Performance analysis of quantum key distribution in underwater turbulence channels

Abstract

The current literature on quantum key distribution (QKD) is mainly limited to the transmissions over ber optic, atmospheric or satellite links and are not directly applicable to underwater environments with di erent channel characteristics. Absorption, scattering, and turbulence experienced in underwater channels severely limit the range of quantum communication links. In the rst part of this thesis, we analyze the quantum bit error rate (QBER) and secret key rate (SKR) performance of the well-known BB84 protocol in underwater channels. As path loss model, we consider a modi ed version of Beer-Lambert formula which takes into account the e ect of scattering. We derive a closed-form expression for the wave structure function to determine the average power transfer over turbulent underwater path and use this to obtain an upper bound on QBER as well as a lower bound on SKR. Based on the derived bounds, we present the performance of BB84 protocol in di erent water types including clear, coastal and turbid water and under di erent atmospheric conditions such as clear, hazy and overcast. We further investigate the e ect of system parameters such as aperture size and detector eld-of-view on QBER and SKR performance metrics. In the second part of this thesis, as a potential solution to overcome range limitations, we investigate a multi-hop underwater QKD where intermediate nodes between the source and destination nodes help the key distribution. We consider the deployment of passive relays which simply redirect the qubits to the next relay node or the receiver without any measurement. Based on the near- eld analysis, we present the performance of relay-assisted QKD scheme in terms of quantum bit error rate and secret key rate in di erent water types and turbulence conditions. We further investigate the e ect of system parameters such as aperture size and detector eld-of-view on the performance. Our results demonstrate under what conditions relay-assisted QKD can be bene cial and what end-to-end transmission distances can be supported with a multi-hop underwater QKD system. In the last part of this thesis, we investigate the fundamental performance limits of decoy BB84 protocol over turbulent underwater channels and provide a comprehensive performance characterization. As path loss model, we consider a modi ed version of Beer-Lambert formula, which takes into account the e ect of scattering. Based on near eld analysis, we utilize the wave structure function to determine the average power transfer over turbulent underwater path and use this to obtain a lower bound on key generation rate. Based on this bound, we present the performance of decoy BB84 protocol in di erent water types (clear and coastal). We further investigate the e ect of transmit aperture size and detector eld of view.Kuantum anahtar da g t m (QKD) hakk ndaki mevcut literatur, esas olarak ber optik, atmosferik veya uydu ba glant lar uzerinden yap lan aktar mlarla s n rl d r ve farkl kanal ozelliklerine sahip su alt ortamlar na do grudan uygulanamaz. Sualt kanallar nda ya sanan absorpsiyon, sa c lma ve turbulans, kuantum ileti sim ba glant lar n n aral g n ciddi sekilde s n rlar. Bu tezin ilk bolumunde, iyi bilinen BB84 protokolunun sualt kanallar nda kuantum bit hata oran (QBER) ve gizli anahtar oran (SKR) performans n analiz ediyoruz. Yol kayb modeli olarak, sa c lma etkisini hesaba katan Beer-Lambert formulunun de gi stirilmi s bir versiyonunu ele al yoruz. Turbulansl su alt yolu uzerindeki ortalama gu c transferini belirlemek i cin dalga yap s fonksiyonu i cin kapal bi cimli bir ifade turetiyoruz ve bunu QBER'de bir ust s n r ve SKR'de bir alt s n r elde etmek i cin kullan yoruz. Elde edilen s n rlara dayanarak, BB84 protokolunun berrak, k y ve bulan k su dahil farkl su turlerinde ve berrak, puslu ve bulutlu gibi farkl atmosferik ko sullar alt nda performans n sunuyoruz. A c kl k boyutu ve dedektor goru s alan gibi sistem parametrelerinin QBER ve SKR performans ol cutleri uzerindeki etkisini ayr ca ara st r yoruz. Bu tezin ikinci bolumunde, menzil s n rlamalar n n ustesinden gelmek i cin potansiyel bir cozum olarak, kaynak ve hedef du gumler aras ndaki ara du gumlerin anahtar da g t m na yard mc oldu gu cok atlamal bir sualt QKD'sini ara st r yoruz. Kubitleri herhangi bir ol cum yapmadan bir sonraki role du gumune veya al c ya yonlendiren pasif rolelerin konu sland r lmas n du sunuyoruz. Yak n alan analizine dayanarak, farkl su turleri ve turbulans ko sullar nda kuantum bit hata oran ve gizli anahtar oran a c s ndan role destekli QKD semas n n performans n sunuyoruz. A c kl k boyutu ve dedektor goru s alan gibi sistem parametrelerinin performans uzerindeki etkisini ayr ca ara st r yoruz. Sonu clar m z, role destekli QKD'nin hangi ko sullar alt nda faydal olabilece gini ve cok sekmeli bir sualt QKD sistemi ile hangi u ctan uca iletim mesafelerinin desteklenebilece gini gostermektedir. Bu tezin son bolumunde, calkant l su alt kanallar uzerinde yem BB84 protokolunun temel performans s n rlar n ara st r yoruz ve kapsaml bir performans karakterizasyonu sa gl yoruz. Yol kayb modeli olarak, sa c lma etkisini hesaba katan Beer-Lambert formulunun de gi stirilmi s bir versiyonunu ele al yoruz. Yak n alan analizine dayanarak, turbulansl su alt yolu uzerindeki ortalama gu c transferini belirlemek i cin dalga yap s fonksiyonunu kullan yoruz ve bunu anahtar uretim h z nda daha du suk bir s n r elde etmek i cin kullan yoruz. Bu s n ra dayanarak, yem BB84 protokolunun farkl su turlerinde (temiz ve k y ) performans n sunuyoruz. _Iletim a c kl g boyutunun ve dedektor goru s alan n n etkisini daha da ara st r yoruz.