# All

We present a quantum algorithm to compute the entanglement spectrum of

arbitrary quantum states. The interesting universal part of the entanglement

spectrum is typically contained in the largest eigenvalues of the density

matrix which can be obtained from the lower Renyi entropies through the

Newton-Girard method. Obtaining the $p$ largest eigenvalues

($\lambda_1>\lambda_2\ldots>\lambda_p$) requires a parallel circuit depth of

$\mathcal{O}(p(\lambda_1/\lambda_p)^p)$ and $\mathcal{O}(p\log(N))$ qubits

An atom moving in a focused laser beam will experience a velocity-dependent

dipole force due to the Doppler effect, which allows the operation of a

Maxwell's demon. Photon scattering and other forms of dissipation can be

negligibly small, which appears to contradict quantum information proofs that a

Maxwell's demon must dissipate a minimum amount of energy. We resolve this

'paradox' by showing that Schrodinger's equation does not predict a

velocity-dependent dipole force. Forces of that kind have been observed

We experimentally study the phase stabilization of a semiconductor double

quantum dot (DQD) single atom maser by injection locking. A voltage-biased DQD

serves as an electrically tunable microwave frequency gain medium. The

statistics of the maser output field demonstrate that the maser can be phase

locked to an external cavity drive, with a resulting phase noise of -99 dBc/Hz

at a frequency offset of 1.3 MHz. The injection locking range, and the phase of

the maser output relative to the injection locking input tone are in good

This paper defines the amortized entanglement of a quantum channel as the

largest difference in entanglement between the output and the input of the

channel, where entanglement is quantified by an arbitrary entanglement measure.

We prove that the amortized entanglement of a channel obeys several desirable

properties, and we also consider special cases such as the amortized relative

entropy of entanglement and the amortized Rains relative entropy. Of especial

We introduce an infinite family of quantifiers of quantum correlations beyond

entanglement which vanish on both classical-quantum and quantum-classical

states and are in one-to-one correspondence with the quantum Fisher

informations. More specifically, these quantifiers are defined as the maximum

local quantum covariances over pairs of local observables with the same fixed

equispaced spectrum. We show that these quantifiers are entanglement monotones

when restricted to pure states of qubit-qudit systems. We also analytically

The Lieb-Schultz-Mattis theorem and its higher dimensional generalizations by

Oshikawa and Hastings require that translationally invariant 2D spin systems

with a half-integer spin per unit cell must either have a continuum of low

energy excitations, spontaneously break some symmetries, or exhibit topological

order with anyonic excitations. We establish a connection between these

constraints and a remarkably similar set of constraints at the surface of a 3D

interacting topological insulator. This, combined with recent work on

The detection of change points is a pivotal task in statistical analysis. In

the quantum realm, it is a new primitive where one aims at identifying the

point where a source that supposedly prepares a sequence of particles in

identical quantum states starts preparing a mutated one. We obtain the optimal

procedure to identify the change point with certainty ---naturally at the price

of having a certain probability of getting an inconclusive answer. We obtain

The study of non-equilibrium properties in topological systems is of

practical and fundamental importance. Here, we analyze the stationary

properties of a two-dimensional bosonic Hofstadter lattice coupled to two

thermal baths in the quantum open-system formalism. Novel phenomena appear like

chiral edge heat currents that are the out-of-equilibrium counterparts of the

zero-temperature edge currents. They support a new concept of dissipative

symmetry-protection, where a set of discrete symmetries protects topological

We propose a method of producing spin-nematic squeezing in ensembles of

integer-spin atoms confined within a high-finesse optical cavity. Our proposal

uses cavity-assisted Raman transitions to engineer a Dicke model for

integer-spin atoms, which, in a suitable limit, becomes a generator of

spin-nematic squeezing in the ensemble. With realistic parameters the scheme

should enable substantial squeezing on time scales that are orders of magnitude

shorter than those required by schemes based upon collisional dynamics in

Memory-assisted quantum key distribution (MA-QKD) has recently been proposed

as a technique to improve the rate-versus-distance behavior of QKD systems by

using existing, or nearly-achievable, quantum technologies. The promise is that

MA-QKD would require less demanding quantum memories than the ones needed for

probabilistic quantum repeaters. Nevertheless, early investigations suggest

that, in order to beat the conventional no-memory QKD schemes, the quantum