87 research outputs found

### Generalization of Sato equation and systems of multidimensional nonlinear Partial Differential Equations

This paper develops one of the methods for study of nonlinear Partial
Differential equations. We generalize Sato equation and represent the algorithm
for construction of some classes of nonlinear Partial Differential Equations
(PDE) together with solutions parameterized by the set of arbitrary functions.Comment: 10 page

### On integration of multidimensional generalizations of classical $C$- and $S$-integrable nonlinear partial differential equations

We develop a new integration technique allowing one to construct a rich
manifold of particular solutions to multidimensional generalizations of
classical $C$- and $S$-integrable Partial Differential Equations (PDEs).
Generalizations of (1+1)-dimensional $C$-integrable and (2+1)-dimensional
$S$-integrable $N$-wave equations are derived among examples. Examples of
multidimensional second order PDEs are represented as well.Comment: 31 page

### Partial structural restoring of two-qubit transferred state

We consider the communication line with two-qubit sender and receiver, the
later is embedded into the four-qubit extended receiver. Using the optimizing
unitary transformation on the extended receiver we restore the structure of the
non-diagonal part of an arbitrary initial sender's state at the remote receiver
at certain time instant. Obstacles for restoring the diagonal part are
discussed. We represent examples of such structural restoring in a
communication line of 42 spin-1/2 particles.Comment: 17 pages, 2 figure

### Informational correlation between two parties of a quantum system: short spin-1/2 chains with XY Hamiltonian

We introduce the informational correlation $E^{AB}$ between two interacting
quantum subsystems $A$ and $B$ of a quantum system as the number of arbitrary
parameters $\varphi_i$ of a unitary transformation $U^A$ (locally performed on
the subsystem $A$) which may be detected in the subsystem $B$ by the local
measurements. This quantity indicates whether the state of the subsystem $B$
may be effected by means of the unitary transformation applied to the subsystem
$A$. Emphasize that $E^{AB}\neq E^{BA}$ in general. The informational
correlations in systems with tensor product initial states are studied in more
details. In particular, it is shown that the informational correlation may be
changed by the local unitary transformations of the subsystem $B$. However,
there is some non-reducible part of $E^{AB}(t)$ which may not be decreased by
any unitary transformation of the subsystem $B$ at a fixed time instant $t$.
Two examples of the informational correlations between two parties of the four
node spin-1/2 chain are studied.Comment: 45 pages, 2 figure

### A variant of the Dressing Method applied to nonintegrable multidimensional nonlinear Partial Differential Equations

We describe a variant of the dressing method giving alternative
representation of multidimensional nonlinear PDE as a system of
Integro-Differential Equations (IDEs) for spectral and dressing functions. In
particular, it becomes single linear Partial Differential Equation (PDE) with
potentials expressed through the field of the nonlinear PDE. The absence of
linear overdetermined system associated with nonlinear PDE creates an obstacle
to obtain evolution of the spectral data (or dressing functions): evolution is
defined by nonlinear IDE (or PDE in particular case). As an example, we
consider generalization of the dressing method applicable to integrable
(2+1)-dimensional $N$-wave and Davey-Stewartson equations. Although represented
algorithm does not supply an analytic particular solutions, this approach may
have a perspective development.Comment: 14 page

### Construction of particular solutions to nonlinear equations of Mathematical Physics by using matrix algebraic equation

The paper develops the method for construction of the families of particular
solutions to the nonlinear Partial Differential Equations (PDE) without
relation to the complete integrability. Method is based on the specific link
between algebraic matrix equations and PDE. Example of (2+2)-dimensional
generalization of Burgers equation is given.Comment: 17 page

### The minimal entanglement of bipartite decompositions as a witness of strong entanglement in a quantum system

We {characterize the multipartite entanglement in a quantum system by the
quantity} which vanishes if only the quantum system may be decomposed into two
weakly entangled subsystems, unlike measures of multipartite entanglement
introduced before. We refer to this {quantity} as the minimal entanglement of
bipartite decompositions (MEBD). Big MEBD means that the system may not be
decomposed into two weakly entangled subsystems. MEBD allows one to define, for
instance, whether the given quantum system may be a candidate for a quantum
register, where the above decomposition is undesirable.
A method of lower estimation of MEBD is represented. Examples of big MEBD in
spin-1/2 chains governed by the $H_{dz}$ Hamiltonian in the strong external
magnetic field are given.Comment: 11 pages, 1 figur

### Partially integrable generalizations of classical integrable models by combination of characteristics method and Hopf-Cole transformation

We represent an integration algorithm combining the characteristics method
and Hopf-Cole transformation. This algorithm allows one to partially integrate
a large class of multidimensional systems of nonlinear Partial Differential
Equations (PDEs).
A specific generalization of the equation describing the dynamics of
two-dimensional viscous fluid and a generalization of the Korteweg-de Vries
equation are examples of such systems. The richness of available solution space
for derived nonlinear PDEs is discussed.Comment: 7 page

### Remote creation of a one-qubit mixed state through a short homogeneous spin-1/2 chain

We consider a method of remote mixed state creation of a one-qubit subsystem
(receiver) in a spin-1/2 chain governed by the nearest-neighbor
$XY$-Hamiltonian. Owing to the evolution of the chain along with the variable
local unitary transformation of the one- or two-qubit sender, a large variety
of receiver states can be created during some time interval starting with a
fixed initial state of the whole quantum system. These states form the
creatable region of the receiver's state-space. It is remarkable that, having
the two-qubit sender, a large creatable region may be covered at a properly
fixed time instant $t_0$ using just the variable local unitary transformation
of the sender. In this case we have completely local control of the remote
state creation. In general, for a given initial state, there are such
receiver's states that may not be created using the above tool. These states
form the unavailable region. In turn, this unavailable region might be the
creatable region of another sender. Thus, in future, we have a way to share the
whole receiver's state-space among the creatable regions of several senders.
The effectiveness of remote state creation is characterized by the density
function of the creatable region.Comment: 30 pages, 5 figure

### Generalized hierarchy of matrix Burgers type and $n$-wave equations

This article concerns the dressing method for solving of multidimensional
nonlinear Partial Differential Equations. In particular, we join hierarchy of
matrix Burgers type equation with hierarchies of equations integrable by the
Inverse Spectral Transform (IST). Example of resonance interaction of wave
packets in (3+1)-dimensions is given.Comment: 7 page

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