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We look for new steps on the dynamical operations that may squeeze

simultaneously some families of quantum states, independently of their initial

shape, induced by softly acting external fields which might produce the

squeezing of the canonical observables $q,p$ of charged particles. Also, we

present some exactly solvable cases of the problem which appear in the

symmetric evolution intervals permitting to find explicitly the time dependence

of the external fields needed to generate the required evolution operators.

The thesis is centred on the theory of experimental methods in solid-state

Nuclear Magnetic Resonance (ssNMR) spectroscopy, which deals with the

interaction of electromagnetic radiation with nuclei in a magnetic field and

possessing a fundamental quantum mechanical property called spin.

Orientation-dependent interactions in ssNMR, while offering a wealth of

information, lead to broad indistinct signal and therefore are averaged out,

predominantly by Magic-Angle Spinning (MAS). Reintroduction of the coupling

Boson Sampling photonic networks can be used to obtain Heisenberg limited

measurements of optical phase gradients, by using quantum Fourier transform

interferometry. Here, we use phase-space techniques and the complex

P-distribution, to simulate a $100$ qubit Fourier transform interferometer with

additional random phases, to simulate decoherence. This is far larger than

possible in conventional calculations of matrix permanents, which is the

standard technique for such calculations. Our results show that this quantum

- Read more about Robustness of quantum Fourier transform interferometry. (arXiv:1711.07153v1 [quant-ph])
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We study the entanglement for a state on linked torus boundaries in $3d$

Chern-Simons theory with a generic gauge group and present the asymptotic

bounds of R\'enyi entropy at two different limits: (i) large Chern-Simons

coupling $k$, and (ii) large rank $r$ of the gauge group. These results show

that the R\'enyi entropies cannot diverge faster than $\ln k$ and $\ln r$,

respectively. We focus on torus links $T(2,2n)$ with topological linking number

$n$. The R\'enyi entropy for these links shows a periodic structure in $n$ and

In the companion paper we motivated a renormalisation flow on

Osterwalder-Schrader data (OS-data) consisting of 1. a Hilbert space, 2. a

cyclic vacuum and 3. a Hamiltonian annihilating that vacuum. As the name

suggests, the motivation was via the OS reconstruction theorem which allows to

reconstruct the OS data from an OS measure satisfying (a subset of) the OS

axioms, in particular reflection positivity. The guiding principle was to map

the usual Wilsonian path integral renormalisation flow onto a flow of the

We demonstrate that quantum Fisher information and superradiance can be

formulated as coherence measures in accordance with the resource theory of

coherence, thus establishing a direct link between metrological information,

superradiance and coherence. We also show that the trivial coherence measure

has a metrological interpretation. The arguments are then generalized to show

that coherence may be considered as the underlying fundamental resource for any

Quantum metrology allows us to attain a measurement precision that surpasses

the classically achievable limit by using quantum characters. The metrology

precision is raised from the standard quantum limit (SQL) to the Heisenberg

limit (HL) by using entanglement. However, it was reported that the HL returns

to the SQL in the presence of local dephasing environments under the long

encoding-time condition. We evaluate here the exact impacts of local

dissipative environments on quantum metrology, based on the Ramsey

We examine Ralph's equivalent circuit model of D-CTCs, which was proposed to

derive Deutsch's maximum entropy rule of D-CTCs. By constructing

counterexamples we show that the equivalent circuit model does not always

reproduce the unique fixed state with the maximal von Neumann entropy. We

speculate that the equivalent circuit model remains the correct description of

D-CTCs and it can reproduce a revised maximum entropy rule of D-CTCs. We also

suggest that the revised maximum entropy rule may eliminate the discontinuous

A nonlinear quantum-classical transition wave equation is proposed for

dissipative systems within the Caldirola-Kanai model. Equivalence of this

transition equation to a scaled Schr\"{o}dinger equation is proved. The

dissipative dynamics is then studied in terms of what we call scaled

trajectories following the standard procedure used in Bohmian mechanics. These

trajectories depend on a continuous parameter allowing us a smooth transition

from Bohmian to classical trajectories. Arrival times and actual momentum

In this paper, we discuss the broken $\cal PT$-symmetric hamiltonians and the

weak values. It was showed that a broken $\cal PT$-symmetric quantum system can

be simulated by weak measurement in a large conventional quantum system.

Moreover, such a paradigm reduces to the embedding paradigm when the system is

unbroken $\cal PT$-symmetric.