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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Channel models for QKD at higher photon flux levels based on spatial entanglement of twin beams in PDC

M. Mondin, F. Daneshgaran, Ivo Pietro Degiovanni, Marco Genovese, Ivano Ruo Berchera

Published Sep 1, 2015• 0 citations
Publisher

Abstract

One of the key issues in QKD is the rather limited data rate at which the secret key can be generated. This paper explores the use of quantum correlation associated with twin beams in Parametric Down Conversion (PDC) to in effect create a number of parallel channels for generation of secret keys, thus significantly boosting the achievable key rate. Such quantum correlations have been effectively used as a tool for many applications, including calibration of single photon detectors and QKD applications.1 Within QKD applications, the natural setup of quantization of Charge Coupled Device (CCD) detection areas and subsequent measurement of the correlation statistic needed to detect the presence of the eavesdropper Eve, leads to a set of QKD parallel channel models that are either binary or multilevel Discrete Memoryless Channels (DMC). This work explores the derivation of proper channel models for this application starting from measured data and the optimization of the secret key rate. Analytical results based on measurements performed on a 30 pixel image suggest that nearly an 8-fold increase in secret key rate may be achievable using this technique.

DOI
10.1117/12.2191537

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One of the key issues in QKD is the rather limited data rate at which the secret key can be generated. This paper explores the use of quantum correlation associated with twin beams in Parametric Down Conversion (PDC) to in effect create a number of parallel channels for generation of secret keys, thus significantly boosting the achievable key rate. Such quantum correlations have been effectively used as a tool for many applications, including calibration of single photon detectors and QKD applications.1 Within QKD applications, the natural setup of quantization of Charge Coupled Device (CCD) detection areas and subsequent measurement of the correlation statistic needed to detect the presence of the eavesdropper Eve, leads to a set of QKD parallel channel models that are either binary or multilevel Discrete Memoryless Channels (DMC). This work explores the derivation of proper channel models for this application starting from measured data and the optimization of the secret key rate. Analytical results based on measurements performed on a 30 pixel image suggest that nearly an 8-fold increase in secret key rate may be achievable using this technique.
A major problem with conventional QKD techniques is the raw key transmission rate which for acceptable level of security is generally low. One way to overcome this problem is to create either directly or indirectly a number of parallel QKD transmission channels thus achieving a rate multiplicity equal to the number of parallel channels. This paper explores how a number of parallel Discrete Memoryless Channels (DMCs) can be created from imaging twin beams from a Parametric Down Conversion (PDC) process and examines the performance of FEC coding for information reconciliation over the resulting parallel channels. Twin beams exhibit quantum correlations that has been effectively used as a tool for many applications including calibration of single photon detectors. By now, detection of multimode spatial correlations is a mature field and in principle, only depends on the transmission and detection efficiency of the devices and the channel. In,1–3 the authors utilized their know-how on almost perfect selection of modes of pairwise correlated entangled beams and the optimization of the noise reduction to below the shot-noise level, for absolute calibration of Charge Coupled Device (CCD) cameras. The same basic principle is currently being considered by the same authors for possible use in Quantum Key Distribution (QKD). The main advantage in such an approach would be the ability to work with much higher photon fluxes than that of a single photon regime that is theoretically required for discrete variable QKD applications (in practice, very weak laser pulses with mean photon count below one are used), and the fact that the QKD data rate is increased significantly since multiple equivalent parallel channels result from quantization of symmetric regions into super-pixels. The natural setup of quantization of CCD detection area and subsequent measurement of the correlation statistic needed to detect the presence of the eavesdropper Eve, leads to a number of parallel QKD channel models each one of which is a Discrete Memoryless Channel (DMC) with a number of inputs and outputs that can be more than two (i.e., each parallel channel is a Multilevel DMC). This paper investigates the use of Low Density Parity Check (LDPC) codes for information reconciliation on the effective parallel channels associated with the multi-level DMCs. The performance of such codes are shown to be close to the theoretical limits.
One of the key issues in QKD is the rather limited data rate at which the secret key can be generated. This paper explores the use of twin beams in a PDC process for imaging CCD devices whose photon counts in symmetric pixel positions can be used to generate secret keys. The fundamental reason is that the two beams are entangled in the photon number state and measurements of the correlation statistics should theoretically expose the presence of the eavesdropper. Via a binning approach the photon counts at Alice and Bob who each image one of the two beams, can be turned into discrete labels that represent elements of the raw key that needs further reconciliation and privacy amplification. Discrepancies between the photon counts can be modeled via a fictitious discrete memoryless channel. Furthermore, the use of multi-pixels images allows to create a number of parallel channels for generation of secret keys, thus significantly boosting the achievable key rate. This work explores the derivation of proper channel models for this application starting from measured data and the optimization of the secret key rate. Trade-offs between error probability and key rate are analyzed, with the final goal of maximizing the system Shannon capacity
