323 research outputs found
Geometric local invariants and pure three-qubit states
We explore a geometric approach to generating local SU(2) and
invariants for a collection of qubits inspired by lattice
gauge theory. Each local invariant or 'gauge' invariant is associated to a
distinct closed path (or plaquette) joining some or all of the qubits. In
lattice gauge theory, the lattice points are the discrete space-time points,
the transformations between the points of the lattice are defined by parallel
transporters and the gauge invariant observable associated to a particular
closed path is given by the Wilson loop. In our approach the points of the
lattice are qubits, the link-transformations between the qubits are defined by
the correlations between them and the gauge invariant observable, the local
invariants associated to a particular closed path are also given by a Wilson
loop-like construction. The link transformations share many of the properties
of parallel transporters although they are not undone when one retraces one's
steps through the lattice. This feature is used to generate many of the
invariants. We consider a pure three qubit state as a test case and find we can
generate a complete set of algebraically independent local invariants in this
way, however the framework given here is applicable to mixed states composed of
any number of level quantum systems. We give an operational interpretation
of these invariants in terms of observables.Comment: 9 pages, 3 figure
Aharonov-Anandan phase in Lipkin-Meskov-Glick model
In the system of several interacting spins, geometric phases have been
researched intensively.However, the studies are mainly focused on the adiabatic
case (Berry phase), so it is necessary for us to study the non-adiabatic
counterpart (Aharonov and Anandan phase). In this paper, we analyze both the
non-degenerate and degenerate geometric phase of Lipkin-Meskov-Glick type
model, which has many application in Bose-Einstein condensates and entanglement
theory. Furthermore, in order to calculate degenerate geometric phases, the
Floquet theorem and decomposition of operator are generalized. And the general
formula is achieved
Background Independent Quantum Mechanics, Metric of Quantum States, and Gravity: A Comprehensive Perspective
This paper presents a comprehensive perspective of the metric of quantum
states with a focus on the background independent metric structures. We also
explore the possibilities of geometrical formulations of quantum mechanics
beyond the quantum state space and Kahler manifold. The metric of quantum
states in the classical configuration space with the pseudo-Riemannian
signature and its possible applications are explored. On contrary to the common
perception that a metric for quantum state can yield a natural metric in the
configuration space with the limit when Planck constant vanishes, we obtain the
metric of quantum states in the configuration space without imposing this
limiting condition. Here, Planck constant is absorbed in the quantity like Bohr
radii. While exploring the metric structure associated with Hydrogen like atom,
we witness another interesting finding that the invariant lengths appear in the
multiple of Bohr radii.Comment: 25 Pages;journal reference added:Published in- Int. J. Theor. Phys.
46 (2007) 3216-3229. References revise
Direct estimations of linear and non-linear functionals of a quantum state
We present a simple quantum network, based on the controlled-SWAP gate, that
can extract certain properties of quantum states without recourse to quantum
tomography. It can be used used as a basic building block for direct quantum
estimations of both linear and non-linear functionals of any density operator.
The network has many potential applications ranging from purity tests and
eigenvalue estimations to direct characterization of some properties of quantum
channels. Experimental realizations of the proposed network are within the
reach of quantum technology that is currently being developed.Comment: This paper supersedes the paper quant-ph/0112073, titled "Universal
Quantum Estimator". We emphasise the estimation of linear and non-linear
functionals of a quantum stat
Quantum renormalization group approach to geometric phases in spin chains
A relation between geometric phases and criticality of spin chains are
studied by using the quantum renormalization-group approach. We have shown how
the geometric phase evolve as the size of the system becomes large, i.e., the
finite size scaling is obtained. The renormalization scheme demonstrates how
the first derivative of the geometric phase with respect to the field strength
diverges at the critical point and maximum value of the first derivative and
its position scales with an exponent of the system size. This exponent is
directly associated with the critical properties of the model where, the
exponent governing the divergence of the correlation length close to the
quantum critical point.Comment: Accepted by Phys. Lett.
Entropy as a function of Geometric Phase
We give a closed-form solution of von Neumann entropy as a function of
geometric phase modulated by visibility and average distinguishability in
Hilbert spaces of two and three dimensions. We show that the same type of
dependence also exists in higher dimensions. We also outline a method for
measuring both the entropy and the phase experimentally using a simple
Mach-Zehnder type interferometer which explains physically why the two concepts
are related.Comment: 19 pages, 7 figure
Heat-conserving three-temperature model for ultrafast demagnetization of 3d ferromagnets
We study the ultrafast magnetization dynamics of bcc Fe and fcc Co using the
recently suggested heat-conserving three-temperature model (HC3TM), together
with atomistic spin- and lattice dynamics simulations. It is shown that this
type of Langevin-based simulation is able to reproduce observed trends of the
ultrafast magnetization dynamics of fcc Co and bcc Fe, in agreement with
previous findings for fcc Ni. The simulations are performed by using parameters
that to as large extent as possible are obtained from electronic structure
theory. The one parameter that was not calculated in this way, was the damping
term used for the lattice dynamics simulations, and here a range of parameters
were investigated. It is found that this term has a large influence on the
details of the magnetization dynamics. The dynamics of iron and cobalt is
compared with previous results for nickel and similarities and differences in
the materials' behavior are analysed following the absorption of a femtosecond
laser pulse. Importantly, for all elements investigated so far with this model,
we obtain a linear relationship between the value of the maximally demagnetized
state and the fluence of the laser pulse, which is in agreement with
experiments.Comment: 9 pages, 9 figures, Submitted to Physical Review
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