Quantum entanglement is an important quantum resource.Entanglement of quantum nodes is the foundation for constructing large-scale quantum networks consisting of quantum nodes and quantum channels.In practical applications of quantum information， the ineluctable optical transmission loss， phase diffusion noise， and mixing with the thermal states lead to decoherence and disruption of entangled states， which limit the communication distance and affect the quality of entanglement between quantum nodes.Entanglement distillation， which can extract a small portion highly entangled states from a quantity of weakly entangled states， in addition to overcoming this detrimental problem.By preparing entangled optical mode twice and interfering with atomic ensembles， the establishment of entanglement between atomic ensembles and entanglement distillation based on quantum memory and balanced homodyne detection （BHD） can be achieved.The first-prepared entangled optical fields are mapped into two atomic ensembles via electromagnetically-induced-transparency （EIT） quantum memory to establish entanglement between atomic ensembles.Subsequently， the second-prepared entangled optical fields are then distributed to these two entangled atomic ensembles through quantum channels to implement interference.The transmitted optical fields from two atomic ensembles are detected by BHDs， the detection results below the triggered threshold determine the success or failure.During the distribution process， the entangled optical fields prepared twice passed through optical choppers， which are divided into three different zones according to the requirements， and each zone is glued with different optical components.Zone I does not have any optics， zone Ⅱ has an optical attenuator， and zone Ⅲ is used to block the optical beams.The second-prepared entangled optical fields interfere with these two entangled atomic ensembles through zone Ⅱ， and the transmittance of the optical attenuator directly affects the effect of entanglement distillation.In this paper， we theoretically analyze the effect of different transmittance of optical attenuator on the effect of entanglement distillation， and find the corresponding quantum writing efficiency when the entanglement distillation achieves the best effect.As the transmittance increases， the effect of entanglement distillation is better； when the transmittance is certain， there exists an optimal writing efficiency which makes the entanglement between atomic ensembles optimal.As the transmittance increases gradually， the optimal writing efficiency becomes smaller， which is easier to realize in the experiment.Additionally， the correlation variaces before and after the entanglement distillation of atomic spin waves with other physical parameters are analyzed， which provides a basis for the selection of physical parameters in the entanglement distillation scheme， and lays a foundation for construction of large-scale quantum networks.
Quantum entanglement is an important quantum resource.Entanglement of quantum nodes is the foundation for constructing large-scale quantum networks consisting of quantum nodes and quantum channels.In practical applications of quantum information， the ineluctable optical transmission loss， phase diffusion noise， and mixing with the thermal states lead to decoherence and disruption of entangled states， which limit the communication distance and affect the quality of entanglement between quantum nodes.Entanglement distillation， which can extract a small portion highly entangled states from a quantity of weakly entangled states， in addition to overcoming this detrimental problem.By preparing entangled optical mode twice and interfering with atomic ensembles， the establishment of entanglement between atomic ensembles and entanglement distillation based on quantum memory and balanced homodyne detection （BHD） can be achieved.The first-prepared entangled optical fields are mapped into two atomic ensembles via electromagnetically-induced-transparency （EIT） quantum memory to establish entanglement between atomic ensembles.Subsequently， the second-prepared entangled optical fields are then distributed to these two entangled atomic ensembles through quantum channels to implement interference.The transmitted optical fields from two atomic ensembles are detected by BHDs， the detection results below the triggered threshold determine the success or failure.During the distribution process， the entangled optical fields prepared twice passed through optical choppers， which are divided into three different zones according to the requirements， and each zone is glued with different optical components.Zone I does not have any optics， zone Ⅱ has an optical attenuator， and zone Ⅲ is used to block the optical beams.The second-prepared entangled optical fields interfere with these two entangled atomic ensembles through zone Ⅱ， and the transmittance of the optical attenuator directly affects the effect of entanglement distillation.In this paper， we theoretically analyze the effect of different transmittance of optical attenuator on the effect of entanglement distillation， and find the corresponding quantum writing efficiency when the entanglement distillation achieves the best effect.As the transmittance increases， the effect of entanglement distillation is better； when the transmittance is certain， there exists an optimal writing efficiency which makes the entanglement between atomic ensembles optimal.As the transmittance increases gradually， the optimal writing efficiency becomes smaller， which is easier to realize in the experiment.Additionally， the correlation variaces before and after the entanglement distillation of atomic spin waves with other physical parameters are analyzed， which provides a basis for the selection of physical parameters in the entanglement distillation scheme， and lays a foundation for construction of large-scale quantum networks.
The development of quantum network relies on high-quality entanglement between remote quantum nodes. In reality the unavoidable decoherence limits the quality of entangled quantum nodes, however, entanglement distillation can overcome this problem. Here we propose an experimentally feasible scheme of continuous-variable entanglement generation, storage, and distillation between distant quantum nodes, which only requires the atomic ensemble quantum memory and balanced homodyne detection (BHD). Initially one copy of a bipartite entangled state of light, suffering phase fluctuations during the distributions, is stored in two distant atomic ensembles so that the atomic ensembles are entangled. Within the storage lifetime, by distributing and storing another copy of entangled optical modes in these two atomic ensembles, the distillation on entangled atomic spin waves can be implemented based on the post-selection of the BHD result. Our scheme provides a highly entangled state between remote quantum nodes for downstream applications, and enables the extension to multipartite entanglement distillation in a large-scale quantum network.
