2. Quantum features

#### 2.1. Detection of measurements

Based on the measurement postulate of quantum mechanics [19], it is impossible to perform a measurement on an unknown quantum state without introducing a disturbance unless the state is an eigenstate to the observable being measured [20]. This means that Eve is unable to perform a measurement on an unknown quantum state without introducing a disturbance that can be discovered by Alice and Bob.

#### 2.2. Uncertainty principle

she needs to break the laws of physics, but this is impossible without her presence being detected. Since there is great need for security in a communication system, it is necessary to

Regardless of the challenges that come with developing unconditional security proofs, a lot of progress has been realised in the last two decades. An unconditional security proof considers all kinds of attacks that Eve can perform and incorporating this into the security proof is a difficult task. However, a new technique for analysing collective attacks due to an eavesdropper was developed in 1995 by Yao [6]. Later, Bennett et al. realised that if the legitimate parties possess a reliable quantum computer, they can implement an entanglement distillation (ED) protocol to obtain a secure version of an EB key distribution [7]. In 1998, based on this idea, Lo and Chau then developed a formal security proof for the protocol [8]. By using the ideas of Mayers, Lo and Chau then Shor and Preskill developed a simple proof of security for the BB84 protocol in 2000 [9]. This was followed by a proof of Biham who was the second to show an unconditional security proof [10]. In 1991, Biham's proof was then used by Gottesman and Preskill to prove the unconditional security proof of a continuous variable protocol where Alice's signals are sufficiently squeezed [11]. In the same spirit, Inamori et al. showed the unconditional security proof of BB84 protocol where Alice's source emits weak coherent states and Bob's detector remains uncharacterised [12]. However, a complete security proof that is secure against arbitrary attacks by the eavesdropper and full realistic implementation of the QKD protocol remains missing. But this progress depicts that major achievements have been made in this field to prove that protocols used in quantum communication are secure for sending messages. Amongst different approaches to security proofs, a number of publications on composable security [13], de Finetti's theorem [5, 14], post-selection technique [15] and recently the finite-length key

Regardless of enormous progress that has been made in QKD, there are still some theoretical and experimental problems of communicating in absolute secrecy in the presence of an eavesdropper. In particular, matching the theoretical security proofs to real devices still remains unknown. The security proofs still contain assumptions concerning the behaviour of devices used by the communicating parties [17]. As a result of this mismatch, an eavesdropper can learn part of the key shared by Alice and Bob, thus rendering some schemes insecure over large distances. Moreover, the existing security proofs have been derived in the asymptotic limit which is not very realistic. In fact, the bits which are processed in QKD are necessarily of finite length. Therefore, thanks to Valerio and Renner for introducing the general framework for the security analysis of QKD with finite resources [16]. The security study is mainly based on the framework introduced by Devetak-Winter, Csiszar-Körner and Renner security [5, 18].

Based on the measurement postulate of quantum mechanics [19], it is impossible to perform a measurement on an unknown quantum state without introducing a disturbance unless the

investigate security proofs for QKD systems.

4 Advanced Technologies of Quantum Key Distribution

analysis [16] are now available.

2. Quantum features

2.1. Detection of measurements

For a detailed overview of QKD, we refer the reader to [2, 4].

The uncertainty principle states that a measurement of one quantum observable intrinsically creates an uncertainty in other properties of the system. This means that it is impossible to measure the simultaneous values of non-commuting observables on a single copy of a quantum state [21]. This ensures that an eavesdropper cannot perform measurements that leave the quantum state undisturbed [22]. This automatic detection of an eavesdropper is impossible with classical cryptography.

#### 2.3. No-cloning theorem

In quantum mechanics, it is impossible to make a perfect copy of an unknown state with perfect fidelity. This is called the no-cloning theorem [23]. This prevents an eavesdropper from simply intercepting the communication channel and making copies (so as to make measurements on them later) of the transmitted quantum states, while passing on an undisturbed quantum state to Bob [24, 25]. Therefore, the no-cloning theorem forms an important property in the security of QKD protocols [26].

#### 2.4. Non-orthogonality principle

Suppose, we have quantum states |ψi⟩ which are not orthogonal, then it can be proved that there exists no quantum measurement that is able to distinguish states [19]. In this case, a nonzero component of the state |ψ1⟩ parallel to the state |ψ2⟩ always gives a non-zero probability of the measurement outcome associated with the state |ψ2⟩ also occurring when the measurement is applied to the state |ψ1⟩. This is because |ψ2⟩ can be decomposed into a non-zero component parallel to |ψ1⟩ and a component orthogonal to |ψ1⟩. Then, there is no measurement of any kind that can reliably determine which of the two non-orthogonal quantum states were measured [27]. This feature is very useful for cryptographic applications such as QKD [20].
