Related papers: Phase properties of hypergeometric states and nega…
Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system…
Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an…
We study phase properties of a displacement operator type nonlinear coherent state. In particular we evaluate the Pegg-Barnett phase distribution and compare it with phase distributions associated with the Husimi Q function and the Wigner…
Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on…
We develop a theory of Gaussian states over general quantum kinematical systems with finitely many degrees of freedom. The underlying phase space is described by a locally compact abelian (LCA) group $G$ with a symplectic structure…
We present a generalization of the geometric phase to pure and thermal states in $\mathcal{PT}$-symmetric quantum mechanics (PTQM) based on the approach of the interferometric geometric phase (IGP). The formalism first introduces the…
Geometric phases arise in a number of physical situations and often lead to systematic shifts in frequencies or phases measured in precision experiments. We describe, by working through some simple examples, a method to calculate geometric…
In recent years, physical models based on noncommutative algebras have attracted considerable interest, as they provide a natural framework to incorporate a fundamental scale, often associated with semiclassical aspects of quantum gravity.…
We consider an experimentally realizable scheme for manipulating quantum states using a general superposition of products of field annihilation ($\hat{a}$) and creation ($\hat{a}^\dag$) operators of the type ($s \hat{a}\hat{a}^\dag+ t…
We demonstrate the emergence of a topological ordered phase for non-Hermitian systems. Specifically, we elucidate that systems with non-Hermitian two-body interactions show a fractional quantum Hall (FQH) state. The non-Hermitian…
We study the influence of geometry of quantum systems underlying space of states on its quantum many-body dynamics. We observe an interplay between dynamical and topological ingredients of quantum non-equilibrium dynamics revealed by the…
We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain…
We investigate a two-parametric family of one-dimensional non-Hermitian complex potentials with parity-time ($\mathcal{PT}$) symmetry. We find that there exist two distinct types of phase transitions, from an unbroken phase (characterized…
This paper focuses on the geometric phase of general mixed states under unitary evolution. Here we analyze both non-degenerate as well as degenerate states. Starting with the non-degenerate case, we show that the usual procedure of…
An explicit parameterization is given for the density matrices for $n$-state systems. The geometry of the space of pure and mixed states and the entropy of the $n$-state system is discussed. Geometric phases can arise in only specific…
Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed…
We present a characterization of states in generalized probabilistic models by appealing to a non-commutative version of geometric probability theory based on algebraic geometry techniques. Our theoretical framework allows for incorporation…
Non-Hermiticity appears ubiquitously in various open classical and quantum systems and enriches classification of topological phases. However, the role of nonsymmorphic symmetry, crystalline symmetry accompanying fractional lattice…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
The geometry of the Quantum State Space, described by Bloch vectors, is a very intricate one. A deeper understanding of this geometry could lead to the solution of some difficult problems in Quantum Foundations and Quantum Information such…