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arXiv:1505.07457

Non-Markovian Reactivation of Quantum Relays

Stefano Pirandola, Carlo Ottaviani, Christian S. Jacobsen, Gaetana Spedalieri, Samuel L. Braunstein, Tobias Gehring, Ulrik L. Andersen

Published May 27, 2015• 2 citations
arXivHTMLPDF

Abstract

We consider a quantum relay which is used by two parties to perform several continuous-variable protocols: Entanglement swapping, distillation, quantum teleportation, and quantum key distribution. The theory of these protocols is extended to a non-Markovian model of decoherence characterized by correlated Gaussian noise. Even if bipartite entanglement is completely lost at the relay, we show that the various protocols can progressively be reactivated by the separable noise-correlations of the environment. In fact, above a critical amount, these correlations are able to restore the distribution of quadripartite entanglement, which can be localized into an exploitable bipartite form by the action of the relay. Our findings are confirmed by a proof-of-principle experiment and show the potential advantages of non-Markovian effects in a quantum network architecture.

DOI
10.48550/arxiv.1505.07457

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We consider a quantum relay which is used by two parties to perform several continuous-variable protocols: Entanglement swapping, distillation, quantum teleportation, and quantum key distribution. The theory of these protocols is extended to a non-Markovian model of decoherence characterized by correlated Gaussian noise. Even if bipartite entanglement is completely lost at the relay, we show that the various protocols can progressively be reactivated by the separable noise-correlations of the environment. In fact, above a critical amount, these correlations are able to restore the distribution of quadripartite entanglement, which can be localized into an exploitable bipartite form by the action of the relay. Our findings are confirmed by a proof-of-principle experiment and show the potential advantages of non-Markovian effects in a quantum network architecture.
Abstract We consider a quantum relay that is used by two parties to perform several continuous-variable protocols of quantum communication, from entanglement distribution (swapping and distillation) to quantum teleportation, and quantum key distribution. The theory of these protocols is suitably extended to a non-Markovian model of decoherence characterized by correlated Gaussian noise in the bosonic environment. In the worst-case scenario where bipartite entanglement is completely lost at the relay, we show that the various protocols can be reactivated by the assistance of classical (separable) correlations in the environment. In fact, above a critical amount, these correlations are able to guarantee the distribution of a weaker form of entanglement (quadripartite), which can be localized by the relay into a stronger form (bipartite) that is exploitable by the parties. Our findings are confirmed by a proof-of-principle experiment where we show, for the first time, that memory effects in the environment can drastically enhance the performance of a quantum relay, well beyond the single-repeater bound for quantum and private communications.
We consider two bosonic Gaussian channels whose thermal noise is strong enough to break bipartite entanglement. In this scenario, we discuss how the presence of separable correlations between the two channels is able to restore the broken entanglement. This reactivation occurs not only in a scheme of direct distribution, where a third party (Charlie) broadcasts entangled states to remote parties (Alice and Bob), but also in a configuration of indirect distribution which is based on entanglement swapping. In both schemes, the amount of entanglement remotely activated can be large enough to be distilled by one-way distillation protocols.
Combining two entanglement-breaking channels into a correlated-noise environment restores the distribution of entanglement. Surprisingly, this reactivation can be induced by the injection of separable correlations from the composite environment. In any dimension (finite or infinite), we can construct classically correlated 'twirling' environments which are entanglement-breaking in the transmission of single systems but entanglement-preserving when two systems are transmitted. Here entanglement is simply preserved by the existence of decoherence-free subspaces. Remarkably, even when such subspaces do not exist, a fraction of the input entanglement can still be distributed. This is found in separable Gaussian environments, where distillable entanglement is able to survive the two-mode transmission, despite being broken in any single-mode transmission by the strong thermal noise. In the Gaussian setting, entanglement restoration is a threshold process, occurring only after a critical amount of correlations has been injected. Such findings suggest new perspectives for distributing entanglement in realistic environments with extreme decoherence, identifying separable correlations and classical memory effects as physical resources for 'breaking entanglement-breaking'.
The present manuscript represents the completion of a research path carried forward during my doctoral studies in the University of Turku. It contains information regarding my scientific contribution to the field of open quantum systems, accomplished in collaboration with other scientists. \n \nThe main subject investigated in the thesis is the non-Markovian dynamics of open quantum systems with focus on continuous variable quantum channels, e.g. quantum Brownian motion models. Non-Markovianity is here interpreted as a manifestation of the existence of a flow of information exchanged by the system and environment during the dynamical evolution. While in Markovian systems the flow is unidirectional, i.e. from the system to the environment, in non-Markovian systems there are time windows in which the flow is reversed and the quantum state of the system may regain coherence and correlations previously lost. \n \nSignatures of a non-Markovian behavior have been studied in connection with the dynamics of quantum correlations like entanglement or quantum discord. Moreover, in the attempt to recognisee non-Markovianity as a resource for quantum technologies, it is proposed, for the first time, to consider its effects in practical quantum key distribution protocols. It has been proven that security of coherent state protocols can be enhanced using non-Markovian properties of the transmission channels. \n \nThe thesis is divided in two parts: in the first part I introduce the reader to the world of continuous variable open quantum systems and non-Markovian dynamics. The second part instead consists of a collection of five publications inherent to the topic.
Decoherence of quantum information carried by single-mode and two-mode Gaussian states is investigated under the influence of non-Markovian quantum channels, where correlation times of reservoir variables are assumed to take finite values. Degradation of purity, distinguishability and non-classicality of single-mode Gaussian states and relaxation of entanglement of two-mode Gaussian states are examined. The results show the importance of the non-Markovian effect of a thermal reservoir. Furthermore, continuous variable quantum teleportation is considered when a sender and a receiver share a two-mode Gaussian state through non-Markovian quantum channels.
The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Below a critical bath temperature entanglement between the two modes is preserved even in the steady state. A separability criterion is derived, which depends on the bath temperature and the response function of the open quantum system. Thus, the extended quantum Brownian motion model of a two-mode continuous variable system in a common reservoir provides an example of environment-induced entanglement.