Twin beams generated by Parametric Down Conversion (PDC) exhibit quantum correlations that has been effectively used as a tool for many applications including calibration of single photon detectors. By now, detection of multi-mode spatial correlations is a mature field and in principle, only depends on the transmission and detection efficiency of the devices and the channel. In [2, 4, 5], the authors utilized their know-how on almost perfect selection of modes of pairwise correlated entangled beams and the optimization of the noise reduction to below the shot-noise level, for absolute calibration of Charge Coupled Device (CCD) cameras. The same basic principle is currently being considered by the same authors for possible use in Quantum Key Distribution (QKD) [3, 1]. The main advantage in such an approach would be the ability to work with much higher photon fluxes than that of a single photon regime that is theoretically required for discrete variable QKD applications (in practice, very weak laser pulses with mean photon count below one are used).The natural setup of quantization of CCD detection area and subsequent measurement of the correlation statistic needed to detect the presence of the eavesdropper Eve, leads to a QKD channel model that is a Discrete Memoryless Channel (DMC) with a number of inputs and outputs that can be more than two (i.e., the channel is a multi-level DMC). This paper investigates the use of Low Density Parity Check (LDPC) codes for information reconciliation on the effective parallel channels associated with the multi-level DMC. The performance of such codes are shown to be close to the theoretical limits
We develop new methods of quantifying the impact of photon detector imperfections on possible secret key rates in Time-Entanglement based Quantum Key Distribution (QKD). We address photon detection timing jitter, detector downtime, and dark photon counts and show how each may decrease the maximum achievable secret key rate differently. We begin with a standard Discrete Memoryless Channel (DMC) model to get a good bound on the mutual information lost due to the timing jitter, then introduce a novel Markov Chain (MC) based model to characterize the effect of detector downtime and show how it introduces memory to the key generation process. Finally, we propose a new method of including dark counts in the analysis that shows how dark counts can be especially detrimental when using the common Pulse Position Modulation (PPM) for key generation. Our results show that these three imperfections can significantly reduce the achievable secret key rate when using PPM for QKD. One of our main results is providing tooling for experimentalists to predict their systems’ achievable secret key rate given the detector specifications.
Quantum key distribution (QKD) enables two parties to establish a secret key over a potentially hostile channel by exchanging photonic quantum states, relying on the fact that it is impossible for an eavesdropper to tap the quantum channel without disturbing these photons in a way that can be detected [1]. Here we introduce a large-alphabet QKD protocol that makes optimal use of temporal and spectral correlations of entangled photons, reaching the maximum number of inde- pendent basis states (the Schmidt number) and enabling extremely high information content per photon together with an optimal rate of secret key generation. This protocol, which we call 'Dense Wavelength Division Multiplexed Quantum Key Distribution' (DWDM-QKD), derives its security by the conjugate nature of the temporal and spectral entanglement of photon pairs generated by spontaneous parametric down conversion. By using a combination of spectral and temporal bases, we can adjust the protocol to be resource efficient. We show that DWDM-QKD is well suited to approach the optimal key generation rate using present-day sources, detectors, and DWDM opti- cal networks from classical communications, as well as emerging optical interconnect and photonic integrated chip (PIC) systems.
A parametric down-conversion (PDC) source can be used as either a triggered single-photon source or an entangled-photon source in quantum key distribution (QKD). The triggering PDC QKD has already been studied in the literature. On the other hand, a model and a post-processing protocol for the entanglement PDC QKD are still missing. We fill in this important gap by proposing such a model and a post-processing protocol for the entanglement PDC QKD. Although the PDC model is proposed to study the entanglement-based QKD, we emphasize that our generic model may also be useful for other non-QKD experiments involving a PDC source. Since an entangled PDC source is a basis-independent source, we apply Koashi and Preskill's security analysis to the entanglement PDC QKD. We also investigate the entanglement PDC QKD with two-way classical communications. We find that the recurrence scheme increases the key rate and the Gottesman-Lo protocol helps tolerate higher channel losses. By simulating a recent $144\text{\ensuremath{-}}\mathrm{km}$ open-air PDC experiment, we compare three implementations: entanglement PDC QKD, triggering PDC QKD, and coherent-state QKD. The simulation result suggests that the entanglement PDC QKD can tolerate higher channel losses than the coherent-state QKD. The coherent-state QKD with decoy states is able to achieve highest key rate in the low- and medium-loss regions. By applying the Gottesman-Lo two-way post-processing protocol, the entanglement PDC QKD can tolerate up to 70dB70\phantom{\rule{0.3em}{0ex}}\mathrm{dB}70dB combined channel losses (35dB35\phantom{\rule{0.3em}{0ex}}\mathrm{dB}35dB for each channel) provided that the PDC source is placed in between Alice and Bob. After considering statistical fluctuations, the PDC setup can tolerate up to 53dB53\phantom{\rule{0.3em}{0ex}}\mathrm{dB}53dB channel losses.