Quantum logic networks for probabilistic and controlled teleportation of unknown quantum states

We present simplification schemes for probabilistic and controlled teleportation of the unknown quantum states of both one-particle and two-particle and construct efficient quantum logic networks for implementing the new schemes by means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neumann measurement and classically controlled operations. In these schemes the teleportation are not always successful but with certain probability.Comment: 9 pages, 5 figure

Controlled and secure direct communication using GHZ state and teleportation

A theoretical scheme for controlled and secure direct communication is proposed. The communication is based on GHZ state and controlled quantum teleportation. After insuring the security of the quantum channel (a set of qubits in the GHZ state), Alice encodes the secret message directly on a sequence of particle states and transmits them to Bob supervised by Charlie using controlled quantum teleportation. Bob can read out the encoded messages directly by the measurement on his qubits. In this scheme, the controlled quantum teleportation transmits Alice's message without revealing any information to a potential eavesdropper. Because there is not a transmission of the qubit carrying the secret messages between Alice and Bob in the public channel, it is completely secure for controlled and direct secret communication if perfect quantum channel is used. The feature of this scheme is that the communication between two sides depends on the agreement of the third side.Comment: 4 pages, no figur

Some Blow-Up Problems for a Semilinear Parabolic Equation with a Potential

The blow-up rate estimate for the solution to a semilinear parabolic equation $u_t=\Delta u+V(x) |u|^{p-1}u$ in $\Omega \times (0,T)$ with 0-Dirichlet boundary condition is obtained. As an application, it is shown that the asymptotic behavior of blow-up time and blow-up set of the problem with nonnegative initial data u(x,0)=M\vf (x) as $M$ goes to infinity, which have been found in \cite{cer}, are improved under some reasonable and weaker conditions compared with \cite{cer}.Comment: 29 page