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arXiv:2006.07945 · Physical Review A

Increasing distillable key rate from bound entangled states by using local filtration

Mayank Mishra, Ritabrata Sengupta, Arvind

Published Sep 22, 2020• 7 citations
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Abstract

We show the enhancement of a distillable key rate for quantum key distribution (QKD) by local filtering for several bound entangled states. Through our paper, it becomes evident that the local filtration operations, whereas transforming one bound entangled state to another, have the potential to increase the utility of the new state for QKD. We demonstrate three examples of ``one-way distillable key rate'' enhancement by local filtering and, in this process, discover new bound entangled states which are key distillable.

DOI
10.1103/physreva.102.032415

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We show the enhancement of a distillable key rate for quantum key distribution (QKD) by local filtering for several bound entangled states. Through our paper, it becomes evident that the local filtration operations, whereas transforming one bound entangled state to another, have the potential to increase the utility of the new state for QKD. We demonstrate three examples of ``one-way distillable key rate'' enhancement by local filtering and, in this process, discover new bound entangled states which are key distillable.
We examine how the structural characteristics of entangled quantum states impact the achievable rates in entanglement-based quantum key distribution (QKD). Focusing on the performance differences between entangled states produced by entanglement distillation protocols and Werner states, we show that the structured nature of distilled states can yield significantly higher secure key rates, even when their fidelity matches that of Werner states. This suggests that while converting arbitrary entangled states into Werner states (through twirling) simplifies the analysis of protocol performance, it also limits potential secret key rates. Our findings underscore the potential of entanglement distillation protocols to enhance QKD performance by additionally improving the structure of entangled states, thus, broadening their utility beyond simple fidelity enhancement.
Quantum entanglement is an indispensable resource for many significant quantum information processing tasks. Thus, distilling more entanglement from less entangled resource is a task of practical significance and has been investigated for decades. The literature [Verstraete \textit{et al}., \href{https://link.aps.org/doi/10.1103/PhysRevA.64.010101}{Phys. Rev. A 64, 010101(2001)}] considered a scenario to increase the entanglement by local filtering operation and qualitatively derived the variance relation of entanglement. We investigate the scenario with general two-qubit resources to find the optimal strategy of filtering operations. We obtain the upper bound for the ratio of entanglement increase and find the corresponding optimal local filtering operation to achieve the maximal ratio. Our analysis shows that the upper bound ratio grows with the length of local Bloch vector while the success probability decrease with it. We further extend the research to investigate the optimal measurement strategy by considering general measurement. Our result shows that local measurement can not increase the expectation of quantum entanglement, which gives more analytical evidence to the well known fact that local operation can not create quantum entanglement.
We present sufficient conditions for states to have positive distillable key rate. Exploiting the conditions, we show that the bound entangled states given by Horodecki et al. [Phys. Rev. Lett. 94, 160502 (2005)] have nonzero distillable key rate and finally exhibit new classes of bound entangled states with positive distillable key rate, but with negative Devetak-Winter lower bound of the distillable key rate for the classical-classical-quantum (ccq) states of their privacy squeezed versions, which represent the states after the local measurement performed in the key part without considering the shield part.
Realizing secure communication between distant parties is one of the main goals of quantum technology. Although quantum key distribution (QKD) promises information-theoretic security for sharing a secret key, the key rate heavily depends on the level of noise in the quantum channel. To overcome the noise, both quantum and classical techniques exist, i.e., entanglement distillation and classical advantage distillation. So far, these techniques have only been used separately from each other. Herein, we present a two-stage distillation scheme concatenating entanglement distillation with classical advantage distillation. For the advantage distillation, we utilize a fixed protocol, specifically, the repetition code; in the case of entanglement distillation, we employ an enumeration algorithm to find an optimal protocol. We test our scheme for noisy entangled states and demonstrate its quantitative advantage: Our two-stage distillation scheme achieves finite key rates even in a high-noise regime where entanglement distillation or advantage distillation alone cannot afford key sharing. We also calculate the security bounds for relevant QKD protocols with our key-distillation scheme and show that they exceed the previous security bounds on the critical quantum bit error rates with only advantage distillation. Since the advantage distillation part does not introduce further requirements for quantum resources other than those required for entanglement distillation, the proposed scheme is well suited for quantum key distribution tasks with entanglement distribution networks.
Abstract Quantum key distribution promises information-theoretically secure communication, with data post-processing playing a vital role in extracting secure keys from raw data. While hardware advancements have significantly improved practical implementations, optimizing post-processing techniques offers a cost-effective avenue to enhance performance. Advantage distillation, which extends beyond standard information reconciliation and privacy amplification, has proven instrumental in various post-processing methods. However, the optimal post-processing remains an open question. Therefore, it is important to develop a comprehensive framework to encapsulate and enhance these existing methods. In this work, we propose an advantage distillation framework for quantum key distribution, generalizing and unifying existing key distillation protocols. Inspired by entanglement distillation, our framework not only integrates current techniques but also improves upon them. Notably, by employing classical linear codes, we achieve higher key rates, particularly in scenarios where one-time pad encryption is not used for post-processing. Our approach provides insights into existing protocols and offers a systematic way for further enhancements in quantum key distribution.
We look into multipartite quantum states on which quantum cryptographic protocols including quantum key distribution and quantum secret sharing can be perfectly performed, and define the quantum cryptographic resource distillable rate as the asymptotic rate at which such multipartite state can be distilled from a given multipartite state. Investigating several relations between entanglement and the rate, we show that there exists a multipartite bound entangled state whose quantum cryptographic resource distillable rate is strictly positive, that is, there exists a multipartite entangled state which is not distillable, but can be useful for quantum cryptography such as quantum key distribution and quantum secret sharing.