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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

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

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