Entanglement Distillation Scheme Research Articles

$O(\sqrt\eta)$ efficiency entanglement distillation with one-time photon subtraction over near-zero transmittance bosonic channel

Entanglement distillation is an efficient method to retrieve high-quality entanglement from a large number of noise-damped entanglement states. Many investigations on continuous variable entanglement distillation have focused on low-loss or medium-loss channels. Herein, we primarily study entanglement distillation in extremely lossy (total channel transmittance η ≪ 1 ) or even near-zero transmittance ( η ≈ 0 ) channels. In particular, we analyze the manner in which entanglement and success probability decrease as η → 0 . The performances of conventional biside photon subtraction and one-time photon subtraction on two optical modes separated by L km are investigated. The motivation for our study includes the recent advancements in twin-field quantum key distribution, wherein single-photon detection is sufficient to provide a useful private key. In the same vein, we propose an entanglement distillation scheme with an efficiency of O ( η ) using one-time photon subtraction and weak coherent state injection. Thus, our proposed scheme provides a method for distilling extremely damped entanglement states for continuous variable quantum information processing.

Optimizing practical entanglement distillation

The goal of entanglement distillation is to turn a large number of weakly entangled states into a smaller number of highly entangled ones. Practical entanglement distillation schemes offer a tradeoff between the fidelity to the target state, and the probability of successful distillation. Exploiting such tradeoffs is of interest in the design of quantum repeater protocols. Here, we present a number of methods to assess and optimize entanglement distillation schemes. We start by giving a numerical method to compute upper bounds on the maximum achievable fidelity for a desired probability of success. We show that this method performs well for many known examples by comparing it to well-known distillation protocols. This allows us to show optimality for many well-known distillation protocols for specific states of interest. As an example, we analytically prove optimality of the distillation protocol utilized within the Extreme Photon Loss (EPL) entanglement generation scheme, even in the asymptotic limit. We proceed to present a numerical method that can improve an existing distillation scheme for a given input state, and we present an example for which this method finds an optimal distillation protocol. An implementation of our numerical methods is available as a Julia package.

Polarization entanglement distillation through local filtering operations

An entanglement distillation scheme is proposed for an amplitude-damped polarization-entangled photon states via local filtering operations. The local filtering operations, i.e. positive operator-valued measure, on photons are realized by a series of Brewster window pairs. The entanglement of the survived photon pairs in the scheme will be much larger than that of the initial ones. In this sense, this distillation scheme is better than the currently existing entanglement protection scheme, where only the entanglement decaying time is prolonged and the entanglement is not enhanced at all. In addition, this scheme is simple and feasible within the current linear optical techniques.

Scheme for generating distillation-favorable continuous-variable entanglement via three concurrent parametric down-conversions in a single χ(2) nonlinear photonic crystal.

We propose to generate a single-mode-squeezing two-mode squeezed vacuum state via a single χ(2) nonlinear photonic crystal. The state is favorable for existing Gaussian entanglement distillation schemes, since local squeezing operations can enhance the final entanglement and the success probability. The crystal is designed for enabling three concurrent quasi-phase-matching parametric-down conversions, and hence relieves the auxiliary on-line bi-side local squeezing operations. The compact source opens up a way for continuous-variable quantum technologies and could find more potential applications in future large-scale quantum networks.

Distillation of multipartite entanglement by local filtering operations

In this work, we study how to distill two typical multipartite entangled noisy states, the amplitude-damped W state and the amplitude-damped Greenberger-Horne-Zeilinger state. Unlike the currently existing multipartite entanglement purification schemes, our scheme is a single-copy-based scheme, i.e., only one noisy state is needed in each distillation round, and the complicated multilateral controlled-not (cnot) operations are replaced by measurements of local positive-operator-valued measures (POVMs). The results show that local POVM measurements on one copy of the noisy state can project the initial state onto a new state with higher entanglement and nonlocality. In this scheme, although the final state can violate the multipartite Bell inequality, the corresponding initial noisy state does not violate it, which means that this distillation scheme can reveal the hidden genuine multipartite nonlocality of these initial states. For the case of the amplitude-damped W state, if the POVM parameters are appropriately chosen, the fidelity of the output state can approach $1.0$ for all the initial states with fidelity bigger than zero. So this single-copy-based multipartite entanglement distillation scheme has a wide range of distillable fidelities, and it is much simpler than the two-copy- or multiple-copy-based schemes. Furthermore, if the POVM measurement is carried out only on some member qubits rather than all of them, the distillation scheme can succeed too, which will greatly decrease the implementation complexity of the scheme. So this multipartite entanglement distillation scheme may be implementable in some physical system.

