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Journal of the Association of Arab Universities for Basic and Applied Sciences

Quantum communication in the presence of noise local environments

A.‐S. F. Obada, N.M. Arafa, NASSER METWALLY

Published Jun 4, 2012• 1 citation
Publisher

Abstract

We investigate the entanglement dynamics of maximum and partial entangled two-qubit states, where each qubit interacts locally with its own noise environment. In the presence of local non-correlated noise, the entangled system loses its entangled properties faster than that depicted for correlated noise. The capacity of the output channel decays gradually and smoothly in the presence of non-correlated noise and hastily for the correlated one. We show that the local non-correlated noise can improve the capacity of the output channel. The possibility of using the output state to perform quantum teleportation is discussed and the effect of the noise parameter on the fidelity of the teleported state is investigated.

DOI
10.1016/j.jaubas.2012.05.002

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We investigate the entanglement dynamics of maximum and partial entangled two-qubit states, where each qubit interacts locally with its own noise environment. In the presence of local non-correlated noise, the entangled system loses its entangled properties faster than that depicted for correlated noise. The capacity of the output channel decays gradually and smoothly in the presence of non-correlated noise and hastily for the correlated one. We show that the local non-correlated noise can improve the capacity of the output channel. The possibility of using the output state to perform quantum teleportation is discussed and the effect of the noise parameter on the fidelity of the teleported state is investigated.
We investigate the dynamics of two qubits state through the Bloch channel. It is found that the degradation and sudden-death of the entanglement depend on the channel's parameters and the structure of the input state. Starting from partially entangled states as input state, the output states are more robust compared with those obtained from initial maximally entangled states. Also the survivability of entanglement increased as the absolute equilibrium values of the channel increased or the ratio between the longitudinal and transverse relaxation times gets smaller. Ability of using the output states as quantum channels to perform quantum teleportation is investigated. The idea that the useful output states are used to achieve the original quantum teleportation protocol is discussed.
We show that the entanglement of the two-qubit teleported state via a class of four-qubit entangled channel states can be increased by collective amplitude damping locally acting on one part of the channel state. Specifically, we compare the entanglement contained in the output state of teleportation before and after the action of the collective amplitude damping on the channel state, and show that for a wide range of input entangled two-qubit states, the local decoherence can result in an increase in the output entanglement. In this process, the average fidelity of the teleportation is also increased. Our result reveals that some quantum properties of the four-qubit channel state are definitely improved in the process of enhancing the fidelity by local noise.
Quantum teleportation relies on entanglement as the quantum resource to be able to communicate with fidelities beyond the classical limit. Nevertheless, the entangled resource may be afflicted by local noise, affecting its ability to serve as the entangled resource for quantum teleportation. We obtain experimental data on the influence of different local environments on the ability of an initially entangled pair of qubits to act as a teleportation resource, after it has been disturbed by noise. We generate selected conditions on the noise parameter space, both theoretically and experimentally, and we find that an already noisy protocol can be made practically insensitive to a further addition of noise. The experimental results are based on a photonic implementation of the quantum teleportation algorithm, with a polarization-entangled pair acting as the quantum resource. The state to be teleported is an additional qubit encoded in the path internal degree of freedom of Alice's photon. Interactions with different local environments on both sides of the system are either implemented with an extra qubit as the environment, or simulated as a weighed average of pure states. We compare our experimental results with the theoretical predictions, and by performing quantum process tomography we can calculate the fidelity of the quantum teleportation scheme and evaluate the effect of local environments.
For single-qubit teleportation, it has been shown that there is a family of two-qubit mixed states whose teleportation fidelity can be enhanced by subjecting one of the qubits to an amplitude damping channel. This is an interesting result, since noise in general degrades quantum entanglement. It is believed that this enhancement is due to an improvement in the classical correlations of the two-qubit states. Here, we consider two-qubit teleportation using a family of four-qubit mixed states as a resource. In this context, we show that one can again achieve enhancement in teleportation fidelity via dissipative interactions with the local environment. For a rather general class of input states, we find that this improvement implies an enhancement in the quantum discord of some teleported states. We conjecture that an improvement in some quantum property of the four-qubit mixed states could have resulted from the local interactions. We expect that our analysis will make an important case study for future investigations on the different aspects of composite quantum systems.
Consider a two-qubit maximally entangled state that gets corrupted when only one of the qubits is subjected to local interaction with the environment via amplitude damping channel. We show there are situations where this corrupted state gets better by allowing the other qubit also to interact with the environment. Moreover if the corrupted state is non teleporting, then it can always be made teleporting by the same prescription i.e. by allowing the second qubit to interact with the environment. Quantum entanglement [1] is a property of composite systems by virtue of which the local subsystems exhibit certain correlations among themselves that cannot be explained in classical terms. Often termed as quantum nonlocality, the subject had been under extensive study and debate since 1935 when Einstein, Podolsky and Rosen questioned the completeness of quantum mechanics [2]. Later, in 1964 in his pioneering work John Bell [3] showed that the correlations exhibited by the local subsystems that may be far apart are inherently quantum mechanical and any model admitting the description of local hidden variables (or one may prefer to say local realism) fails to explain such correlations.
Quantum teleportation in the presence of noisy channels acting on a bipartite resource state is considered. We consider a family of generalized noisy channels that continuously connect the amplitude damping and the dephasing channels, encompassing a wide family of in-between scenarios, to delve into the relation between the teleportation success and the amount of three- and four-partite entanglement (distributed among the qubits of the resource state and those representing local environments) generated during the evolution. Our analysis reveals that for a fixed entanglement of the resource state, the channels that better protect the teleportation fidelity against the detrimental effects of noise are those that generate higher amounts of (Greenberger-Horne-Zeilinger--type) multipartite entanglement. This suggests that the dynamically induced multipartite correlations may serve as an additional resource for teleportation and provides insight into the characterization of processes and of the type of induced entanglement according to their ability to assist the protocol.