67,267 research outputs found
Eigenvalues, Peres' separability condition and entanglement
The general expression with the physical significance and positive definite
condition of the eigenvalues of Hermitian and trace-one matrix are
obtained. This implies that the eigenvalue problem of the density
matrix is generally solved. The obvious expression of Peres' separability
condition for an arbitrary state of two qubits is then given out and it is very
easy to use. Furthermore, we discuss some applications to the calculation of
the entanglement, the upper bound of the entanglement, and a model of the
transfer of entanglement in a qubit chain through a noisy channel.Comment: 12 pages (Revtex); Revised Version; The example of transfer of
entanglement is rewritte
Quantum mechanics in general quantum systems (II): Perturbation theory
We propose an improved scheme of perturbation theory based on our exact
solution [An Min Wang, quant-ph/0611216] in general quantum systems independent
of time. Our elementary start-point is to introduce the perturbing parameter as
late as possible. Our main skills are Hamiltonian redivision so as to overcome
a flaw of the usual perturbation theory, and the perturbing Hamiltonian matrix
product decomposition in order to separate the contraction and anti-contraction
terms. Our calculational technology is the limit process for eliminating
apparent divergences. Our central idea is ``dynamical rearrangement and
summation" for the sake of the partial contributions from the high order even
all order approximations absorbed in our perturbed solution. Consequently, we
obtain the improved forms of the zeroth, first, second and third order
perturbed solutions absorbing the partial contributions from the high order
even all order approximations of perturbation. Then we deduce the improved
transition probability. In special, we propose the revised Fermi's golden rule.
Moreover, we apply our scheme to obtain the improved forms of perturbed energy
and perturbed state. In addition, we study an easy understanding example of
two-state system to illustrate our scheme and show its advantages. All of this
implies the physical reasons and evidences why our improved scheme of
perturbation theory are actually calculable, operationally efficient,
conclusively more accurate. Our improved scheme is the further development and
interesting application of our exact solution, and it has been successfully
used to study on open system dynamics [An Min Wang, quant-ph/0601051].Comment: 51 pages, no figure. The second paper in our serial studies. Its
earlier version is quant-ph/060205
Quantum mechanics in general quantum systems (III): open system dynamics
We investigate the exact solution, perturbation theory and master equation of
open system dynamics based on our serial studies on quantum mechanics in
general quantum systems [An Min Wang, quant-ph/0611216 and quant-ph/0611217].
In a system-environment separated representation, a general and explicit
solution of open system dynamics is obtained, and it is an exact solution since
it includes all order approximations of perturbation. In terms of the cut-off
approximation of perturbation and our improved scheme of perturbation theory,
the improved form of the perturbed solution of open systems absorbing the
partial contributions from the high order even all order approximations is
deduced. Moreover, only under the factorizing initial condition, the exact
master equation including all order approximations is proposed.
Correspondingly, the perturbed master equation and its improved form different
from the existed master equation are given. In special, the Redfield master
equation is derived out without using Born-Markov approximation. The solution
of open system dynamics in the Milburn model is also gained. As examples, Zurek
model of two-state open system and its extension with two transverse fields are
studied.Comment: 20 pages, no figure. Citations were revised. This is the third
preprint in our serial studies. The previous two manuscripts are
quant-ph/0611216 and quant-ph/061121
Chiral Symmetry Breaking in the Dynamical Soft-Wall Model
In this paper a model incorporating chiral symmetry breaking and dynamical
soft-wall AdS/QCD is established. The AdS/QCD background is introduced
dynamically as suggested by Wayne de Paula etc al and chiral symmetry breaking
is discussed by using a bulk scalar field including a cubic term. The mass
spectrum of scalar, vector and axial vector mesons are obtained and a
comparison with experimental data is presented.Comment: 4 page
Generalized GHZ-class and W-class concurrence and entanglement vectors of the multipartite systems consisting of qubits
We propose two classes of the generalized concurrence vectors of the
multipartite systems consisting of qubits. Making use of them, we are able to,
respectively, describe and quantify GHZ-class and W-class entanglement both in
total and between arbitrary two partite in the multipartite system consisting
of qubits. In the case of pure state of three qubits that one partite is
separable, it is shown to exactly back to the usual Wootters' concurrence after
introduce a whole concurrence vector. In principle, our method is applicable to
any -partite systems consisting of qubits.Comment: 4 pages, Revtex. Adding: to show how to exactly back to the usual
Wootters' concurrenc
Bounds on the generalized entanglement of formation for multi-party systems
We present a general method to find the upper and lower bounds on the
generalized entanglement of formation for multi-party systems. The upper and
lower bounds can be expressed in terms of the bi-partite entanglements of
formation and/or entropies of various subsystems. The examples for tri- and
four-party systems in the both pure states and mixed states are given. We also
suggest a little modified definition of generalized entanglement of formation
for multi-party systems if EPR pairs are thought of belonging to the set of
maximally entangled states.Comment: 4 pages, Revte
Entanglement versus observables
A general scheme to seek for the relations between entanglement and
bservables is proposed in principle. In two-qubit systems with enough general
Hamiltonian, we find the entanglement to be the functions of observables for
six kinds of chosen state sets and verify how these functions be invariant with
time evolution. Moreover, we demonstrate and illustrate the cases with
entanglement versus a set of commutable observables under eight kinds of given
initial states. Our conclusions show how entanglement become observable even
measurable by experiment, and they are helpful for understanding of the nature
of entanglement in physics.Comment: 4.3 pages, 8 figures, Revised figure caption
Simplified and obvious expression of concurrence in Wootters' measure of entanglement of a pair of qubits
We obtain a simplified and obvious expression of "concurrence" in Wootters'
measure of entanglement of a pair of qubits having no more than two non-zero
eigenvalues in terms of concurrences of eigenstates and their simple
combinations. It not only simplifies the calculation of Wootters' measure of
entanglement, but also reveals some its general and important features. Our
conclusions are helpful to understand and use quantum entanglement further.Comment: 5 page
Quantum mechanics in general quantum systems (IV): Green operator and path integral
We first rewrite the perturbation expansion of the time evolution operator
[An Min Wang, quant-ph/0611216] in a form as concise as possible. Then we
derive out the perturbation expansion of the time-dependent complete Green
operator and prove that it is just the Fourier transformation of the Dyson
equation. Moreover, we obtain the perturbation expansion of the complete
transition amplitude in the Feynman path integral formulism, and give an
integral expression that relates the complete transition amplitude with the
unperturbed transition amplitude. Further applications of these results can be
expected and will be investigated in the near future.Comment: 6 pages, no figure. This is the fourth preprint in our serial
studies. The previous three preprints are, respectively, quant-ph/0611216,
quant-ph/0611217 and quant-ph/060105
Quantum CPU and Quantum Simulating
Making use of an universal quantum network or QCPU proposed by me [6], some
special quantum networks for simulating some quantum systems are given out.
Specially, it is obtained that the quantum network for the time evolution
operator which can simulate, in general, Schr\"odinger equation.Comment: 8 pages, Revised Versio
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