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Physical Review A

Enhancing entanglement and total correlation dynamics via local unitaries

Joab M. Varela, Ranieri Nery, George Moreno, Alice Caroline de Oliveira Viana, Gabriel Teixeira Landi, Rafael Chaves

Published Feb 22, 2022• 1 citation
Publisher

Abstract

The interaction with the environment is one of the main obstacles to be circumvented in practical implementations of quantum information tasks. The use of local unitaries, while not changing the initial entanglement present in a given state, can enormously change its dynamics through a noisy channel, and consequently its ability to be used as a resource. In this way, local unitaries provide an easy and accessible way to enhance quantum correlations in a variety of different experimental platforms. Given an initial entangled state and a certain noisy channel, what are the local unitaries providing the most robust dynamics? In this paper we solve this question considering two-qubit states, together with paradigmatic and relevant noisy channels, showing its consequences for teleportation protocols and identifying cases where the most robust states are not necessarily the ones imprinting the least information about themselves into the environment. We also derive a general multipartite law relating the interplay between the total correlations in the system and environment with their mutual information built up over the noisy dynamics. Finally, we employ the IBM Quantum Experience to provide a proof-of-principle experimental implementation of our results.

DOI
10.1103/physreva.105.022430

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The interaction with the environment is one of the main obstacles to be circumvented in practical implementations of quantum information tasks. The use of local unitaries, while not changing the initial entanglement present in a given state, can enormously change its dynamics through a noisy channel, and consequently its ability to be used as a resource. In this way, local unitaries provide an easy and accessible way to enhance quantum correlations in a variety of different experimental platforms. Given an initial entangled state and a certain noisy channel, what are the local unitaries providing the most robust dynamics? In this paper we solve this question considering two-qubit states, together with paradigmatic and relevant noisy channels, showing its consequences for teleportation protocols and identifying cases where the most robust states are not necessarily the ones imprinting the least information about themselves into the environment. We also derive a general multipartite law relating the interplay between the total correlations in the system and environment with their mutual information built up over the noisy dynamics. Finally, we employ the IBM Quantum Experience to provide a proof-of-principle experimental implementation of our results.
The interaction with the environment is one of the main obstacles to be circumvented in practical implementations of quantum information tasks. The use of local unitaries, while not changing the initial entanglement present in a given state, can enormously change its dynamics through a noisy channel, and consequently its ability to be used as a resource. This way, local unitaries provide an easy and accessible way to enhance quantum correlations in a variety of different experimental platforms. Given an initial entangled state and a certain noisy channel, what are the local unitaries providing the most robust dynamics? In this paper we solve this question considering two qubits states, together with paradigmatic and relevant noisy channels, showing its consequences for teleportation protocols and identifying cases where the most robust states are not necessarily the ones imprinting the least information about themselves into the environment. We also derive a general law relating the interplay between the total correlations in the system and environment with their mutual information built up over the noisy dynamics. Finally, we employ the IBM Quantum Experience to provide a proof-of-principle experimental implementation of our results.
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.
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.
One of the main challenges for the manipulation and storage of multipartite entanglement is its fragility under noise. We present a simple recipe for the systematic enhancement of the resistance of multipartite entanglement against any local noise with a privileged direction in the Bloch sphere. For the case of exact local dephasing along any given basis, and for all noise strengths, our prescription grants full robustness: Even states with exponentially decaying entanglement are mapped to states whose entanglement is constant. In contrast to previous techniques resorting to complex logical-qubit encodings, such enhancement is attained simply by performing local-unitary rotations before the noise acts. The scheme is therefore highly experimentally friendly, as it brings no overhead of extra physical qubits to encode logical ones. In addition, we show that, apart from entanglement, the resiliences of the relative entropy of quantumness and the usefulness as resources for practical tasks such as metrology and nonlocality-based protocols are equivalently enhanced.
The estimation of the entanglement of multipartite systems undergoing decoherence is important for assessing the robustness of quantum information processes. It usually requires access to the final state and its full reconstruction through quantum tomography. General dynamical laws may simplify this task. We found that when one of the parties of an initially entangled two-qubit system is subject to a noisy channel, a single universal curve describes the dynamics of entanglement for both pure and mixed states, including those for which entanglement suddenly disappears. Our result, which is experimentally demonstrated using a linear optics setup, leads to a direct and efficient determination of entanglement through the knowledge of the initial state and single-party process tomography alone, foregoing the need to reconstruct the final state.
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.