementation of quantum key distributions (QKD), it requires

efficient, real-time feedback control to maintain system stability when facing

disturbance from either external environment or imperfect internal components.

Usually, a "scanning-and-transmitting" program is adopted to compensate

physical parameter variations of devices, which can provide accurate

compensation but may cost plenty of time in stopping and calibrating processes,

resulting in reduced efficiency in key transmission. Here we for the first

Based on his extension of the classical argument of Einstein, Podolsky and

Rosen, Schr\"odinger observed that, in certain quantum states associated with

pairs of particles that can be far away from one another, the result of the

measurement of an observable associated with one particle is perfectly

correlated with the result of the measurement of another observable associated

with the other particle. Combining this with the assumption of locality and

some ``no hidden variables" theorems, we showed in a previous paper [11] that

Langevin and Fokker-Planck equations for the Brownian motion in steep

(extremally anharmonic) potential wells of the form $U(x)= x^m/m, m=2n, n>1$

are interpreted as reliable approximations of the reflected Brownian motion in

the interval, as the potential steepness grows indefinitely. We investigate a

familiar transformation of the involved Fokker-Planck operator to the Hermitian

(eventually self-adjoint) Schr\"{o}dinger - type one $-\Delta + {\cal{V}}$,

with the two-well (bistable) potential ${\cal{V}}(x)= {\cal{V}}_m(x)=

We present a comprehensive study of the impact of non-uniform, i.e.\

path-dependent, photonic losses on the computational complexity of

linear-optical processes. Our main result states that, if each beam splitter in

a network induces some loss probability, non-uniform network designs cannot

circumvent the efficient classical simulations based on losses.

The characterization of an operator by its eigenvectors and eigenvalues

allows us to know its action over any quantum state. Here, we propose a

protocol to obtain an approximation of the eigenvectors of an arbitrary

Hermitian quantum operator. This protocol is based on measurement and feedback

processes, which characterize a reinforcement learning protocol. Our proposal

is composed of two systems, a black box named environment and a quantum state

named agent. The role of the environment is to change any quantum state by a

We experimentally studied the microwave response of a transmon artificial

atom coupled to two closely spaced resonant modes. When the atom is under

driven with one of the modes, the atom state and mode photons are superposed,

forming the dressed states. Dressed states with 1st, 2nd and 3rd excited states

of the atom were prepared and probed via the strong coupling to the other

resonant mode from the point of view of cavity quantum electrodynamics. The

We develop new protocols for high-fidelity single qubit gates that exploit

and extend theoretical ideas for accelerated adiabatic evolution. Our protocols

are compatible with qubit architectures with highly isolated logical states,

where traditional approaches are problematic; a prime example are

superconducting fluxonium qubits. By using an accelerated adiabatic protocol we

can enforce the desired adiabatic evolution while having gate times that are

comparable to the inverse adiabatic energy gap (a scale that is ultimately set