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Chinese Optics Letters

Constructing a universal set of quantum gates via probabilistic teleportation

Libing Chen, H. Lu, Weicheng Chen

Published Jan 1, 2005• 1 citation
OpenAlex

Abstract

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.

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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 method to construct quantum logic gates using one-bit``teleportation'' as a basic primitive, extending previous results based ontraditional two-bit teleportation (D. Gottesman and I. L. Chuang, Nature {\\bf402}, 390, 1999). This allows the realization of a variety of useful quantumoperations that cannot be directly performed due to some physical constraints.In particular, this technique leads to straightforward and systematicconstruction of many fault-tolerant encoded operations, including the pi/8\\pi/8pi/8and Toffoli gates, and remote quantum operations.
By means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neuman measurement and classically controlled operations, we construct efficient quantum logic networks for implementing probabilistic teleportation of a single qubit, a two-particle entangled state and an N -particle entanglement. Based on the quantum networks, we show that after the partially entangled states are concentrated into maximal entanglement, the above three kinds of probabilistic teleportation are the same as the standard teleportation using the corresponding maximally entangled states as the quantum channels.
By eans of the primitive operations consisting of single-qubit gates.two-qubit controlled-not gates,Von Neuman measurement and classically controlled operations.,we construct efficient quantum logic networks for implementing probabilistic teleportation of a single qubit,a two-particle entangled state,and an N-particle entanglement.Based on the quantum networks,we show that after the partially entangled states are concentrated into maximal entanglement,the above three kinds of probabilistic teleportation are the same as the standard teleportation using the corresponding maximally entangled states as the quantum channels.
We present a general method to construct fault-tolerant quantum logic gates with a simple primitive, which is an analog of quantum teleportation. The technique extends previous results based on traditional quantum teleportation [Gottesman and Chuang, Nature (London) 402, 390 (1999)] and leads to straightforward and systematic construction of many fault-tolerant encoded operations, including the $\ensuremath{\pi}/8$ and Toffoli gates. The technique can also be applied to the construction of remote quantum operations that cannot be directly performed.
We describe a new protocol where, by using a non-maximally entangled basis as the measurement basis, one can use a general pure entangled state as a resource for quantum teleportation. Using this protocol one can teleport a state with unit fidelity though less than unit probability. We also use the more natural language of quantum operations to describe this probabilistic teleportation. We also provide success and failure probabilities for this protocol. This scheme could be of use in real experiments which may be tested in the near future.
We consider a generalized quantum teleportation protocol for an unknown qubit using non-maximally entangled state as a shared resource. Without recourse to local filtering or entanglement concentration, using standard Bell-state measurement and classical communication one cannot teleport the state with unit fidelity and unit probability. We show that using non-maximally entangled measurements one can teleport an unknown state with unit fidelity albeit with reduced probability. We also give a generalized protocol for entanglement swapping using non-maximally entangled states. I.