Related papers: The Bloch-vector space for N-level systems -- the …
We introduce the super-qubit quantum state, determined by superposition of the zero and the one super-particle states, which can be represented by points on the super-Bloch sphere. In contrast to the one qubit case, the one super-particle…
A Lie-algebraic approach successfully used to describe one-dimensional Bloch oscillations in a tight-binding approximation is extended to two dimensions. This extension has the same algebraic structure as the one-dimensional case while the…
In this paper, we exploit the concept of Kolmogorov $n$-widths to establish optimality benchmarks for reduced-order methods used in phononic, acoustic, and photonic band structure calculations. The Bloch-transformed operators are entire…
In the study of d-dimensional quantum channels $(d \geq 2)$, an assumption which is not very restrictive, and which has a natural physical interpretation, is that the corresponding Kraus operators form a representation of a Lie algebra.…
We fully characterize orthogonal projections of infinite right circular (round) cones in real Hilbert spaces. Another interpretation is that, given two vectors in a real Hilbert space, we establish the optimal estimate on the angle between…
Topologically protected states can be found in physical systems, that show singularities in some energy contour diagram. These singularities can be characterized by winding numbers, defined on a classification surface, which maps physical…
We show that the Bloch vectors lying on any great circle is the largest set S(L) for which the parallel states |n,n> can always be transformed into the anti-parallel states |n,-n>. Thus more information about the Bloch vector is not…
We study the dimension of the manifold of quantum states (called orbit) that a given quantum state of light can reach under the dynamics of linear or Gaussian quantum optics. That is, we investigate how many directions in the Hilbert space…
Traditionally, the characterization of quantum resources has focused on individual quantum states. Recent literature, however, has increasingly explored the characterization of resources in multi-states (ordered collections of states…
Non-Abelian and non-adiabatic variants of Berry's geometric phase have been pivotal in the recent advances in fault tolerant quantum computation gates, while Berry's phase itself is at the heart of the study of topological phases of matter.…
Quantum geometry, describing the geometric properties of the Bloch wave function in momentum space, has recently been recognized as a fundamental concept in condensed matter physics. The flat-band system offers the paradigmatic platform…
It is recognized that Grover arrived at his original quantum search algorithm inspired by his comprehension of the interference of classical waves originating from an array of antennas. It is also known that quantum-mechanical…
We discuss a generalization to 2 qubits of the standard Bloch sphere representation for a single qubit, in the framework of Hopf fibrations of high dimensional spheres by lower dimensional spheres. The single qubit Hilbert space is the…
Band formation in periodic media is a central topic in undergraduate solid-state physics, typically introduced through Bloch's theorem as an eigenvalue problem in reciprocal space for infinitely periodic systems. While mathematically…
We investigate a reverse Faber-Krahn type inequality for the Robin Laplacian in a bounded smooth domain $\Omega \subset \mathbb{R}^N$ whose boundary has two connected components. We prove that a concentric spherical shell maximizes the…
The dynamics of states representing arbitrary N-level quantum systems, including dissipative systems, can be modelled exactly by the dynamics of classical coupled oscillators. There is a direct one-to-one correspondence between the quantum…
We demonstrate that nonlinearity may play a constructive role in supporting Bloch oscillations in a model which is discrete, in one dimension and continuous in the orthogonal one. The model can be experimentally realized in several fields…
The performance of key tasks in quantum technology, such as accurate state preparation, can be maximized by utilizing external controls and deriving their shape with optimal control theory. For non-pure target states, the performance…
We study the spectrum of SU(2) x SO(2) matrix supersymmetric quantum mechanics. We use angular coordinates that allow us to find an explicit solution of the Gauss law constraints and single out the quantum number n (the Lorentz angular…
We study the dynamics of electrons in crystalline solids in the presence of inhomogeneous external electric and magnetic fields. We present a manifestly gauge-invariant operator-based approach without relying on a semiclassical wavepacket…