Entangled photons are ideally suited to the transmission of photonic quantum information. Mitigating the effects of decoherence is fundamental to distributing photonic entanglement across large distances. One such proposal is entanglement distillation, in which operations on a large ensemble of weakly entangled states generate a smaller ensemble of more strongly entangled states. In this thesis, we experimentally and theoretically analyse various tools required for demonstrating continuous-variable (CV) entanglement distillation, following the proposal by Browne et al., [Phys. Rev. A 67, 062320 (2003)]. Specifically, we propose figures of merit to account for the practical limitations of non-deterministic non-Gaussian operations, and analyse the experimental parameters necessary to optimise them. We develop a source of pulsed two-mode squeezed states, which are the initial states of our entanglement distillation protocol. We use weak-field homodyne detection as a phase-dependent photon counting detector, and demonstrate its utility in conditional state generation. Using these states, we demonstrate sub-binomial light as a tool for benchmarking quantum states. Finally, we applied two-mode weak-field homodyne detection to two entangled states and demonstrate correlations in the photon counting statistics which depend on a joint phase from two independent local oscillators. This setup is sufficient to apply an entanglement witness developed by Puentes et al. [New J. Phys. 12, 033042 (2010)]. Despite encouraging simulations, we do not witness entanglement with this scheme, which we attribute to a noise source unaccounted for in the simulations. Although we do not demonstrate entanglement distillation outright, the tools we develop to do so represent a general, hybrid approach to CV quantum optics. Developing tools such as phase-resolved projective measurement on two-mode states allows us to probe both the wave and particle nature of entangled light at the single-photon level. Using and expanding these techniques to probe larger quantum systems may prove useful in studies of fundamental physics and quantum enhanced technologies.
Atomic ensembles are effective memory nodes for quantum communication network due to the long coherence time and the collective enhancement effect for the nonlinear interaction between an ensemble and a photon. Here we investigate the possibility of achieving the entanglement distillation for nonlocal atomic ensembles by the input-output process of a single photon as a result of cavity quantum electrodynamics. We give an optimal entanglement concentration protocol (ECP) for two-atomic-ensemble systems in a partially entangled pure state with known parameters and an efficient ECP for the systems in an unknown partially entangled pure state with a nondestructive parity-check detector (PCD). For the systems in a mixed entangled state, we introduce an entanglement purification protocol with PCDs. These entanglement distillation protocols have high fidelity and efficiency with current experimental techniques, and they are useful for quantum communication network with atomic-ensemble memories.
Quantum entanglement is an essential quantum resource. With the development of quantum information science, quantum network consisting of quantum nodes and quantum channels has attracted extensive attention. The development of quantum information network requires the capability of generating, storing and distributing quantum entanglement among multiple quantum nodes. It is significant to construct the quantum information, and it has very important applications in the distributed quantum computation and quantum internet. Here we propose a simple and feasible scheme to deterministically entangle three distant atomic ensembles via the interference and feedforward network of the light-atom mixed entanglement. Firstly, three atomic ensembles placed at three remote nodes in a quantum network are prepared into the mixed entangled state of light and atomic ensembles via the spontaneous Raman scattering (SRS) process. Then, the first and second Stokes optical field are interfered on an R1∶T1 optical beam splitter (BS1), and one of the output optical fields from the first optical beam splitter is interfered with the third Stokes field on the second R2∶T2 optical beam splitter (BS2). The quantum fluctuations of the amplitude and phase quadratures of these three output optical fields from BS1 and BS2 are detected by three sets of balanced homodyne detectors, respectively. Finally, the detected signals of the amplitude and phase quadratures are fed to the three atomic ensembles via the radio frequency coils to establish the entanglement among three remote atomic ensembles. At the user-controlled time, three read optical pulses can be applied to these three atomic ensembles to convert the stored entangled state from the atomic spin waves into the anti-Stokes optical fields via the SRS process. According to the tripartite inseparability criterion, the correlation variance combinations of these three anti-Stokes optical fields can be used to verify the performance of entanglement of three atomic ensembles. This scheme can be extended to larger-scale quantum information network with different physical systems and more atomic nodes. Moreover, the entanglement distillation can be combined with this scheme to realize the entanglement among longer distance quantum nodes.
Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibres are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to date. Here, we present the theory for an efficient iterative entanglement distillation protocol without quantum memories and provide a proof-of-principle experimental demonstration. The scheme is applied to phase-diffused two-mode-squeezed states and proven to distil entanglement for up to three iteration steps. The data are indistinguishable from those that an efficient scheme using quantum memories would produce. Since our protocol includes the final measurement it is particularly promising for enhancing continuous-variable quantum key distribution.
Many different quantum-information communication protocols such as teleportation, dense coding, and entanglement-based quantum key distribution are based on the faithful transmission of entanglement between distant location in an optical network. The distribution of entanglement in such a network is, however, hampered by loss and noise that is inherent in all practical quantum channels. Thus, to enable faithful transmission one must resort to the protocol of entanglement distillation. In this paper we present a detailed theoretical analysis and an experimental realization of continuous variable entanglement distillation in a channel that is inflicted by different kinds of non-Gaussian noise. The continuous variable entangled states are generated by exploiting the third order nonlinearity in optical fibers, and the states are sent through a free-space laboratory channel in which the losses are altered to simulate a free-space atmospheric channel with varying losses. We use linear optical components, homodyne measurements, and classical communication to distill the entanglement, and we find that by using this method the entanglement can be probabilistically increased for some specific non-Gaussian noise channels.