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Modern Physics Letters B

TELEPORTING N ROTATIONS ONTO N REMOTE QUBITS BY AN ENTANGLED QUDIT CHANNEL

Libing Chen, HONG LU, Weicheng Chen, Rui‐Bo Jin

Published Apr 20, 2009• 1 citation
Publisher

Abstract

N rotations can be teleported simultaneously onto a group of remote qubits deterministically or probabilistically with the aid of an entangled qudit pair. We present a scheme for such a kind of remote control of quantum gate. We are mainly focused on the remote rotation around a fixed axis. We first present an explicit scheme for deterministically and exactly teleporting the N rotations by using a maximally entangled qudit pair as quantum channel. We also put forward a scheme for probabilistically implementing the N remote rotations with unit fidelity by employing a partially entangled qudit pair as the quantum channel. An analysis of the scheme indicates that use of partially entangled quantum channel for teleporting the N rotations leads to the problem of "the general optimal information extraction".

DOI
10.1142/s0217984909019429

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N rotations can be teleported simultaneously onto a group of remote qubits deterministically or probabilistically with the aid of an entangled qudit pair. We present a scheme for such a kind of remote control of quantum gate. We are mainly focused on the remote rotation around a fixed axis. We first present an explicit scheme for deterministically and exactly teleporting the N rotations by using a maximally entangled qudit pair as quantum channel. We also put forward a scheme for probabilistically implementing the N remote rotations with unit fidelity by employing a partially entangled qudit pair as the quantum channel. An analysis of the scheme indicates that use of partially entangled quantum channel for teleporting the N rotations leads to the problem of "the general optimal information extraction".
Teleportation of quantum gates using partially entangled states is considered. Different from the known probability schemes, we propose and study a method for teleporting a prototypical single-qubit rotation on a remote receiver with unit fidelity and unit probability by using two partially entangled pairs. The method is applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients γ and η are (2γ+2η-2γη-1)≥0. In our scheme, the sender's local generalized measurement described by a positive operator-valued measurement (POVM) lies at the heart. We construct the required POVM. The fact that the controlled teleportation of single-qubit rotation could be realized exactly using two partially entangled pairs is also notable. A sender could teleport a rotation on a remote receiver, an arbitrary one of the two receivers, via the control of the other in a network.
We present a scheme for realizing open-destination and controlled teleportation of a single-qubit rotation gate, albeit probabilistically, by using partially entangled pairs of particles. In the scheme, a quantum rotation is faithfully teleported onto any one of N spatially separated receivers under the control of the (N-1) unselected receivers in a network. We first present the three-destination and controlled teleportation of a rotation gate by using three partially entangled pairs, and then generalize the scheme to the case of N-destination. In our scheme, the sender's local generalized measurement described by a positive operator-valued measurement (POVM) lies at the heart. We construct the required POVM. The fact that deterministic and exact teleportation of a rotation gate could be realized using partially entangled pairs is notable.
We show how a many-to-one and a one-to-many controlled remote quantum rotations (CRQRs) can be implemented deterministically and exactly by using partially entangled quantum channels. Firstly, we present a theoretical scheme for a N -to-1 CRQR, in which the quantum rotations initially distributed in N spatially separated qubits can be exactly and deterministically performed onto a remote single qubit via two partially entangled ( N + M +1)-qubit Greenberger-Horne-Zeilinger (GHZ) states without performing any global operations. The feature of this scheme is that, apart from N senders and a receiver, M agents are included in the process as controllers. Should any one of the M agents not cooperate, the receiver could not gain the original rotations. Then, we design another scheme for implementing a 1-to- N CRIC with unit fidelity and unit probability by employing a partially entangled (2 M + N +1)-qubit Einstein-Podolsky-Rosen (EPR)-GHZ state or K partially entangled ( M +2)-qubit GHZ states, in which a quantum rotation can be divided into N pieces ( N K ) and performed from a sender onto N distant receivers via the control of M agents in a quantum network. In these schemes, the senders (or the receivers, or the controllers) local positive operator valued measurement (POVM) lies at the heart. We construct the required POVMs. The fact that deterministic and exact implementation of a many-to-one or a one-to-many CRQR could be realized using partially entangled quantum channel is notable. These schemes can be used to quantum secret sharing, quantum voting, and so on. They definitely have the strong security.
In this study,we will investigate the problem of teleportation of an arbitrary two-qubit state.Firstly,we show how the two-qubit state can be teleported with unit fidelity and unit probability by using a maximally entangled four-dimensional qudit pair as a quantum channel.Then,we put forward a scheme for probabilistic teleporting the state with unit fidelity via a partially entangled quantum qudit channel.The probability of successful teleportation is determined by the smallest Schmidt coefficient of the entangled qudit pair.
We present a general method to construct a universal set of quantum gates using probabilistic teleportation as a basic primitive. The technique generalizes the teleportation method of gate construction to partially entangled quantum channels. Without recourse to local filtering or entanglement concentration, using local rotation and CNOT operations followed by measurements in the computational basis, one can construct many encoded quantum operations with unit fidelity but less than unit probability. The technique can also be applied to the construction of remote quantum gates that cannot be directly performed.
We present a general scheme for multiparty-controlled teleportation of an arbitrary m -qudit ( d -dimensional quantum system) state by using non-maximally entangled states as the quantum channel. The sender performs m generalized Bell-state measurements on her 2 m particles, the controllers take some single-particle measurements with the measuring basis X d and the receiver only needs to introduce one auxiliary two-level particle to extract quantum information probabilistically with the fidelity unit if he cooperates with all the controllers. All the parties can use some decoy photons to set up their quantum channel securely, which will forbid a dishonest party to eavesdrop freely. This scheme is optimal as the probability that the receiver obtains the originally unknown m -qudit state equals the entanglement of the quantum channel.