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Physics Letters A

Loss of entanglement after propagation in a quantum noisy channel modeled by a canonical unitary operation in two qubits

Wellington Alves de Brito, Rubens Viana Ramos

Published Aug 25, 2006• 5 citations
Publisher
DOI
10.1016/j.physleta.2006.08.039

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In this work, we analyze the entanglement variation of pure bipartite states during quantum noisy channel propagation. The quantum noisy channel is modeled by the interaction between the bipartite state and the environment through a canonical unitary form of a two-qubit gate. We have found an analytical expression for the entanglement of the bipartite state at the channel output as function of the channel parameters. At last, we used numerical simulation to show that a canonical unitary form of a three qubit gate is not a good model for a quantum noisy channel.
This work is divided into two parts. In the first one, the use of the Sagnac interferometer in quantum information is analyzed applying it in three problems: interaction-free measurement, quantum key distribution, and secret sharing. For the interaction-free measurement two systems using Sagnac interferometer were proposed. Considering ideal detectors and loss less devices, one of them has a success probability of 25% for each photon used while the other presents the probability of getting success to detect the presence of the object close to 100% for each photon used. For quantum key distribution, it was proposed a different setup, where the main difference is that the pulse sent by the transmitter does not come back to him/her as happen with the systems based on Sagnac proposed before. This avoids the Trojan horse attack. Finally, it was proposed an optical configuration where it is possible to share a secret among five users, locally distant, that could be used only when all five persons agreed. The second part of this dissertation presents an analytical and numerical study of the entanglement variation of bipartite states of qubits during propagation in a quantum noisy channel. Particularly, it was found an exactly formula which relates the entanglement of states in the input and output of the channel, when the input state is pure and the channel is modeled by a canonical unitary operation.
We report a bulk optics experiment demonstrating the possibility of restoring the entanglement distribution through noisy quantum channels by inserting a suitable unitary operation (filter) in the middle of the transmission process. We focus on two relevant classes of single-qubit channels consisting in repeated applications of rotated phase-damping or rotated amplitude-damping maps, both modeling the combined Hamiltonian and dissipative dynamics of the polarization state of single photons. Our results show that interposing a unitary filter between two noisy channels can significantly improve entanglement transmission. This proof-of-principle demonstration could be generalized to many other physical scenarios where entanglement-breaking communication lines may be amended by unitary filters.