Enhancing and expanding remote photonic entanglement via local filtering operations

We present an entanglement distillation scheme for enhancing remote two-photon polarization entanglement of mixed states. Although the main idea of the current scheme is based on Gisin׳s work (Phys. Lett. A 210 (1996) 151 [21]), there are new advantages in our new scheme, which are guaranteed by the nondemolition measurement of photonic state and the re-distillation of the garbage states. This entanglement distillation scheme not only can enhance the remote entanglement of mixed states, but also can expand two-photon entangled states to four-photon entangled states. So this scheme is an apparently feasible way for preparing multi-photon entangled states. The main idea is based on the principle of the cross-Kerr nonlinearity and the parity-check measurements (a nondemolition measurement) on photonic states. Two distant users Alice and Bob first start with one shared but less entangled photon pair, and with the help of local auxiliary photons, parity-check measurements and classical communication they can get a four-photon highly entangled states with a high success probability. For the fail result, although the garbage state is less entangled than the initial one, there is still entanglement in it. So these garbage states can be re-collected and distilled again instead of being discarded. In this sense, we can see that this protocol has a high yield, and the fidelity (with respect to the Bell state) of the initial state is not required to be bigger than 1/2 (a common threshold of the standard entanglement purification theory). In addition, post-selection measurements on the entangled photons are not needed here because of the nondemolition measurement. The nondemolition character of the measurement allows further processing of the resulting states. These advantages make the current scheme more feasible within the current technology.

Roles of thermal noise and detector efficiency in distillation of continuous variable entanglement state

We address the degradation of continuous variable (CV) entanglement distillation in the presence of thermal environment and nonunity detecting efficiency. We explore the logarithmic negativity as a criteria and compare the output entanglement between the schemes of single-photon subtraction (PS) and two-PS. The probability of success is also investigated. We show that compared with detector efficiency, thermal noise plays a more dominant role in Gaussian entanglement distillation. Our results shed more light on the noise mechanism that influences realistic CV entanglement distillation and is of experimental relevance in developing a more efficient entanglement distillation scheme.

Continuous-variable entanglement distillation and noncommutative central limit theorems

Entanglement distillation transforms weakly entangled noisy states into highly entangled states, a primitive to be used in quantum repeater schemes and other protocols designed for quantum communication and key distribution. In this work, we present a comprehensive framework for continuous-variable entanglement distillation schemes that convert noisy non-Gaussian states into Gaussian ones in many iterations of the protocol. Instances of these protocols include (a) the recursive-Gaussifier protocol, (b) the temporally-reordered recursive-Gaussifier protocol, and (c) the pumping-Gaussifier protocol. The flexibility of these protocols give rise to several beneficial trade-offs related to success probabilities or memory requirements, which that can be adjusted to reflect experimental demands. Despite these protocols involving measurements, we relate the convergence in this protocols to new instances of non-commutative central limit theorems, in a formalism that we lay out in great detail. Implications of the findings for quantum repeater schemes are discussed.

Local Gaussian operations can enhance continuous-variable entanglement distillation

Entanglement distillation is a fundamental building block in long-distance quantum communication. Though known to be useless on their own for distilling Gaussian entangled states, local Gaussian operations may still help to improve non-Gaussian entanglement distillation schemes. Here we show that by applying local squeezing operations both the performance and the efficiency of existing distillation protocols can be enhanced. We find that such an enhancement through local Gaussian unitaries can be obtained even when the initially shared Gaussian entangled states are mixed, as, for instance, after their distribution through a lossy-fiber communication channel.

Iterative Entanglement Distillation: Approaching the Elimination of Decoherence

We experimentally demonstrate the two-step distillation of entanglement. The output of a first distillation stage underwent a second distillation step and was made available for subsequent steps. Our experiment displays the realization of the building blocks required for an entanglement distillation scheme that can fully overcome decoherence.

Practical entanglement distillation scheme using recurrence method and quantum low density parity check codes

Many entanglement distillation schemes use either universal random hashing or breeding as their final step to obtain almost perfect shared EPR pairs. In spite of a high yield, the hardness of decoding a random linear code makes the use of random hashing and breeding infeasible in practice. In this pilot study, we analyze the performance of the recurrence method, a well-known entanglement distillation scheme, with its final random hashing or breeding procedure being replaced by various efficiently decodable quantum codes. Among all the replacements investigated, the one using a certain adaptive quantum low density parity check (QLDPC) code is found to give the highest yield for Werner states over a wide range of noise level—the yield for using this QLDPC code is higher than the first runner up by more than 25% over a wide parameter range. In this respect, the effectiveness of using QLDPC codes in practical entanglement distillation is illustrated.

Distilling entanglement from random cascades with partial “which path” ambiguity

We develop a framework to calculate the density matrix of a pair of photons emitted in a decay cascade with partial ``which path'' ambiguity. We describe an appropriate entanglement distillation scheme which works also for certain random cascades. The qualitative features of the distilled entanglement are presented in a two dimensional ``phase diagram.'' The theory is applied to the quantum tomography of the decay cascade of a biexciton in a semiconductor quantum dot. Agreement with experiment is obtained.

How to distill entanglement from a finite amount of qubits?

AbstractWe discuss a specific entanglement distillation scheme [D. Deutsch et al., Phys. Rev. Lett. 77, 2818 (1996)] under the constraint of finite samples of entangled qubit pairs. It is shown that an iterative process based on this method can be explicitly formulated. The average fidelity of this process can be strongly enhanced by introducing a conditional storing of entangled qubit pairs in each step of the iteration. We investigate the corresponding limitations on the size and the initial fidelity of the sample.

ITERATIVE ENTANGLEMENT DISTILLATION FOR FINITE RESOURCES

We discuss a specific entanglement distillation scheme under the constraint of finite samples of entangled qubit pairs. It is shown that an iterative process can be explicitly formulated. The average fidelity of this process can be enhanced by introducing conditional storing of entangled qubit pairs in each step of the iteration. We investigate the corresponding limitations on the size and the initial fidelity of the sample.