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arXiv:1512.01020 · Physical Review A

Heralded single-photon sources for quantum-key-distribution applications

Matteo Schiavon, Giuseppe Vallone, Francesco Ticozzi, Paolo Villoresi

Published Jan 20, 2016• 31 citations
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Abstract

Single-photon sources (SPSs) are a fundamental building block for optical implementations of quantum information protocols. Among SPSs, multiple crystal heralded single-photon sources seem to give the best compromise between high pair production rate and low multiple photon events. In this work, we study their performance in a practical quantum-key-distribution experiment, by evaluating the achievable key rates. The analysis focuses on the two different schemes, symmetric and asymmetric, proposed for the practical implementation of heralded single-photon sources, with attention on the performance of their composing elements. The analysis is based on the protocol proposed by Bennett and Brassard in 1984 and on its improvement exploiting decoy state technique. Finally, a simple way of exploiting the postselection mechanism for a passive, one decoy state scheme is evaluated.

DOI
10.1103/physreva.93.012331

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Single-photon sources (SPSs) are a fundamental building block for optical implementations of quantum information protocols. Among SPSs, multiple crystal heralded single-photon sources seem to give the best compromise between high pair production rate and low multiple photon events. In this work, we study their performance in a practical quantum-key-distribution experiment, by evaluating the achievable key rates. The analysis focuses on the two different schemes, symmetric and asymmetric, proposed for the practical implementation of heralded single-photon sources, with attention on the performance of their composing elements. The analysis is based on the protocol proposed by Bennett and Brassard in 1984 and on its improvement exploiting decoy state technique. Finally, a simple way of exploiting the postselection mechanism for a passive, one decoy state scheme is evaluated.
We present a scheme for realizing passive quantum key distribution with heralded single-photon sources. In this scheme, the idler light from the parametric down-conversion process is split into two parts and sent into two local detectors individually. Then all the clicking and nonclicking events are used to herald the arrival and nonarrival of the signal light. As a result, a precise estimation of the behavior of the single-photon pulses can be achieved without changing the light intensity. Furthermore, we compare our scheme with other existing methods with the Bennett-Brassard 1984 (BB84) protocol through numerical simulations. Our simulations demonstrate that the performance of our scheme can greatly overcome other existing practical methods and approach very close to the asymptotic case of using infinite-decoy-state methods.
We have experimentally demonstrated a decoy-state quantum key distribution scheme (QKD) with a heralded single-photon source based on parametric down-conversion. We used a one-way Bennett-Brassard 1984 protocol with a four states and one-detector phase-coding scheme, which is immune to recently proposed time-shift attacks, photon-number splitting attacks, and can also be proven to be secure against Trojan horse attacks and any other standard individual or coherent attacks. In principle, the setup can tolerate the highest losses or it can give the highest secure key generation rate under fixed losses compared with other practical schemes. This makes it a quite promising candidate for future quantum key distribution systems.
Recently the performance of the quantum key distribution (QKD) is substantially improved by the decoy state method and the non-orthogonal encoding protocol, separately. In this paper, a practical non-orthogonal decoy state protocol with a heralded single photon source (HSPS) for QKD is presented. The protocol is based on 4 states with different intensities, i.e. one signal state and three decoy states. The signal state is for generating keys; the decoy states are for detecting the eavesdropping and estimating the fraction of single-photon and two-photon pulses. We have discussed three cases of this protocol, i.e. the general case, the optimal case and the special case. Moreover, the final key rate over transmission distance is simulated. For the low dark count of the HSPS and the utilization of the two-photon pulses, our protocol has a higher key rate and a longer transmission distance than any other decoy state protocol.
We study decoy-state measurement-device-independent quantum key distribution using heralded single-photon sources. This has the advantage that the observed error rate in the XXX basis is at higher order and not so large. We calculate the key rate and transmission distance for two cases: one using only triggered events, and the other using both triggered and nontriggered events. We compare the key rates of various protocols and find that our scheme using triggered and nontriggered events can give a higher key rate and a longer secure distance. Moreover, we also show the different behavior of our scheme when using different heralded single-photon sources, i.e., in Poisson or thermal distributions. We demonstrate that the former can generate a higher secure key rate than the latter and can thus work more efficiently in practical quantum key distributions.
Quantum key distribution (QKD) relies on single photon sources (SPSs), e.g. from solid-state systems, as flying qubits, where security strongly requires sub-Poissonian photon statistics with low second-order correlation values ($g^{(2)}(0)$). However, achieving such low $g^{(2)}(0)$ remains experimentally challenging. We therefore propose a decoy-like QKD protocol that relaxes this constraint while maintaining security. This enables the use of many SPSs with $g^{(2)}(0) > $0.1, routinely achieved in experiments but rarely considered viable for QKD. Monte Carlo simulations and our experiment from defects in hexagonal boron nitride show that, under linear loss, $g^{(2)}(0)$ remains constant, whereas photon-number-splitting (PNS) attacks introduce nonlinear effects that modify the measured $g^{(2)}(0)$ statistics. Exploiting this $g^{(2)}(0)$ variation as a diagnostic tool, our protocol detects PNS attacks analogously to decoy-state methods. Both single- and two-photon pulses consequently securely contribute to the secret key rate. Our protocol outperforms the Gottesman--Lo--Lutkenhaus--Preskill (GLLP) framework under high channel loss across various solid-state SPSs and is applicable to the satellite-based communication. Since $g^{(2)}(0)$ can be extracted from standard QKD experiments, no additional hardware is required. The relaxed $g^{(2)}(0)$ requirement simplifies the laser system for SPS generation. This establishes a practical route toward high-performance QKD without the need for ultra-pure SPSs.
For the Bennett-Brassard 1984 (BB84) quantum key distribution, longer distance and higher key generation rate is shown with a heralded single photon source (HSPS). In this paper, the nonorthogonal encoding protocol SARG04 based on one vacuum and two weak decoy states with HSPS is presented. According to the public announcement of Alice's detection events, the overall gain of Bob's detector and quantum bit error rate (QBER) can be divided into two groups, triggered components and nontriggered components. We present a new protocol that use both triggered and nontriggered components to estimate the fraction and QBER of single-photon and two-photon pulses, and then deduce the final secure key generation rate. The final key generation rate over transmission distance is simulated, which shows that we can obtain a higher key rate than that of the existing methods.