Abstract This work presents a security analysis of the semi-quantum key distribution protocol when the transmitted states are modeled as a depolarizing channel i.e. a mixture of the ideal state and the maximally mixed state. This scenario can occur either by the deliberate addition of noise by Alice to the states before their transmission, or in a practical situation where Eve cannot substitute the noisy quantum channel with an ideal one. We derive the maximum amount of information that Eve can obtain from Alice in the case of individual attacks, for protocols employing two and three mutually unbiased bases. The findings show that depolarization decreases Eve’s information gain compared to that of Bob.
Abstract This work presents a security analysis of the semi-quantum key distribution protocol when the transmitted states are modeled as a depolarizing channel i.e. a mixture of the ideal state and the maximally mixed state. This scenario can occur either by the deliberate addition of noise by Alice to the states before their transmission, or in a practical situation where Eve cannot substitute the noisy quantum channel with an ideal one. We derive the maximum amount of information that Eve can obtain from Alice in the case of individual attacks, for protocols employing two and three mutually unbiased bases. The findings show that depolarization decreases Eve’s information gain compared to that of Bob.
We study eavesdropping in quantum key distribution with the six state protocol, when the signal states are mixed with white noise. This situation may arise either when Alice deliberately adds noise to the signal states before they leave her lab, or in a realistic scenario where Eve cannot replace the noisy quantum channel by a noiseless one. We find Eve's optimal mutual information with Alice, for individual attacks, as a function of the qubit error rate. Our result is that added quantum noise reduces Eve's mutual information more than Bob's.
Quantum communication is at the heart of the quantum information theory. We study two types of quantum communication protocols over noisy transmission channels, i.e. super dense coding and cryptography protocols. In the first part of this thesis, for various scenarios, it is discussed how the super dense coding capacity is influenced by noisy quantum channels. The case of memoryless channels as well as those channels with memory which are modelled by uncorrelated and correlated noise, respectively, are considered. Explicitly Pauli channels over arbitrary dimensions are treated and the super dense coding capacity for some resource states is derived. For the qubit depolarizing channel, when noise is uncorrelated, the super dense coding capacity with respect to the input state is also optimized. This illustrates a threshold value of the noise parameter below which the super dense coding capacity is optimized by a maximally entangled initial state, while above the threshold value the super dense coding capacity is optimized by a product state. For Pauli channels, with correlated noise, the case of non unitary encoding is studied and the super dense coding capacity is derived. The first part of this thesis is concluded with an example for multipartite super dense coding.
In the second part of the thesis, the problem of optimal eavesdropping on noisy states in quantum key distribution is investigated. The case of the six state protocol, when the signal states are mixed with white noise, is considered. This situation may arise either when Alice deliberately adds noise to the signal states before they leave her lab, or, in a realistic scenario when the eavesdropper (referred to as Eve) is not assumed to replace the noisy quantum channel by a noiseless one. For individual attacks, we find Eve's optimal mutual information with Alice as a function of the quantum bit error rate. Finally, the results illustrate that adding noise on the quantum level can make quantum key distribution more robust against eavesdropping.
The security of two-state quantum-key distribution against individual attack is estimated when the channel has losses and noises. We assume that Alice and Bob use two nonorthogonal single-photon polarization states. To make our analysis simple, we propose a modified B92 protocol in which Alice and Bob make use of inconclusive results, and Bob performs a kind of symmetrization of received states. Using this protocol, Alice and Bob can estimate Eve's information gain as a function of a few parameters that reflect the imperfections of devices, or Eve's disturbance. In some parameter regions, Eve's maximum information gain shows counterintuitive behavior, namely, it decreases as the amount of disturbances increases. For a small noise rate, Eve can extract perfect information in the case where the angle between Alice's two states is small or large, while she cannot extract perfect information for intermediate angles. We also estimate the secret key gain, which is the net growth of the secret key per pulse. We show the region where the modified B92 protocol over a realistic channel is secure against individual attack.
Most prior semi-quantum key distribution (SQKD) protocols are designed in the context of qubits. In this paper, we proposed an SQKD protocol using ([Formula: see text]+1) quantum states in two mutually unbiased bases in the context of qudits without invoking the classical party’s measurement capability. It not only decreases the quantum states sent by quantum party by half, but also improves the efficiency of key rate than qubits do. To prove the security of present protocol, we first illustrate that the present protocol is completely robust, and then prove its unconditional security from information theoretical perspective by computing its key rate and noise tolerance against cloning-based individual attack. The unconditional security proof demonstrates that the higher dimension of quantum system is, the higher key rate can be obtained and the higher noise tolerance is allowed in depolarization channel.
In this thesis, we analyze the security of the Bennett 1992 quantum key-distribution protocol (B92 protocol) over a realistic channel assuming that bit values are encoded in single photon polarization states. First, we study the security of the B92 protocol against individual attack. In the individual attack, eavesdropper (Eve) interacts a qubit emitted by the sender (Alice) with her probe system followed by a measurement on each probe. To make our analysis simple, we propose a modified B92 protocol. Using this protocol, Alice and the receiver (Bob) can estimate Eve's information gain as a function of a few parameters that reflect the imperfections of devices or Eve's disturbance. We find a counter-intuitive behavior of Eve's maximum information gain, i.e., it decreases as the amount of disturbances increases. We also estimate the secret key gain that is the net growth of the secret key per one pulse. We show the region where the modified B92 protocol over a realistic channel is secure against individual attack. Next, we study the unconditional security of the B92 protocol, which is the security against any attack. To prove the security, we first propose a protocol that is unconditionally secure and can be reduced to the B92 protocol. This protocol employs the entanglement distillation protocol (EDP) based on a filtering operation and the Calderbank-Shor-Steane (CSS) quantum error correcting codes. The bit errors and the phase errors, which have to be estimated for the EDP based on the CSS codes, are correlated after the filtering operation, and we can bound the amount of phase errors from the observed bit errors by an estimation method involving nonorthogonal measurements. The angle between the two states shows a trade-off between accuracy of the estimation and robustness to noises. We show a way to run the unconditionally secure B92.
We investigate the effect of collective-rotation noise on the security of the six-state quantum key distribution. We study the case where the eavesdropper, Eve, performs an intercept-resend attack on the quantum communication between Alice, the sender, and Bob, the receiver. We first derive the collective-rotation noise model for the six-state protocol and then parameterize the mutual information between Alice and Eve. We then derive quantum bit error rate for three intercept-resend attack scenarios. We observe that the six-state protocol is robust against intercept-resend attacks on collective rotation noise channels when the rotation angle is kept within certain bounds.