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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

An Optimal Strategy to Recover Nonlocality of Polarization-Entangled State from a SPDC Source via Entanglement Swapping Relay

Yoshiaki Tsujimoto, Masahiro Takeoka, Chenglong You, Kentaro Wakui, Mikio Fujiwara, Kazuhiro Hayasaka, Shigehito Miki, Hirotaka Terai, Masahide Sasaki, Jonathan P. Dowling

Published Jun 1, 2019• 0 citations
Publisher

Abstract

To realize the practical implementation of device-independent quantum key distribution (DIQKD), the main difficulty is that its security is solely based on the detection loophole-free violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality i.e. the CHSH value S > 2 [1]. To circumvent the inevitable losses in the transmission channels which create the detection loophole, several probabilistic methods to recover the nonlicality have been proposed. Here, we theoretically and experimentally investigate the optimal strategy for the method utilizing linear optical entanglement swapping relay (ESR) with photon pairs from spontaneous parametric-down conversion (SPDC) sources [2,3]. In the previous methods, it is common to employ the ESR node in Bob's system as shown in Fig. 1(a) (Hereafter, we call this configuration the local-heralding (LH).). We employ another configuration: The middle-heralding (MH) shown in Fig. 1(b), where the ESR node is placed in the middle of Alice and Bob similar to the measurement device independent QKD. We numerically compare S of the above two schemes by using the numerical simulation based on the characteristic-function approach [3]. The results are shown in Fig. 1(c). We see that the larger values of S are expected in the MH scheme when the dark count probabilities (ν) of the detectors are considered. In experiment, we perform the Bell-test experiment using the ESR with SPDC sources. We employ the MH scheme, and measure S changing the transmission losses. The experimental parameters (the average photon numbers and measurement angles) are chosen such that S is maximized under the condition of the experimental imperfections (mode-mismatch, dark count and so on) and the assumption of the unit local detection efficiencies (η = 1). While the overall detection efficiencies of our system (η ~ 15 %) are not the range of directly observing the violation of the CHSH inequality, S obtained by the experiment well agree with the numerical simulation with experimental parameters. When the overall transmission loss is set to be 10 dB, which corresponds to the transmittance of a 50 km-optical fiber, we observe Sexp= 1.478, while Sth= 1.487 is expected by the numerical simulation. This result means that our numerical simulation can rigorously model the experiment. This allows us to estimate the nonlocality of the quantum state just before the local detection losses by the numerical simulation. The CHSH value is estimated to be Sexpη=1= 2.104 > 2, which indicates that the quantum state with experimental imperfections possesses the potential to violate the CHSH inequality.

