We propose a minimalistic model of quantum measurements within a finite

system that undergoes a regular unitary evolution. Based on information theory,

the measurement process requires a sacrifice of information entropy. This loss

in our model is represented by a single cubit being isolated from the rest of

the system. As a result of the partitioning, the classical domain emerges and

the measurement occurs. The effect of the measurement on the quantum state of

# All

The complex collisional properties of atoms fundamentally limit

investigations into a range of processes in many-atom ensembles. In contrast,

the bottom-up assembly of few- and many-body systems from individual atoms

offers a controlled approach to isolating and studying such collisional

processes. Here, we use optical tweezers to individually assemble pairs of

trapped $^{85}$Rb atoms, and study the spin dynamics of the two-body system in

a thermal state. The spin-2 atoms show strong pair correlation between magnetic

Long-lived sub-levels of the electronic ground-state manifold of rare-earth

ions in crystals can be used as atomic population reservoirs for photon

echo-based quantum memories. We measure the dynamics of the Zeeman sub-levels

of erbium ions that are doped into a lithium niobate waveguide, finding

population lifetimes at cryogenic temperatures as long as seconds. Then, using

these levels, we prepare and characterize atomic frequency combs, which can

serve as a memory for quantum light at 1532 nm wavelength. The results allow

Motivated by the problem of classifying individuals with a disease versus

controls using functional genomic attributes as input, we encode the input as a

string of 1s (presence) or 0s (absence) of the genomic attribute across the

genome. Blocks of physical regions in the subdivided genome serve as the

feature dimensions, which takes full advantage of remaining in the

computational basis of a quantum computer. Given that a natural distance

between two binary strings is the Hamming distance and that this distance

Localization in one-dimensional disordered or quasiperiodic non-interacting

systems in presence of power-law hopping is very different from localization in

short-ranged systems. Power-law hopping leads to algebraic localization as

opposed to exponential localization in short-ranged systems. Exponential

localization is synonymous with insulating behavior in the thermodynamic limit.

Here we show that the same is not true for algebraic localization. We show, on

In quantum computation the target fidelity of the qubit gates is very high,

with the admissible error being in the range from $10^{-3}$ to $10^{-4}$ and

even less, depending on the protocol. The direct experimental determination of

such an extremely small error is very challenging by standard quantum-process

tomography. Instead, the method of randomized benchmarking, which uses a random

sequence of Clifford gates, has become a standard tool for determination of the

A classical stochastic formalism is presented and applied to the case of two

linearly coupled harmonic oscillators. It is shown that phenomena such as

state-swap, quadrature squeezing, entanglement and violation of entanglement

inequalities naturally occur in a stochastic framework, as a consequence of the

interaction. Based on these results, it is discussed how these effects arise in

fully classical systems, such as cholesteric liquid crystals in the presence of

a magnetic field.

Given two pairs of quantum states, we want to decide if there exists a

quantum channel that transforms one pair into the other. The theory of quantum

statistical comparison and quantum relative majorization provides necessary and

sufficient conditions for such a transformation to exist, but such conditions

are typically difficult to check in practice. Here, by building upon work by

Matsumoto, we relax the problem by allowing for small errors in one of the

Pure state entanglement transformations have been thought of as irreversible,

with reversible transformations generally only possible in the limit of many

copies. Here, we show that reversible entanglement transformations do not

require processing on the many copy level, but can instead be undertaken on

individual systems, provided the amount of entanglement which is produced or

consumed is allowed to fluctuate. We derive necessary and sufficient conditions

We study the large-time behaviour of a sample $\mathcal{S}$ consisting of an

ensemble of fermionic walkers on a graph interacting with a structured infinite

reservoir of fermions $\mathcal{E}$ through an exchange of particles in

preferred states. We describe the asymptotic state of $\mathcal{S}$ in terms

the initial state of $\mathcal{E}$, with especially simple formulae in the

limit of small coupling strength. We also study the particle fluxes into the

different parts of the reservoir.