Related papers: Phase properties of hypergeometric states and nega…
Phase transitions are fundamental in nature. A small parameter change near a critical point leads to a qualitative change in system properties. Across a regular phase transition, the system remains in thermal equilibrium and, therefore,…
When a quantum state traverses a path, while being under the influence of a gauge potential, it acquires a geometric phase that is often more than just a scalar quantity. The variety of unitary transformations that can be realised by this…
Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for {\it mixed} input states. We report the first experiment to…
We investigate a generalized Aubry-Andr\'{e}-Harper (AAH) model with non-reciprocal hopping and power-law quasiperiodic potentials $V(i) = V\left[ \cos(2\pi \beta i) \right]^p$. Our study reveals that the interplay between nonreciprocity,…
A conventional quantum phase transition (QPT) can be accessed by varying a real parameter at absolute zero temperature. Motivated by the discovery of the pseudo-Hermiticity of non-Hermitian systems, we explore the QPT in non-Hermitian…
We introduce a new density for the representation of quantum states on phase space. It is constructed as a weighted difference of two smooth probability densities using the Husimi function and first-order Hermite spectrograms. In contrast…
Non-Hermitian (NH) systems, owing to the existence of exceptional point (or ring and surface), exhibit exotic topological features which are inaccessible in Hermitian systems. While current studies on NH topology has primarily focused on…
We discuss a pairwise-comparison viewpoint on finite families of qubit states. Starting from transition amplitudes between pure states, we distinguish three associated levels of comparison data: complex amplitudes, transition probabilities,…
Classical chimera states are paradigmatic examples of partial synchronization patterns emerging in nonlinear dynamics. These states are characterized by the spatial coexistence of two dramatically different dynamical behaviors, i.e.,…
We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the…
We propose a new strategy to physically implement a universal set of quantum gates based on geometric phases accumulated in the nondegenerate eigenstates of a designated invariant operator in a periodic physical system. The system is driven…
We demonstrate how to discriminate two non-orthogonal, entangled quantum state which are slightly different from each other by using pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian systems…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
Geometric Phase in Quantum Mechanics is generally formulated entirely in terms of geometric structure of the Complex Hilbert Space. We will exploit this fact in case of mixed states for three level open systems undergoing depolarization…
A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the…
A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles…
Few-particle dynamics in a three-well potential are investigated numerically. It is shown that periodically shaking the potential can considerably increase the fidelity of emerging spatial quantum superpositions. Such NOON-states are…
W consider the problem of testing if a given matrix in the Hilbert space formulation of quantum mechanics or a function in the phase space formulation of quantum theory represent a quantum state. We propose several practical criteria to…
The geometric properties of quantum states is fully encoded by the quantum geometric tensor. The real and imaginary parts of the quantum geometric tensor are the quantum metric and Berry curvature, which characterize the distance and phase…
Hypergraph states, a generalization of graph states, constitute a large class of quantum states with intriguing non-local properties and have promising applications in quantum information science and technology. In this paper, we generalize…