Program

P.56 -- Poster, NCTP-40

Date: Tuesday, 28 July 2015

Time: 08h30 - 10h00

CONTROLLED TELEPORTATION WITH PARTIALY ENTANGLED QUANTUM CHANNEL: DETERMINISM AND POWER OF THE CONTROLLER

Nguyen Van Hop (1), Cao Thi Bich (2), and Nguyen Ba An (2)

(1) Physics Department, Hanoi National University of Education, 136 Xuan Thuy, Hanoi (2) Center for Theoretical Physics, Institute of Physics, 10 Dao Tan, Hanoi

Nonlocal correlation inherent in entangled channel enables transmission of quantum states between two remote locations without actually carrying the states through space. This process is named teleportation which always succeeds if the channel is maximally entangled. This work studies controlled teleportation (i.e., teleportation under supervision of a controller) of a general two-qubit state via a quantum channel of the form ${\left| Q \right\rangle _{1233'45}} = {\sum\nolimits_{m = 0}^1 {\sum\nolimits_{n = 0}^1 {{x_{mn}}\left| {{B_{mn}}} \right\rangle } } _{12}}{\left| {m,n} \right\rangle _{33'}} \otimes {\left| {{B_{00}}} \right\rangle _{45}},$ where ${\sum\nolimits_{m = 0}^1 {\sum\nolimits_{n = 0}^1 {\left| {{x_{mn}}} \right|} } ^2} = 1$ and ${\left| {{B_{mn}}} \right\rangle _{12}} = \sum\nolimits_{j = 0}^1 {{{\left( { - 1} \right)}^{mj}}} {\left| {j,j \oplus n} \right\rangle _{12}}$, while qubits 1 and 4, 2 and 5 and 3 and 3' belong to the sender, the receiver and the controller, respectively. We show in detail that, not only for $\left| {{x_{mn}}} \right| = 1/2$ but even for $\left| {{x_{mn}}} \right| \ne 1/2$ (i.e., ${\left| Q \right\rangle _{1233'45}}$ is not maximally entangled), any unknown two-qubit state can be teleported deterministically (i.e., with unit success probability). We also prove that if $\left| {{x_{00}}} \right| \ge 1/2$ then the teleported state's average fidelity F$_{av}$ obtained without the controller's cooperation is not smaller than the classical fidelity F$_{cl}$ = 2/5. Therefore, in order for the controller to play a useful role $\left| {{x_{00}}} \right|$ should be chosen less than 1/2 and the smaller $\left| {{x_{00}}} \right|$ the more powerful the controller.

Presenter: Nguyen Van Hop