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.
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.
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
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
The focus of this research activity is to work on pragmatic information reconciliation applied to QKD schemes based on single photon or weak pulse laser (WPL) sources, so as to use feed-forward techniques which minimize the interaction between transmitter and receiver. The core ideas of the thesis are employing Forward Error Correction (FEC) coding as opposed to two-way communication for information reconciliation in QKD schemes, exploiting all the available information for data processing at the receiver including information available from the quantum channel, since optimized use of this information can lead to significant performance improvement, and providing a security versus secret-key rate trade-off to the end-user within the context of QKD systems. Moreover, as shown by accurate experimental studies, the communication channel used for quantum key exchange is not able to reach high levels of reliability (the Quantum Bit Error Rate -QBER may have a high value), both because of the inherent characteristics of the system, and of the presence of a possible attacker. In order to obtain acceptable residual error rates, it is necessary to use a parallel classical and public channel, characterized by high transmission rates and low error rates, on which to transmit only the redundancy bits of systematic channel codes with performance possibly close to the capacity limit. Furthermore, since the more redundancy is added by the channel code, the more the corresponding information can be used to decipher the private message itself, it becomes necessary to design high-rate codes obtained by puncturing a low-rate mother code, possibly achieving a redundancy such that elements of the secret message cannot be uniquely determined from the redundancy itself, so for that purpose we designed high rate LDPC codes. Using high rate codes increases the security with trade-off to performance. Other low photon number applications have also been considered, such as weak-laser pulses (WLP) communication. For that purpose, a low-complexity photon-counting receiver has been considered which may be employed in long-distance amplification-free classical optical communication schemes, and which is typically modeled as an equivalent Binary Symmetric Channel (BSC). We have developed a time varying Binary Input-Multiple Output (BIMO) channel model for this low-complexity photon-counting receiver, and analyzed its performance in presence of soft-metric based capacity approaching iteratively decoded error correcting codes, such as soft-metric based Low Density Parity Check (LDPC) codes and polar codes. We show that the classical channel capacity of the suggested BIMO model is higher than the capacity of the BSC model, and that the use of the BIMO model allows to feed the channel decoder with soft information, in the form of Log-Likelihood Ratios (LLRs), achieving a significant reduction in Bit Error Rate (BER) and Frame Error Rate (FER) with respect to classical hard-metric-based schemes which should be used in conjunction with a BSC channel model.
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 review and compare the results of quantum spatial correlation measurements in parametric down-conversion in the high-gain pulsed regime, with preliminary measurements performed in the low-gain cw-pumped regime. The diagnostics is based on a high quantum efficiency CCD camera, and in the second case the radiation pattern is recorded after temporal integration of the "single-photon" spatial distribution. The effect of the detected number of temporal modes on the accessibility of the sub-shot noise regime is discussed, together with the identification of suitable regimes for weak image detection.