DOI
10.1109/cleoe-eqec.2019.8873175

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To realize the practical implementation of device-independent quantum key distribution (DIQKD), the main difficulty is that its security is solely based on the detection loophole-free violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality i.e. the CHSH value S > 2 [1]. To circumvent the inevitable losses in the transmission channels which create the detection loophole, several probabilistic methods to recover the nonlicality have been proposed. Here, we theoretically and experimentally investigate the optimal strategy for the method utilizing linear optical entanglement swapping relay (ESR) with photon pairs from spontaneous parametric-down conversion (SPDC) sources [2,3]. In the previous methods, it is common to employ the ESR node in Bob's system as shown in Fig. 1(a) (Hereafter, we call this configuration the local-heralding (LH).). We employ another configuration: The middle-heralding (MH) shown in Fig. 1(b), where the ESR node is placed in the middle of Alice and Bob similar to the measurement device independent QKD. We numerically compare S of the above two schemes by using the numerical simulation based on the characteristic-function approach [3]. The results are shown in Fig. 1(c). We see that the larger values of S are expected in the MH scheme when the dark count probabilities (ν) of the detectors are considered. In experiment, we perform the Bell-test experiment using the ESR with SPDC sources. We employ the MH scheme, and measure S changing the transmission losses. The experimental parameters (the average photon numbers and measurement angles) are chosen such that S is maximized under the condition of the experimental imperfections (mode-mismatch, dark count and so on) and the assumption of the unit local detection efficiencies (η = 1). While the overall detection efficiencies of our system (η ~ 15 %) are not the range of directly observing the violation of the CHSH inequality, S obtained by the experiment well agree with the numerical simulation with experimental parameters. When the overall transmission loss is set to be 10 dB, which corresponds to the transmittance of a 50 km-optical fiber, we observe Sexp= 1.478, while Sth= 1.487 is expected by the numerical simulation. This result means that our numerical simulation can rigorously model the experiment. This allows us to estimate the nonlocality of the quantum state just before the local detection losses by the numerical simulation. The CHSH value is estimated to be Sexpη=1= 2.104 > 2, which indicates that the quantum state with experimental imperfections possesses the potential to violate the CHSH inequality.
Abstract To observe the loophole-free violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality between distant two parties, i.e. the CHSH value S > 2 , the main limitation of distance stems from the loss in the transmission channel. The entanglement swapping relay (ESR) is a simple way to amplify the signal and enables us to evade the impact of the transmission loss. Here, we experimentally test the heralded nonlocality amplifier protocol based on the ESR. We observe that the obtained probability distribution is in excellent agreement with those expected by the numerical simulation with experimental parameters which are precisely characterized in a separate measurement. Moreover, we experimentally estimate the nonlocality of the heralded state after the transmission of 10 dB loss just before final detection. The estimated CHSH value is S = 2.113 > 2 , which indicates that our final state possesses nonlocality even with transmission loss and various experimental imperfections. Our result clarifies an important benchmark of the ESR protocol, and paves the way towards the long-distance realization of the loophole-free CHSH-violation as well as device-independent quantum key distribution.
Device-independent quantum key distribution (DIQKD) guarantees unconditional security of a secret key without making assumptions about the internal workings of the devices used for distribution. It does so using the loophole-free violation of a Bell's inequality. The primary challenge in realizing DIQKD in practice is the detection loophole problem that is inherent to photonic tests of Bell' s inequalities over lossy channels. We revisit the proposal of Curty and Moroder [Phys. Rev. A 84, 010304(R) (2011)] to use a linear optics-based entanglement-swapping relay (ESR) to counter this problem. We consider realistic models for the entanglement sources and photodetectors: more precisely, (a) polarization-entangled states based on pulsed spontaneous parametric down-conversion sources with infinitely higher-order multiphoton components and multimode spectral structure, and (b) on-off photodetectors with nonunit efficiencies and nonzero dark-count probabilities. We show that the ESR-based scheme is robust against the above imperfections and enables positive key rates at distances much larger than what is possible otherwise.
We theoretically and experimentally investigate the optimal conditions for the Bell experiment using spontaneous parametric down-conversion (SPDC) sources. In theory, we show that a relatively large average photon number (typically $\ensuremath{\sim}0.5$) is desirable to observe the maximum violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. Moreover, we show that the violation converges to 0.27 in the limit of large average photon number. In experiment, we perform the Bell experiment without postselection using polarization-entangled photon pairs at 1550-nm telecommunication wavelength generated from SPDC sources. While the violation of the CHSH inequality is not directly observed due to the overall detection efficiencies of our system, the experimental values agree well with those obtained by the theory with experimental imperfections. Furthermore, in the range of small average photon numbers ($\ensuremath{\le}0.1$), we propose and demonstrate a method to estimate the ideal CHSH value intrinsically contained in the tested state from the lossy experimental data without assuming the input quantum state.
The concept of the Device-Independent Quantum Key Distribution (DI-QKD) constitutes the minimalist paradigm for quantum cryptography, in which the security of the distributed secret key is fully assured by the statistical properties of the data being shared between the parties that perform a quantum-based protocol. In particular, the secrecy of the distributed key is ultimately guaranteed not only thanks to the quantum nature of the underlying scheme, but also without making any assumptions about the operation of the devices being employed. Such a conservative approach is possible thanks to the non-local correlations exhibited within the shared data, i.e., the correlations of genuine quantum origin that, due to violation of a particular Bell inequality, cannot be explained by any form of common randomness pre-available to the parties. Such violation, however, must be revealed without performing any post-selection on the data, what would then open the so-called detection loophole and jeopardize the security of the protocol. In spite of the tremendous advances recently made to achieve higher detection efficiencies in Bell-violation experiments, DI-QKD remains a very experimentally difficult task due to the exponential increase of loss in the channel, e.g., implemented with optical fibres, with the distance separating the parties involved. Here, we describe a new and plausible solution to overcome the crucial problem of channel loss in the frame of DI-QKD optical implementations. In particular, we propose a novel protocol inspired by the entanglement swapping schemes, which by the usage of the state-of-the-art (e.g., quantum-dot-based or heralded) single-photon sources has potential, for the first time, to be implementable with current photonic and linear optics technologies. While allowing for any transmission losses that only decrease the rate of the key distribution without creating vulnerability, it tolerates overall detection efficiency at the 90% level even when requiring strict device-independence. We compare our scheme against protocols that involve sources based on spontaneous parametric down-conversion (SPDC), in order to explicitly show and explain why such SPDC-based proposals—even when enhanced by the entanglement swapping or qubit amplification techniques—are then largely outperformed when physical imperfections are rigorously taken into account.
What is the most efficient way to generate random numbers deviceindependently using a photon pair source based on spontaneous parametric down conversion (SPDC)? We consider this question by comparing two implementations of a detection-loophole-free Bell test. In particular, we study in detail a scenario where a heralded single photon source (HSPS) is used to herald path-entangled states, i.e. entanglement between two spatial modes sharing a single photon and where nonlocality is revealed using photon counting preceded by small displacement operations. ar X iv :1 40 9. 80 51 v1 [ qu an tph ] 2 9 Se p 20 14 Device-independent quantum random number generator with a photon pair source 2 We start by giving a theoretical description of such a measurement. We then show how to optimize the Bell-CHSH violation through a non-perturbative calculation, taking the main experimental imperfections into account. We finally bound the amount of randomness that can be extracted and compare it to the one obtained with the conventional scenario using photon pairs entangled e.g. in polarization and analyzed through photon counting. While the former requires higher overall detection efficiencies, it is far more efficient in terms of both the entropy per experimental run and the rate of random bit generation. PACS numbers: 03.65.Ud Device-independent quantum random number generator with a photon pair source 3
We theoretically analyze the feasibility of entanglement-based quantum key distribution (QKD) protocols-both device-independent QKD (DI-QKD) and entanglement-based BB84 (EPR-BB84)-using widely employed spontaneous parametric down-conversion (SPDC) and what we believe to be a novel semiconductor quantum-dot (QD) sources. Within a unified photodetection-theory framework, we jointly evaluate the Bell parameter, quantum bit error rate (QBER), and asymptotic Devetak-Winter secret key rate for both source types, accounting for multiphoton emission in SPDC, fine-structure splitting (FSS) in the QD, and imperfect detection including finite efficiency and dark counts. Our results demonstrate that, despite the detrimental effect of FSS, QD sources achieve sufficient Bell violation and positive secret key rates under realistic experimental conditions. In contrast, within the standard CHSH-based DI-QKD framework and the detection and binning strategies, bare SPDC sources do not yield a positive secret key rate, despite the feasibility of loophole-free Bell tests with such sources. Our findings are crucial for the practical implementation of entanglement-based QKD protocols using realistic sources and detectors.