In a many-body quantum system, local operators in Heisenberg picture $O(t) =

e^{i H t} O e^{-i H t}$ spread as time increases. Recent studies have attempted

to find features of that spreading which could distinguish between chaotic and

integrable dynamics. The operator entanglement - the entanglement entropy in

operator space - is a natural candidate to provide such a distinction. Indeed,

while it is believed that the operator entanglement grows linearly with time

# All

Quantum Teleportation is the key communication functionality of the Quantum

Internet, allowing the ``transmission'' of qubits without either the physical

transfer of the particle storing the qubit or the violation of the quantum

mechanical principles. Quantum teleportation is facilitated by the action of

quantum entanglement, a somewhat counter-intuitive physical phenomenon with no

direct counterpart in the classical word. As a consequence, the very concept of

Self-testing refers to a device-independent way to uniquely identify the

state and the measurement for uncharacterized quantum devices. The only

information required comprises the number of measurements, the number of

outputs of each measurement, and the statistics of each measurement. Earlier

results on self-testing of multipartite state were restricted either to Dicke

states or graph states. In this paper, we propose self-testing schemes for a

large family of symmetric three-qubit states, namely the superposition of W

We derive the entanglement entropy of chiral fermions on the circle at

arbitrary temperature. The spin-sector contribution depends only on the total

length of the entangling region, regardless of the configuration of the

intervals. Thus three-partite information provides a global indicator for the

spin boundary conditions. Together with the modular Hamiltonian, our results

provide a systematic way of obtaining relative entropy on the torus.

We formulate an optimization problem of finding optimal Hamiltonians by

analogy to the variational principle. Given a variational ansatz for a

Hamiltonian we construct a loss function as a weighted sum of relevant

Hamiltonian properties specifying thereby the search query. Using fractional

quantum Hall effect as a test system we illustrate how the framework can be

used to determine a generating Hamiltonian of a finite-size model wavefunction

(Moore-Read Pfaffian and Read-Rezayi states) or to find optimal parameters for

We establish an important duality correspondence between topological order in

quantum many body systems and criticality in ferromagnetic classical spin

systems. We show how such a correspondence leads to a classical and simple

procedure for characterization of topological order in an important set of

quantum entangled states, namely the Calderbank-Shor-Steane (CSS) states. To

this end, we introduce a particular quantum Hamiltonian which allows us to

consider the existence of a topological phase transition from quantum CSS

Nonclassicality is studied through a quasidistribution of phases for the

Raman process under both weak and strong pump conditions. In the former case,

the solution is applicable to both resonant and off-resonant Raman processes,

while strong classical pump is assumed at resonance. Under weak pump conditions

(i.e., in a complete quantum treatment), the phase difference of phases

described by single nonclassical modes is required to be filtered to describe a

The quantum speed limit sets a bound on the minimum time required for a

quantum system to evolve between two states. For open quantum systems this

quantity depends on the dynamical map describing the time evolution in presence

of the environment, on the evolution time {\tau} , and on the initial state of

the system. We consider a general single qubit open dynamics and show that

there is no simple relationship between memory effects and the tightness of the

Quantum Ising model in a transverse field is of the simplest quantum many

body systems used for studying universal properties of quantum phase

transitions. Interestingly, it has been shown that such phase transitions can

be mapped to topological phase transitions in Toric code models by a dual

transformation [M. H. Zarei, Phys. Rev. B 96, 165146 (2017)]. Therefore, one

can expect that well-known properties of the transverse Ising model are used

for characterizing topological phase transition in Toric code model. In this

This paper proposes a multi-mode Gaussian modulated continuous variable

quantum key distribution (CV-QKD) scheme able to operate at high bandwidth

despite using conventional noisy, coherent detectors. We demonstrate

enhancement in shotnoise sensitivity as well as reduction in the electronic

noise variance of the coherent receiver of the multi-mode CV-QKD system. A

proof-of-concept simulation is presented using multiple modes; this

demonstrates an increase in signal-to-noise ratio and secure key rate at