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arXiv:quant-ph/0510078 · Physical Review A

Entanglement activation and the robustness of quantum correlations

Fernando G. S. L. Brandão

Published Sep 5, 2007• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.76.030301

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arXiv:1601.01236•Physical Review A•Jun 20, 2016•4 citations
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 \ensuremathσ\ensuremath{\sigma}\ensuremathσ is linked to the maximum increase in the fidelity of teleportation of any other state when \ensuremathσ\ensuremath{\sigma}\ensuremathσ 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.
In distributed quantum computing, quantum networks provide a potential infrastructure for long-range quantum information processing. Controlled quantum teleportation (CQT) is a key practically relevant protocol that can connect two parties on a network and enables a third party, the controller to allow or abort the secure teleportation of an arbitrary single-qubit state between the two parties. We investigate the robustness of a three-qubit GHZ resource under bit-flip, phase-flip, depolarizing, and amplitude-damping noise. Using the Kraus-operator formalism, we characterize the noisy resource through multipartite quantum discord, genuine multipartite concurrence (GMC), localizable entanglement (LE), and CQT fidelity. We also outline a proof-of-concept photonic implementation for preparing the three-qubit GHZ resource and realizing the CQT protocol, which could enable experimental investigation of the effects of noise. Our results show that bit-flip and amplitude-damping noise generally preserve useful mutipartite quantum correlations over broader noise parameter ranges. Interestingly, multipartite discord exhibits freezing under bit-flip noise over a finite parameter regime. Moreover, discord can persist beyond the sudden death of genuine multipartite entanglement, revealing the distinct robustness of nonclassical correlations. We further demonstrate that CQT fidelity which characterizes the performance of CQT can exceed the classical threshold even after GMC vanishes, while LE more closely reflects the operational usefulness of the noisy resource. These findings highlight the complementary roles of quantum correlations and entanglement in assessing the resilience of GHZ-based protocols.
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.
The standard benchmark for teleportation is the average fidelity of teleportation and according to this benchmark not all states are useful for teleportation.It was recently shown, however, that all entangled states lead to nonclassical teleportation, with there being no classical scheme able to reproduce the states teleported to Bob.Here we study the operational significance of this result.On the one hand, we demonstrate that every state is useful for teleportation if a generalization of the average fidelity of teleportation is considered which concerns teleporting quantum correlations.On the other hand, we show the strength of a particular entangled state and entangled measurement for teleportation-as quantified by the robustness of teleportation-precisely characterizes their ability to offer an advantage in the task of subchannel discrimination with side information.This connection allows us to prove that every entangled state outperforms all separable states when acting as a quantum memory in this discrimination task.Finally, within the context of a resource theory of teleportation, we show that the two operational tasks considered provide complete sets of monotones for two partial orders based on the notion of teleportation simulation, one classical and one quantum.
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.
Quantum correlations in a physical system are usually studied with respect to a unique and fixed decomposition of the system into subsystems, without fully exploiting the rich structure of the state space. Here, we show several examples in which the consideration of different ways to decompose a physical system enhances the quantum resources and accounts for a more flexible definition of quantumness measures. Furthermore, we give a different perspective regarding how to reassess the fact that local operations play a key role in general quantumness measures that go beyond entanglement---as discordlike ones. We propose a family of measures to quantify the maximum quantumness of a given state. For the discord-based case, we present some analytical results for $2\ifmmode\times\else\texttimes\fi{}d$-dimensional states. Applying our definition to low-dimensional bipartite states, we show that different behaviors can be reported for separable and entangled states vis-\`a-vis those corresponding to the usual measures of quantum correlations. We show that there is a close link between our proposal and the criterion to witness quantum correlations based on the rank of the correlation matrix, proposed by Daki\ifmmode \acute{c}\else \'{c}\fi{}, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)].