# All

We study the quantum speed limit for open quantum systems described by the

Lindblad master equation. The obtained inequality shows a trade-off relation

between the operation time and the physical quantities such as the energy

fluctuation and the entropy production. We further identify a quantity

characterizing the speed of the state transformation, which appears only when

we consider the open system dynamics in the quantum regime. When the thermal

relaxation is dominant compared to the unitary dynamics of the system, we show

We propose a physical mechanism to generate and selectively amplify

anisotropic Rudermann-Kittel-Kasuya-Yosida (RKKY) interactions between two

local spins. The idea is to combine the deflection of the carrier velocity by a

P-N interface and the locking of this velocity to the carrier spin orientation

via spin-orbit coupling. We provide analytical and numerical results to

demonstrate this mechanism on the surface of a topological insulator P-N

junction. This work identifies the P-N interface as a second knob which,

Superconducting metamaterials are a promising resource for quantum

information science. In the context of circuit QED, they provide a means to

engineer on-chip, novel dispersion relations and a band structure that could

ultimately be utilized for generating complex entangled states of quantum

circuitry, for quantum reservoir engineering, and as an element for quantum

simulation architectures. Here we report on the development and measurement at

millikelvin temperatures of a particular type of circuit metamaterial resonator

We give arguments for the existence of a thermodynamics of quantum complexity

that includes a "Second Law of Complexity". To guide us, we derive a

correspondence between the computational (circuit) complexity of a quantum

system of $K$ qubits, and the positional entropy of a related classical system

with $2^K$ degrees of freedom. We also argue that the kinetic entropy of the

classical system is equivalent to the Kolmogorov complexity of the quantum

Hamiltonian. We observe that the expected pattern of growth of the complexity

We study the quantum dynamics of many-body arrays of two-level atoms in a

driven cavity subject to collective decay and interactions mediated by the

cavity field. We work in the bad cavity limit accessible, for example, using

long-lived electronic clock states of alkaline earth atoms, for which the bare

atomic linewidth is much less than the cavity linewidth. In the absence of

interactions, our system reduces to previously studied models of collective

fluorescence. We show that while interactions do not qualitatively change the

In the process of parametric optical image amplification, images are formed

at new frequencies in addition to the amplified original image. We show that

the parametric multiplexing of optical images can be used to produce an image

with improved quality. As an example, we study the parametric amplification of

an optical image at low-frequency pumping in which multiplexed optical images

turn out to be quantum-correlated. Additional improvement is made possible by

There is evidence that Planck's constant shows statistical variations with

altitude above the earth due to Kentosh and Mohageg, and yearly systematic

changes with the orbit of the earth about the sun due to Hutchins. Many others

have postulated that the fundamental constants of nature are not constant

either locally or universally. This work is a mathematical study examining the

impact of a position dependent Planck's constant in the Schrodinger equation.

A discrete-time Quantum Walk (QW) is an operator driving the evolution of a

single particle on the lattice, through local unitaries. Some QW admit, as

their continuum limit, a well-known equation of Physics. In arXiv:1803.01015

the QW is over the honeycomb and triangular lattices, and simulates the Dirac

equation. We apply a spacetime coordinate transformation upon the lattice of

this QW, and show that it is equivalent to introducing spacetime-dependent

Banaszek, W\'odkiewicz and others

(\cite{Banaszek},\cite{Chen},\cite{Chen-Zhang}) made the surprising discovery

that Einstein-Bell locality inequalities can be violated by the two mode

squeezed vacuum by a factor $\sqrt{2}$, in spite of the fact that the state has

a positive Wigner function. I use here the more general Gleason-Kochen-Specker

assumption of non-contextuality \cite{Gleason} to express classicality. I then

derive non-contextuality Bell inequalities for correlations of $N$ pseudo spins

We investigate the performance of error mitigation via measurement of

conserved symmetries on near-term devices. We present two protocols to measure

conserved symmetries during the bulk of an experiment, and develop a zero-cost

post-processing protocol which is equivalent to a variant of the quantum

subspace expansion. We develop methods for inserting global and local symetries

into quantum algorithms, and for adjusting natural symmetries of the problem to