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Commutations Relations for Modular Variables, Connection to Action-Angle Variables; Periodic Potentials with the Aharonov-Bohm Effect; Paradox of a superposed flux shielded by a superconductor.

When we estimate a quantum state, we normally use the quantum state tomography. However, this needs the post-information processing. Here, we propose a new idea on visualizing technique of the quantum state. Under the specific configuration, in which the optical vortex beam is used, we experimentally demonstrate the visualization of the specific two-dimensional quantum state; the polarized state of light by the weak measurement initiated by Yakir Aharonov and his colleagues. The entangled state can be also visualized via the concurrence as the extension of this idea. This work is collaborated with Hirokazu Kobayashi (Kochi University of Technology).

I will give an overview of two ways to estimate parameters with a quantum system when the dynamics is nontrivial.  In the first case, the parameter is changing in an irregular way, and we use consider the use of continuous measurement to track it in time.  Tracking speed is of the essence for feedback purposes, and I will present our new and improved way to speed up the estimation algorithm.   In the second case, I will consider the use of Hamiltonian control to estimate a fixed parameter, but of a time-dependent Hamiltonian.  In this case established scaling bounds on the quantum Fisher information can be broken, and the quantum control is needed to do it.  A simple spin example will be given to illustrate the general results.

The Aharonov-Bohm Effect with an infinite grating with solenoids between each slit, Modular Momentum; Nonlocal exchange of Modular Momentum and Modular Energy; Scattering with both local and nonlocal interactions.

Fault-tolerant quantum computers will compute by applying
a sequence of elementary unitary operations, or gates, to an
error-protected subspace.   While algorithms are typically expressed
over arbitrary local gates, there is unfortunately no known theory
that can correct errors for a continuous set of quantum gates.
However, theory does support the fault-tolerant construction of
various finite gate sets, which in some cases generate circuits that
can approximate arbitrary gates to any desired precision.   In this
talk, I will present a framework for approximating arbitrary qubit
unitaries over a very general but natural class of gate sets derived
from the theory of integral quaternions over number fields, where the
complexity of a unitary is algebraically encoded in the length of a
corresponding quaternion.  Then I will explore the role played by
higher-dimensional generalizations of the Pauli gates in various
physical and mathematical settings, from classifying bulk-boundary
correspondences of abelian fractional quantum Hall states to
generating optimal symmetric quantum measurements with surprising
connections to Hilbert's 12th problem on explicit class field theory
for real quadratic number fields.

Nonrelativistic quantum mechanics with a Hamiltonian that causes instantaneous translations;  Nonlocal Heisenberg equations of motion for 2 boxes with a permeable common barrier and the 2-slit interferometer

Throughout the development of quantum mechanics, the striking refusal of nature to obey classical reasoning and intuition has driven both curiosity and confusion. From the apparent inescapably probabilistic nature of the theory, to more subtle issues such as entanglement, nonlocality, and contextuality, it has always been the `nonclassical’ features that present the most interesting puzzle. More recently, it has become apparent that these features are also the primary resource for quantum information processing.
In this talk, we will introduce several types of nonclassical logical structures contained within the N-qubit Pauli group, corresponding in general to preparation and/or measurement schemes for systems of several qubits that demonstrate violation of some notion of classical reasoning. These structures are geometric in nature, and we identify the primitive elements from which more elaborate types are constructed. We will review the key types of structures that are available and explain their hierarchy. Finally we will use them to give simple and transparent proofs of entanglement correlations, quantum contextuality via the Kochen-Specker theorem, and quantum nonlocality via the Bell-GHZ theorem.
These structures have many applications in quantum information processing, but the real purpose of this talk is simply to introduce unfamiliar researchers to the simplest known logical proofs of these nonclassicality theorems, which can be understood using only the algebra of the Pauli spin matrices and simple counting arguments.

We investigate the quantum trajectories of jointly monitored transmon qubits, tracking measurement-induced entanglement creation as a continuous process.  The quantum trajectories naturally split into low and high entanglement classes corresponding to partial parity collapse.  We theoretically calculate the distribution of concurrence at any given time and show good agreement with the constructed histogram of measured concurrence trajectories.  The distribution exhibits a sharp cut-off in the high concurrence limit, defining a maximal concurrence boundary.  The most probable paths of the two classes, starting in a separable state and ending in either an entangled state or separable state, are found and compared with the experimentally constructed paths of the sub-ensemble.  The most likely time for the transmon qubits to reach their highest concurrence can also be extracted from the most likely path analysis.

In the device-independent paradigm, the labeling of parties/inputs/outputs has no physical meaning and thus the behavior of the system should be studied up to symmetry. We conduct the first formal study of relabelings appearing in Bell scenarios. The talk includes a review of previous works, a definition of Bell relabeling groups illustrated by examples, and applications, including the classification of Bell inequalities, the generalization of binary correlators to d outcomes and the computation of exact bounds using the NPA hierarchy.