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Modern Physics Letters B

DETERMINISTIC AND EXACT TELEPORTATION OF A SINGLE-QUBIT ROTATION ON REMOTE QUBITS USING TWO PARTIALLY ENTANGLED STATES

Libing Chen, Rui‐Bo Jin, H. Lu

Published Jan 30, 2008• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s0217984908014729

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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.
Teleportation of an arbitrary single-qubit state using two partially entangled states is considered.Firstly,we present a method for realizing probabilistically two-destination teleportation by using two partially entangled pairs as quantum channel.Then,we put forward a scheme for realizing deterministic and exact teleportation by using same quantum channel.In these schemes,the sender's local generalized measurement described by a positive operator valued measurement(POVM) lies at the heart.We construct the required POVM.The methods are applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients μ and v are 2μ+2μv-2v-1≥0.
This paper considers the teleportation of quantum controlled-Not (CNOT) gate by using partially entangled states. Different from the known probability schemes, it presents a method for teleporting a CNOT gate with unit fidelity and unit probability by using two partially entangled pairs as quantum channel. The method is applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients μ and v are (2μ + 2 v – 2μ v – 1) ≥ 0. In this scheme, the sender's local generalized measurement described by a positive operator valued measurement (POVM) lies at the heart. It constructs the required POVM. It also puts forward a scheme for teleporting a CNOT with two targets gate with unit fidelity by using same quantum channel. With assistance of local operations and classical communications, three spatially separated users are able to complete the teleportation of a CNOT with two targets gate with probability of (2μ + 2 v – 1). With a proper value of μ and v , the probability could reach nearly 1.
A scheme for teleporting an unknown quantum state via a partially entangled particle pair is proposed. We show that teleportation can be successful realized with unit fidelity but less than unit probability if the sender performs a rotational operation on the teleported qubit and then performs computation basis measurements on the teleported particle and the half of the entangled particle pair respectively. The probability of successful teleportation is determined by both Schmidt coefficients of the entangled pair. This method can be generalized to the teleportation of an arbitrary and unknown multi-qubit state.
It deserves mentioning that the quantum circuit, i.e. quantum logic network, is essential to the practical realization of teleportation in experiment. Using only one partially entangled pair, we first propose two novel strategies for probabilistically teleporting any partially entangled state of a bipartite system. The feature of the present protocol is to weaken the requirement for the quantum channel, and also to cut down the number of entangled particles initially shared by the sender and receiver. On the other hand, we explicitly construct the generalized measurement described by the positive operator-valued measure (POVM). Two kinds of efficient quantum circuits for implementing the teleportation are offered. In addition, we generalize the two-particle probabilistic teleportation to the system of many particles.
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".