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arXiv:1410.5771 · Physical Review A

Noisy quantum teleportation: An experimental study on the influence of local environments

Laura T. Knoll, Christian Tomás Schmiegelow, M. A. Larotonda

Published Oct 28, 2014• 59 citations
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Abstract

We report experimental results on the action of selected local environments on the fidelity of the quantum teleportation protocol, taking into account nonideal, realistic entangled resources. Different working conditions are theoretically identified, where a noisy protocol can be made almost insensitive to the further addition of noise. We put to test these conditions on a photonic implementation of the quantum teleportation algorithm, where two polarization entangled qubits act as the entangled resource and a path qubit on Alice encodes the state to be teleported. Bob's path qubit is used to implement a local environment, while the environment on Alice's qubit is simulated as a weighted average of different pure states. We obtain a good agreement with the theoretical predictions, experimentally recreate the conditions to obtain a noise-induced enhancement of the protocol fidelity, and identify parameter regions of increased insensibility to interactions with specific noisy environments.

DOI
10.1103/physreva.90.042332

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In this work, we consider the following teleportation protocol: There is an arbitrary two-qubit resource state, shared between two spatially separated parties, Alice and Bob. Applying local unitary operators, they transform the resource state into the canonical form. To teleport an unknown qubit, Alice now measures her qubits in the Bell basis. Then, the measurement outcome is communicated by Alice to Bob via noisy classical channel(s). Finally, after receiving the classical message, Bob applies the necessary unitary operator to his qubit. Under this protocol, we find the exact formulae of teleportation fidelity and its deviation. We further find conditions for non-classical fidelity within this protocol. If the classical communication is noiseless in the above protocol then there are resource states which can lead to zero fidelity deviation. However, we show that such states may not lead to zero fidelity deviation when the classical communication is noisy in the same protocol. We also explore the opposite case, i.e., the states, which cannot lead to zero fidelity deviation in the above protocol when the classical communication is noiseless, may lead to zero fidelity deviation when the classical communication is noisy in the same protocol without compromising the non-classical fidelity. Moreover, we exhibit scenarios within the present protocol, where the fidelity deviation increases if the entanglement of the resource state is increased.

•Feb 1, 2021•0 citations
We report experimental results on the action of selected local environments on the fidelity of the quantum teleportation protocol, taking into account nonideal, realistic entangled resources. Different working conditions are theoretically identified, where a noisy protocol can be made almost insensitive to the further addition of noise. We put to test these conditions on a photonic implementation of the quantum teleportation algorithm, where two polarization entangled qubits act as the entangled resource and a path qubit on Alice encodes the state to be teleported. Bob's path qubit is used to implement a local environment, while the environment on Alice's qubit is simulated as a weighted average of different pure states. We obtain a good agreement with the theoretical predictions, experimentally recreate the conditions to obtain a noise-induced enhancement of the protocol fidelity, and identify parameter regions of increased insensibility to interactions with specific noisy environments.
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.
Achieving near-unity fidelity of Quantum Teleportation (QT) in a noisy environment is an essential requirement for its real-world applications. Towards this goal, we devise a distinctive protocol based on the timing of the sender Alice's Bell-basis measurement, synchronous with the suitably engineered structure of noise in the receiver Bob's wing, without requiring any knowledge or manipulation of Alice's local noise. For this purpose, to finally obtain the teleported states by performing the required unitary operations, Bob has to retain his qubits for only two particular Bell-basis outcomes communicated by Alice, whose corresponding reduced states have no dependence on the noise parameters in Alice's wing. Such postselection is crucial for enhancing the fidelity of the teleported state towards its ideal limit, while ensuring its full independence of Alice's noise. We formulate the specifics of our protocol in terms of a generic two-level quantum system, subjected to a general non-Markovian spin-boson model for dephasing noise. The proposed scheme is illustrated by using any pure maximally/non-maximally entangled state as well as a Werner-type mixed state as resource. In particular, using resource states having small values of entanglement measure, we show that the high fidelity of QT is achievable in the presence of noise. Further, using our scheme, considering even the local regime of Werner states, wherein the Bell-CHSH inequalities are not violated, we show that the QT fidelity in the presence of noise can be appreciably high.
We extend the research program initiated in [Phys. Rev. A 92, 012338 (2015)] from noisy deterministic teleportation protocols to noisy probabilistic (conditional) protocols. Our main goal now is to study how we can increase the fidelity of the teleported state in the presence of noise by working with probabilistic protocols. We work with several scenarios involving the most common types of noise in realistic implementations of quantum communication tasks and find many cases where adding more noise to the probabilistic protocol increases considerably the fidelity of the teleported state, without decreasing the probability of a successful run of the protocol. Also, there are cases where the entanglement of the channel connecting Alice and Bob leading to the greatest fidelity is not maximal. Moreover, there exist cases where the optimal fidelity for the probabilistic protocols are greater than the maximal fidelity (2/3)(2/3)(2/3) achievable by using only classical resources, while the optimal ones for the deterministic protocols under the same conditions lie below this limit. This result clearly illustrates that in some cases we can only get a truly quantum teleportation if we use probabilistic instead of deterministic protocols.
Quantum teleportation is one of the most pioneering features of the quantum world. Typically, the quality of a teleportation protocol is solely judged by its average fidelity. In this work, we analyze the performance of teleportation in terms of both fidelity and the deviation in fidelity. Specifically, we define a quantity called teleportability score, which incorporates contributions from both the fidelity and its deviation. It also takes into account the sensitivity one requires for a protocol in which the teleportation of a quantum state is required in one or many intermediate steps. We compute the teleportability score in the noiseless scenario and find that it increases monotonically with the entanglement content of the considered pure resource states. The result remains the same even if we consider an nnn-chain repeater-like configuration. However, in the presence of noise, the teleportability score can sometime display a nonmonotonic behavior with respect to the entanglement content of the initially shared resource state. Specifically, under local bit-flip and bit-phase-flip noise, less entangled states can have higher teleportability score for certain choices of system parameters. In the presence of global depolarizing noise, for low entangled resource states and high sensitivity requirements, the noisy states can have better a teleportability score in comparison to the noiseless scenario.
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.
In this work, we consider the following teleportation protocol: There is an arbitrary two-qubit resource state, shared between two spatially separated parties, Alice and Bob. Applying local unitary operators, they transform the resource state into the canonical form. To teleport an unknown qubit, Alice now measures her qubits in the Bell basis. Then, the measurement outcome is communicated by Alice to Bob via noisy classical channel(s). Finally, after receiving the classical message, Bob applies the necessary unitary operator to his qubit. Under this protocol, we find the exact formulae of teleportation fidelity and its deviation. We further find conditions for non-classical fidelity within this protocol. If the classical communication is noiseless in the above protocol then there are resource states which can lead to zero fidelity deviation. However, we show that such states may not lead to zero fidelity deviation when the classical communication is noisy in the same protocol. We also explore the opposite case, i.e., the states, which cannot lead to zero fidelity deviation in the above protocol when the classical communication is noiseless, may lead to zero fidelity deviation when the classical communication is noisy in the same protocol without compromising the non-classical fidelity. Moreover, we exhibit scenarios within the present protocol, where the fidelity deviation increases if the entanglement of the resource state is increased.