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
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
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.
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 Quantum Key Distribution (QKD) protocol describes how two remote parties can establish a secret key by communicating over a quantum and a public classical channel that both can be accessed by an eavesdropper. QKD protocols using energy-time entangled photon pairs are of growing practical interest because of their potential to provide a higher secure key rate over long distances by carrying multiple bits per entangled photon pair. We consider a system where information can be extracted by measuring random times of a sequence of entangled photon arrivals. Our goal is to maximize the utility of each such pair. We propose a discrete time model for the photon arrival process, and establish a theoretical bound on the number of raw bits that can be generated under this model. We first analyse a well known simple binning encoding scheme, and show that it generates significantly lower information rate than what is theoretically possible. We then propose three adaptive schemes that increase the number of raw bits generated per photon, and compute and compare the information rates they offer. Moreover, the effect of public channel communication on the secret key rates of the proposed schemes is investigated.
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.
When using quantum key distribution (QKD), one of the trade-offs for security is that the generation rate of a secret key is typically very low. Recent works have shown that using a weak coherent source allows for higher secret key generation rates compared to an entangled photon source, when a channel with low loss is considered. In most cases, the system that is being studied is over a fiber-optic communication channel. Here a theoretical QKD system using the BB92 protocol and entangled photons over a free-space maritime channel with multiple spatial modes is presented. The entangled photons are generated from a spontaneous parametric down conversion (SPDC) source of type II. To employ multiple spatial modes, the transmit apparatus will contain multiple SPDC sources, all driven by the pump lasers assumed to have the same intensity. The receive apparatuses will contain avalanche photo diodes (APD), modeled based on the NuCrypt CPDS-1000 detector, and located at the focal point of the receive aperture lens. The transmitter is assumed to be located at Alice and Bob will be located 30 km away, implying no channel crosstalk will be introduced in the measurements at Alice’s side due to turbulence. To help mitigate the effects of atmospheric turbulence, adaptive optics will be considered at the transmitter and the receiver. An eavesdropper, Eve, is located 15 km from Alice and has no control over the devices at Alice or Bob. Eve is performing the intercept resend attack and listening to the communication over the public channel. Additionally, it is assumed that Eve can correct any aberrations caused by the atmospheric turbulence to determine which source the photon was transmitted from. One, four and nine spatial modes are considered with and without applying adaptive optics and compared to one another.