# All

Quantum mechanics is strictly incompatible with local realism. It has been

shown by Bell and others that it is possible, in principle, to experimentally

differentiate between local realism and quantum mechanics. Numerous experiments

have attempted to falsify local realism; however, they have consistently failed

to close the detection loophole under strict locality conditions, thereby

allowing local realistic explanations for their observations. In 2015, three

The discrete-time quantum walk (QW) is determined by a unitary matrix whose

component is complex number. Konno (2015) extended the QW to a walk whose

component is quaternion.We call this model quaternionic quantum walk (QQW). The

probability distribution of a class of QQWs is the same as that of the QW. On

the other hand, a numerical simulation suggests that the probability

distribution of a QQW is different from the QW. In this paper, we clarify the

difference between the QQW and the QW by weak limit theorems for a class of

Cyber-security has become vital for modern networked control systems (NCS).

In this paper, we propose that the emerging technology of quantum key

distribution (QKD) can be applied to enhance the privacy and security of NCS up

to an unbreakable level. QKD can continuously distribute random secret keys

with much higher privacy between communication parties, and thus enable the

one-time pad encryption that cannot be truly applied in classical networks. We

show that the resulting overall security of NCS can be essentially improved,

We characterize a close connection between the continuous-time quantum-walk

model and a discrete-time quantum-walk version, based on the staggered model

with Hamiltonians in a class of Cayley graphs, which can be considered as a

discretization of continuous-time quantum walks. This connection provides

examples of perfect state transfer and instantaneous uniform mixing in the

staggered model. On the other hand, we provide some more examples of perfect

state transfer and instantaneous uniform mixing in the staggered model that

We extend the Born-Oppenheimer type of approximation scheme for the

Wheeler-DeWitt equation of canonical quantum gravity to arbitrary orders in the

inverse Planck mass squared. We discuss in detail the origin of unitarity

violation in this scheme and show that unitarity can be restored by an

appropriate modification which requires back reaction from matter onto the

gravitational sector. In our analysis, we heavily rely on the gauge aspects of

the standard Born-Oppenheimer scheme in molecular physics.

Logical qubit encoding and quantum error correction (QEC) have been

experimentally demonstrated in various physical systems with multiple physical

qubits, however, logical operations are challenging due to the necessary

nonlocal operations. Alternatively, logical qubits with bosonic-mode-encoding

are of particular interest because their QEC protection is hardware efficient,

but gate operations on QEC protected logical qubits remain elusive. Here, we

experimentally demonstrate full control on a single logical qubit with a

We prove a lower bound on the rate of Greenberger-Horne-Zeilinger states

distillable from pure multipartite states by local operations and classical

communication (LOCC). Our proof is based on a modification of a combinatorial

argument used in the fast matrix multiplication algorithm of Coppersmith and

Winograd. Previous use of methods from algebraic complexity in quantum

information theory concerned transformations with stochastic local operations

and classical operation (SLOCC), resulting in an asymptotically vanishing

We investigate the resonant regime of a mesoscopic cavity made of graphene or

a doped beam splitter. Using Non-Hermitian Quantum Mechanics, we consider the

Bender-Boettcher assumption that a system must obey parity and time reversal

symmetry. Therefore, we describe such system by coupling chirality, parity and

time reversal symmetries through the scattering matrix formalism and apply it

in the shot noise functions, also derived here. Finally we show how to achieve

A continuous-time quantum walk on a graph $X$ is represented by the complex

matrix $\exp (-\mathrm{i} t A)$, where $A$ is the adjacency matrix of $X$ and

$t$ is a non-negative time. If the graph models a network of interacting

qubits, transfer of state among such qubits throughout time can be formalized

as the action of the continuous-time quantum walk operator in the

characteristic vectors of the vertices.

We develop the point of view where Quantum Mechanics results from the

interplay between the quantized number of "modalities" accessible to a quantum

system, and the continuum of "contexts" that are required to define these

modalities. We point out the specific roles of "extracontextuality" and

"extravalence" of modalities, and relate them to the Kochen-Specker and Gleason

theorems.