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We study the behaviour of the fidelity and the Uhlmann connection in

two-dimensional systems of free fermions that exhibit non-trivial topological

behavior. In particular, we use the fidelity and a quantity closely related to

the Uhlmann factor in order to detect phase transitions at zero and finite

temperature for topological insulators and superconductors. We show that at

zero temperature both quantities predict quantum phase transitions: a sudden

drop of fidelity indicates an abrupt change of the spectrum of the state, while

Privacy amplification (PA) is a vital procedure in quantum key distribution

(QKD) to generate the secret key that the eavesdropper has only negligible

information from the identical correcting key for the communicating parties.

With the increase of repeat frequency of discrete-variable QKD (DV-QKD) system,

the processing speed of PA has become the bottle neck restricting DV-QKD's

secure key rate. The PA using Toeplitz-based Hash function is adopted widely

We propose to manipulate the statistic properties of the photons transport

nonreciprocally via quadratic optomechanical coupling. We present a scheme to

generate quadratic optomechanical interactions in the normal optical modes of a

whispering-gallery-mode (WGM) optomechanical system by eliminating the linear

optomechanical couplings via anticrossing of different modes. By optically

pumping the WGM optomechanical system in one direction, the effective quadratic

Multiple quantum (MQ) NMR coherence spectra, which can be obtained

experimentally in MQ NMR, can be transferred from the sender to the remote

receiver without mixing the MQ-coherences of different orders and distortions.

The only effect of such transfer is scaling of the certain blocks of sender's

density matrix (matrices of MQ-coherences of different order). Such a

block-scaled transfer is an alternative to the perfect state transfer. In

particular, equal scaling of higher order MQ-coherences matrices is possible.

We consider the communication line with two-qubit sender and receiver, the

later is embedded into the four-qubit extended receiver. Using the optimizing

unitary transformation on the extended receiver we restore the structure of the

non-diagonal part of an arbitrary initial sender's state at the remote receiver

at certain time instant. Obstacles for restoring the diagonal part are

discussed. We represent examples of such structural restoring in a

communication line of 42 spin-1/2 particles.

We derive an effective equation of motion within the steady-state subspace of

a large family of Markovian open systems (i.e., Lindbladians) due to

perturbations of their Hamiltonians and system-bath couplings. Under mild and

realistic conditions, competing dissipative processes destructively interfere

without the need for fine-tuning and produce no dissipation within the

steady-state subspace. In quantum error-correction, these effects imply that

continuously error-correcting Lindbladians are robust to calibration errors,

Vortices in electron beams can manifest several types of topological

phenomena, such as the formation of exotic structures or interactions with

topologically structured electromagnetic fields. For instance, the wavefunction

of an electron beam can acquire a phase vortex upon propagating through a

magnetic monopole, which, in practice, provides a convenient method for

generating electron vortex beams. Here, we show how an electric field must be

structured in order to achieve a similar effect. We find that, much as in the

We study the production of photons in a model of three bosonic atomic modes

non-linearly coupled to a cavity mode. In absence of external driving and

dissipation, the energy levels at different photon numbers assemble into the

steps of an energy staircase which can be employed as guidance for preparing

multi-photon states. We consider adiabatic photon production, driving the

system through a sequence of Landau-Zener transitions in the presence of

external coherent light pumping. We also analyse the non-equilibrium dynamics

This proposal investigates the photon-statistics of light emitted by a

statistical ensemble of cold atoms excited by the near-field of an optical

nanofiber tip. Dipole-dipole interactions of atoms at such short distance from

each other suppress the simultaneous emission of more than one photon and lead

to antibunching of photons. We consider a mean atom number on the order of one

and deal with a poissonian mixture of one and two atoms including dipole-dipole

interactions and collective decay. Time tracks of the atomic states are

Quantum measurements can be interpreted as a generalisation of probability

vectors, in which non-negative real numbers are replaced by positive

semi-definite operators. We extrapolate this analogy to define a generalisation

of doubly stochastic matrices that we call doubly normalised tensors (DNTs),

and formulate a corresponding version of Birkhoff-von Neumann's theorem, which

states that permutations are the extremal points of the set of doubly

stochastic matrices. We prove that joint measurability arises as a mathematical