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arXiv:1804.10612 · Physical Review A

Methods to estimate entanglement in teleportation experiments

Ivan Šupić, Paul Skrzypczyk, Daniel Cavalcanti

Published Mar 22, 2019• 20 citations
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Abstract

Quantum state teleportation is a protocol where a shared entangled state is used as a quantum channel to transmit quantum information between distinct locations. Here we consider the task of estimating entanglement of the underlying shared state in teleportation protocols. We show that the data accessible in a teleportation experiment allows us to put a lower bound on some entanglement measures, such as entanglement negativity and robustness. Furthermore, we show cases in which the lower bounds are tight. The introduced lower bounds can also be interpreted as quantifiers of the nonclassicality of a teleportation experiment. Thus, our findings provide a quantitative relation between teleportation and entanglement.

DOI
10.1103/physreva.99.032334

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Quantum state teleportation is a protocol where a shared entangled state is used as a quantum channel to transmit quantum information between distinct locations. Here we consider the task of estimating entanglement of the underlying shared state in teleportation protocols. We show that the data accessible in a teleportation experiment allows us to put a lower bound on some entanglement measures, such as entanglement negativity and robustness. Furthermore, we show cases in which the lower bounds are tight. The introduced lower bounds can also be interpreted as quantifiers of the nonclassicality of a teleportation experiment. Thus, our findings provide a quantitative relation between teleportation and entanglement.
In a previous work [Phys. Rev. Lett. 119, 110501] we proved that every entangled quantum state can be used to implement a non-classical teleportation channel. Here we turn to the question of quantifying how non-classical these channels are. We define several quantifiers of non-classical teleportation which can be computed using semidefinite programming. Furthermore, we prove quantitative relations between these quantifiers and the amount of entanglement in the underlying states. Apart from providing further insight on the relation between teleportation and entanglement, our work introduces a method to estimate entanglement in a teleportation experiment.
Quantum teleportation establishes a correspondence between an entangled state shared by two separate parties that can communicate classically and the presence of a quantum channel connecting the two parties. The standard benchmark for quantum teleportation, based on the average fidelity between the input and output states, indicates that some entangled states do not lead to channels which can be certified to be quantum. It was recently shown that if one considers a finer-grained witness, then all entangled states can be certified to produce a nonclassical teleportation channel. Here we experimentally demonstrate a complete characterization of a new family of such witnesses, of the type proposed in Phys. Rev. Lett. 119, 110501 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.110501 under different conditions of noise. We report nonclassical teleportation using quantum states that cannot achieve average fidelity of teleportation above the classical limit. We further use the violation of these witnesses to estimate the negativity of the shared state. Our results have fundamental implications in quantum information protocols and may also lead to new applications and quality certification of quantum technologies.
Quantum teleportation, the process by which Alice can transfer an unknown quantum state to Bob by using preshared entanglement and classical communication, is one of the cornerstones of quantum information. The standard benchmark for certifying quantum teleportation consists in surpassing the maximum average fidelity between the teleported and the target states that can be achieved classically. According to this figure of merit, not all entangled states are useful for teleportation. Here we propose a new benchmark that uses the full information available in a teleportation experiment and prove that all entangled states can implement a quantum channel which cannot be reproduced classically. We introduce the idea of nonclassical teleportation witness to certify if a teleportation experiment is genuinely quantum and discuss how to quantify this phenomenon. Our work provides new techniques for studying teleportation that can be immediately applied to certify the quality of quantum technologies.
We show that the usefulness of a state as an activator in teleportation protocols is equivalent to the robustness of its entanglement to noise. The robustness of entanglement of a bipartite state $\ensuremath{\sigma}$ is linked to the maximum increase in the fidelity of teleportation of any other state when $\ensuremath{\sigma}$ is used as an extra resource. On the one hand, this connection gives an operational meaning to the robustness of entanglement. On the other hand, it shows that the activation capability---which has a central role as an operational way of quantifying bound entangled states---can be estimated experimentally by measuring entanglement witnesses.
We use the entanglement sampling techniques developed by Dupuis, Fawzi and Wehner to find a lower bound on the entanglement needed by a coalition of cheater attacking the quantum position verification protocol using the four BB84 states in the scenario where the cheaters have no access to a quantum channel but share a (possibly mixed) entangled state Φ~\tildeΦΦ~. For a protocol using n qubits, a necessary condition for cheating is that the max- relative entropy of entanglement Emax⁡(Φ~)≥n−O(log⁡n)E_{\max}(\tildeΦ)\ge n-O(\log n)Emax​(Φ~)≥n−O(logn). This improves previously known best lower bound by a factor ∼4\sim4∼4, and it is essentially tight, since this protocol is vulnerable to a teleportation based attack using n−O(1)n-O(1)n−O(1) ebits of entanglement.