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Chinese Physics B

Teleporting a quantum controlled-Not with one target/two targets gate using two partially entangled states

Libing Chen, Jin Rui-Bo, Haiping Lu

Published Jan 1, 2009• 6 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/18/1/005

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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.
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.
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 show how a nonlocal and open-target destination quantum controlled-Not （CNOT） gate can be probabilistically implemented by using partially entangled pairs of particles. We first investigate the controlled implementation of a nonlocal and three-target destination CNOT gate using three partially entangled pairs, and then generalize the scheme to the case of N-target destination. In this scheme, Alice’s local generalized measurement described by a positive operator valued measurement （POVM） plays a key role. We construct the required POVM. It is worth noting that deterministic and exact implementation of a nonlocal CNOT gate can be realized using partially entangled pairs.
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 non-local quantum controlled-NOT (CNOT) gate with multiple targets can be implemented with unit fidelity and unit probability. The explicit quantum circuit for implementing the operation is presented. Two schemes for probabilistic implementing the operation via partially entangled quantum channels with unit fidelity are put forward. The overall physical resources required for accomplishing these schemes are different, and the successful implementation probabilities are also different.
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.