Related papers: General Description of Mixed State Geometric Phase
A model of evolution of bipartite quantum state entanglement is studied. It involves recently introduced quantum block spin-flip dynamics on a lattice. We find that for initially separable states the considered evolution leads, in general,…
Two representations of mixed states by state-vectors, known as purified state and thermal vacuum, have been realized on quantum computers. While the two representations look similar, they differ by a partial transposition in the ancilla…
Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually…
A geometrical characterization of robustly separable (that is, remaining separable under sufficiently small variiations) mixed states of a bipartite quantum system is given. It is shown that the density matrix of any such state can be…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
We study quantum metrology for unitary dynamics. Analytic solutions are given for both the optimal unitary state preparation starting from an arbitrary mixed state and the corresponding optimal measurement precision. This represents a…
This paper presents an introduction to geometric representations of quantum states in which each distinct quantum state, pure and mixed, corresponds to a unique point in a Euclidean space. Beginning with a review of some underappreciated…
We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the…
We describe a generalisation of the well known Pancharatnam geometric phase formula for two level systems, to evolution of a three-level system along a geodesic triangle in state space. This is achieved by using a recently developed…
We introduce algebraic sets in the complex projective spaces for the mixed states in bipartite quantum systems as their invariants under local unitary operations. The algebraic sets of the mixed state have to be the union of the linear…
We investigate the level surfaces of geometric measure of quantum discord, and provide a pictorial interpretation of geometric discord for Bell-diagonal states. We have observed its nonanalytic behavior under decoherence employing this…
I consider a landscape containing three vacua and study the topology of global spacelike slices in eternal inflation. A discrete toy model, which generalizes the well studied Mandelbrot model, reveals a rich phase structure. Novel phases…
We investigate the topological properties of dynamical states evolving on periodic oriented graphs. This evolution, that encodes the scattering processes occurring at the nodes of the graph, is described by a single-step global operator, in…
We study the evolution of the hybrid entangled states in a bipartite (ultra) strongly coupled qubit-oscillator system. Using the generalized rotating wave approximation the reduced density matrices of the qubit and the oscillator are…
By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient…
We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…
In this paper, the projective geometry is used to describe the features of spherical manifold and discreteness in quantum evolution. As a system evolves in time the state vector changes and it traces out a curve in Hilbert space.…
This paper present a geometric diagram of a separable state: If a mixed state $\sigma $ is separable, there are $2^{nS(\sigma)}$ linearly independant product vectors which span the same Hilbert space as the $2^{nS(\sigma)}$ ``likely''…
An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state of n qubits. This approach reveals the geometrical structure of the quantum search process,…
We present a split-beam neutron interferometric experiment to test the non-cyclic geometric phase tied to the spatial evolution of the system: the subjacent two-dimensional Hilbert space is spanned by the two possible paths in the…