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arXiv:1911.04550 · Journal of Physics Conference Series

Featuring Causal Order in Teleportation With Two Quantum Teleportation Channels

Carlos Cardoso-Isidoro, Francisco Delgado

Published Apr 1, 2020• 12 citations
arXivHTMLPDF

Abstract

Abstract Causal order can improve the quantum information transmission in teleportation due a noisy entangled resource being present in it by using additionally an appropriate measurement state on the control state ruling the causal order. In this work, we get analytically the fidelity for the entire process under an arbitrary initialization of such control state and performing an optimal measurement on it, thus obtaining a perfect teleportation. We also analyse other values characterizing the imperfect entangled state where a perfect teleportation can not be reached. Notably, we determine that the best fidelity does not depend on the preparation of the control state but instead on the imperfect initial entangled resource.

DOI
10.1088/1742-6596/1540/1/012024

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Abstract Causal order can improve the quantum information transmission in teleportation due a noisy entangled resource being present in it by using additionally an appropriate measurement state on the control state ruling the causal order. In this work, we get analytically the fidelity for the entire process under an arbitrary initialization of such control state and performing an optimal measurement on it, thus obtaining a perfect teleportation. We also analyse other values characterizing the imperfect entangled state where a perfect teleportation can not be reached. Notably, we determine that the best fidelity does not depend on the preparation of the control state but instead on the imperfect initial entangled resource.
Quantum teleportation has had notorious advances in the last decade, being successfully deployed in the experimental domain. In other terrains, the understanding of indefinite causal order has demonstrated a valuable enhancement in quantum communication to correct channel imperfections. In this work, we address the symmetries underlying imperfect teleportation when it is assisted by indefinite causal order to correct the use of noisy entangled resources. In the strategy being presented, indefinite causal order introduces a control state to address the causal ordering. Then, by using post-selection, it fulfills the teleportation enhancement to recover the teleported state by constructive interference. By analysing primarily sequential teleportation under definite causal order, we perform a comparison basis for notable outcomes derived from indefinite causal order. After, the analysis is conducted by increasing the number of teleportation processes, thus suggesting additional alternatives to exploit the most valuable outcomes in the process by adding weak measurement as a complementary strategy. Finally, we discuss the current affordability for an experimental implementation.
In this work, we investigate controlled quantum teleportation in the presence of noisy channels acting on the three-qubit resource state. We employ a series of generalized noisy channels that bridge the dephasing channels and amplitude damping channels while encompassing extensive intermediate scenarios. We provide an in-depth analysis of the degradation of the maximal average fidelity and the optimal average fidelity in controlled quantum teleportation induced by such noisy channels by deriving the analytical expression and examining several special cases. The analytical expression shows that attaining the optimal average fidelity requires Charlie's cooperation in performing a measurement at suitably chosen angles, and is also related to the initial state and the channel parameters. Our analysis reveals that the optimal average fidelity does not always decrease monotonically with the evolution parameter, instead, it first decreases and then increases. This non-monotonic behavior depends on the entanglement of the initial resource state, as well as on the parameters of the channel traversed by the first qubit.
Abstract We show that the fidelity offered by the standard teleportation protocol under noisy channels applied successively can be significantly improved, when used in conjunction with a quantum switch. In particular, we find that for two such teleportation channels conjugated with an indefinite causal order, teleportation fidelity beyond the classical threshold is achieved for significantly larger noise than would be possible conventionally. One can even make the effective teleportation channel perfectly faithful for very large noise. We also discuss the generalization of our scheme for more than two pathways, and define a figure of merit in that context.
Noisy entangled resource and non-standard teleportation operations result in imperfect teleportation. In this paper, we derive an explicit expression for the output states of imperfect teleportation processes, thereby establishing a correspondence between teleportation and quantum channels. This result offers a different insight into teleportation. Also, it enables us to derive an expression for the fidelity of teleportation. Our results analytically reveal the dependence of the output states and the fidelity on the entangled resource and teleportation operations. The Nielsen–Caves teleportation formalism is used in the derivation.
Quantum teleportation is a fundamental protocol in quantum information science, whose performance is conventionally evaluated under the assumption of ideal Bell-state measurements. In realistic implementations, however, joint measurements are often imperfect and can deviate from maximally entangled bases due to coherent errors in entangling operations. In this work, we analytically show how the entanglement of joint measurements determines teleportation performance, and we propose a strategy to overcome the limitations imposed by partially entangled joint measurements to recover the unit teleportation fidelity with a nonzero success probability. This is achieved by optimizing a reversing operation on the teleported state to compensate for the known coherent deformation of the Bell-state measurement. We then derive an exact equation revealing a quantitative relation between measurement entanglement, channel entanglement, and the success probability to realize the unit-fidelity two-qubit teleportation. We illustrate our results using elegant joint measurements and realistic coherent error models arising from imperfect entangling operations in quantum systems. Our work provides fundamental insight into the role of measurement entanglement in quantum teleportation and offers a practical framework for achieving faithful teleportation without requiring substantial modifications to existing hardware.
We study the activation of entanglement in teleportation protocols. To this end, we a present derivation of the average fidelity of teleportation process with noisy classical channel for qudits. In our work we do not make any assumptions about the entangled states shared by communicating parties. Our result allows us to specify the minimum amount of classical information required to beat the classical limit when the protocol is based on the Bell measurements. We also compare average fidelity of teleportation obtained using noisy and perfect classical channel with restricted capacity. The most important insight into the intricacies of quantum information theory that we gain is that though entanglement, obviously, is a necessary resource for efficient teleportation it requires a certain threshold amount of classical communication to be more useful than classical communication. Another interesting finding is that the amount of classical communication required to activate entanglement for teleportation purposes depends on the dimension d of the system being teleported but is not monotonic reaching maximum for d = 4.