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Journal of Physics Conference Series

LDPC Coding for QKD at Higher Photon Flux Levels Based on Spatial Entanglement of Twin beams in PDC

F. Daneshgaran, M. Mondin, Inam Bari

Published Apr 9, 2014• 1 citation
Publisher

Abstract

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

DOI
10.1088/1742-6596/497/1/012037

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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
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 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.
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
Istituto Nazionale di Ricerca Metrologica (INRIM), Strada delle Cacce 91, 10135 Torino, Italy. E-mail:i.ruoberchera@inrim.it Quantum correlations of twin beams represent a resource of great importance for the developments of quantum technologies allowing unprecedented results in quantum information, metrology and quantum imaging. Focusing on the measurement of the photon numbers, spatial multimode correlations beyond the shot noise limit have been experimentally demonstrated by using parametric down conversion (PDC) and CCD camera (both at the single photon level and at higher photon flux) [1], and also with other interesting techniques [2]. One of their natural application is the quantum imaging of weak absorbing objects, showed in Fig.1, with sensitivity beyond the shot-noise-level [3]. The idea consists in measuring the intensity pattern on one branch of PDC, where the object has been inserted, and then subtracting the correlated noise pattern measured in the other branch that does not interact with the object. In our presentation we overview the sub-shot noise imaging protocol mentioned above and other applications where the spatial quantum correlation can give some advantages over the classical ones. As an example, we studied the signalto-noise ratio (SNR) of ghost imaging protocols with quantum and classical light [4]. We realized a ghost imaging experiment in the mesoscopic regime (one thousand of photon per pixel per shot), obtaining substantial quantum enhanced performances (see Fig.1). We also demonstrated that spatial quantum correlations provide the possibility for the absolute calibration of analog and/or photon number resolving detectors, providing the first absolute calibration (without any comparison with reference standards, neither optical source nor detector) of a scientific CCD camera [5]. In this first realization we already reached interesting uncertainty level. All these findings indicate that the control and detection of quantum spatial correlation is a rather mature field and other application to different sensing scenarios can be envisaged.
We report on the absolute calibration of a Charge-Coupled Device (CCD) camera by exploiting quantum correlation. This method exploits a certain number of spatial pairwise quantum correlated modes produced by spontaneous parametric-down-conversion. We develop a measurement model accounting for all the uncertainty contributions, and we reach the relative uncertainty of 0.3% in low photon flux regime. This represents a significant step forward for the characterization of (scientific) CCDs used in mesoscopic light regime.