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arXiv:2207.13284 · Physical Review A

Comparison of techniques for distillation of entanglement over a lossy channel

Caroline Mauron, Timothy C. Ralph

Published Dec 5, 2022• 5 citations
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Abstract

We analyze three quantum communication protocols that have been proposed in the literature and compare how well they communicate single-rail entanglement. We use specific metrics for output-state purity and probability of success and include the presence of imperfect photon source and detection components. We find that a distributed noiseless linear amplification (NLA) protocol with a relay point placed halfway between Alice and Bob outperforms NLA at Bob's end and a recently proposed purification protocol under most conditions, unless the distance is very small or the photon source component is very good.

DOI
10.1103/physreva.106.062603

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We analyze three quantum communication protocols that have been proposed in the literature and compare how well they communicate single-rail entanglement. We use specific metrics for output-state purity and probability of success and include the presence of imperfect photon source and detection components. We find that a distributed noiseless linear amplification (NLA) protocol with a relay point placed halfway between Alice and Bob outperforms NLA at Bob's end and a recently proposed purification protocol under most conditions, unless the distance is very small or the photon source component is very good.
Entanglement distribution is crucial for quantum communication and cryptography but is hindered by channel loss and decoherence. Noiseless linear amplification (NLA) is a probabilistic protocol that supports noiseless amplification without violating the no-cloning theorem, aiding in tasks like entanglement distillation and enhanced metrology. The probabilistic nature of NLA and other quantum repeater elements creates a significant resource overhead, which depends on the success rate of each individual probabilistic step. We experimentally demonstrate a technique to increase NLA success probability while maintaining the amplification gain and the fidelity of the amplified state with a maximally entangled state. We show that symmetrically distributing loss before and after the amplification provides an improved scaling of the success rates of NLA. Our results are a critical step towards scalable quantum repeaters and enable efficient long-distance quantum communication
Quantum entanglement distillation is a probabilistic process which protects entanglement from environment-induced decoherence. In this paper, we investigate the distillation of a continuousvariable optic entangled state with noiseless linear amplification (NLA). NLA schemes perform better than the conventional photon-subtraction-based distillation scheme, particularly in distributing entanglement over extremely low efficiency quantum channels. Finally, a comparison between the NLA-based scheme and the local squeezing-enhanced photon subtraction scheme is also investigated.
Quantum communication can realize secure information transmission based on the fundamental principles of quantum mechanics. Photon is a crucial information carrier in quantum communication. The photonic quantum communication protocols require the transmission of photons or photonic entanglement between communicating parties. However, in this process, photon transmission loss inevitably occurs due to environmental noise. Photon transmission loss significantly reduces the efficiency of quantum communication and even threatens its security, so that it becomes a major obstacle for practical long-distance quantum communication. Quantum noiseless linear amplification (NLA) is a promising method for mitigating photon transmission loss. Through local operations and post-selection, NLA can effectively increase the fidelity of the target state or the average photon number in the output state while perfectly preserving the encoded information of the target state. As a result, employing NLA technology can effectively overcome photon transmission loss and extend the secure communication distance. In this paper, the existing NLA protocols are categorized into two types, i.e. the NLA protocols in DV quantum systems and CV quantum systems. A detailed introduction is given to the quantum scissor (QS)-based NLA protocols for single photons, single-photon polarization qubits, and single-photon spatial entanglement in the DV quantum systems. The QS-based NLA can effectively increase the fidelity of the target states while perfectly preserving its encodings. In recent years, researchers have made efforts to study various improvements to the QS-based NLA protocols. In the CV quantum systems, researchers have adopted parallel multiple QS structure and generalized QS to increase the average photon numbers of the Fock states, coherent states and two-mode squeezed vacuum states. In addition to theoretical advancements, significant progress has also been made in the experimental implementations of NLA. The representative experimental demonstrations of QS-based NLA protocols are summarized. Finally, the future development directions for NLA to facilitate its practical applications are presented. This review can provide theoretical support for practically developing NLA in the future.
Entanglement distillation is an indispensable ingredient in extended quantum communication networks. Distillation protocols are necessarily non-deterministic and require non-trivial experimental techniques such as noiseless amplification. We show that noiseless amplification could be achieved by performing a post-selective filtering of measurement outcomes. We termed this protocol measurement-based noiseless linear amplification (MBNLA). We apply this protocol to entanglement that suffers transmission loss of up to the equivalent of 100km of optical fibre and show that it is capable of distilling entanglement to a level stronger than that achievable by transmitting a maximally entangled state through the same channel. We also provide a proof-of-principle demonstration of secret key extraction from an otherwise insecure regime via MBNLA. Compared to its physical counterpart, MBNLA not only is easier in term of implementation, but also allows one to achieve near optimal probability of success.
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Quantum entanglement distillation protocols are LOCC protocols that, over ``imperfect'' EPR pairs shared between Alice and Bob as input, output perfect or near-perfect EPR pairs. In this paper, we study the communication complexity of these protocols, that is, the minimal number of (classical) bits needed for Alice and Bob. To our knowledge, it is the first paper that studies entanglemend distillation protocols in the resource-bounded case. We consider 3 models for imperfect EPR pairs. In the measure-rrr model, rrr out of nnn EPR pairs are measured by an adversary (and thus become ``corrupted''); in the depolarization model, the qubits of Bob underwent a depolarization channel; in the fidelity model, the only information Alice and Bob possess is the fidelity of the shared state. For the first 2 models, we prove tight and almost-tight bounds on the base case, i.e., how well Alice and Bob can do if they are not allowed to communicate. For the fidelity model, we prove a very tight lower bound (up to an additive constant) on the communication complexity. This lower bound implies the optimality of the Random Hash protocol in [ASY02].