Quantum cloning can be reviewed as the optimal individual eavesdropping on quantum cryptography. Specifically, the optimal phase-covariant cloning is regarded as the optimal individual attack on the BB84 protocol. In this paper, by exploring Cerf s formalism, we prove the optimality of the asymmetric economical 1→2 phase-covariant quantum cloning in 2 dimensions working without ancilla. In proof, we derive another independent unitary transformation of this cloner. Our result covers previous contributions [Durt T, et al. Phys. Rev. A, 2004, 69:062316].
The quantum key distribution protocol BB84, published by C. H. Bennett and G. Brassard in 1984, describes how two spatially separated parties can generate a random bit string fully known only to them by transmission of single-qubit quantum states. Any attempt to eavesdrop on the protocol introduces disturbance which can be detected by the legitimate parties. In this Master's Thesis a novel modification to the BB84 protocol is analyzed. Instead of sending single particles one-by-one as in BB84, they are grouped and a non-local transformation is applied to each group before transmission. Each particle is sent to the intended receiver, always delaying the transmission until the receiver has acknowledged the previous particle on an authenticated classical channel, restricting eavesdropping to accessing the quantum transmission one particle at a time. Hence, an eavesdropper cannot undo the non-local transformation perfectly. Even if perfect cloning of quantum states was possible the state of the group could not be cloned. We calculate the maximal information on the established key provided by an intercept-resend attack and the induced disturbance for different transformations. We observe that it is possible to significantly reduce the eavesdropper's maximal information on the key--to one eighth of that in BB84 for a fixed, reasonable amount of disturbance. We also show that the individual access to the particles poses a fundamental restriction to the eavesdropper, and discuss a novel attack type against the proposed protocol.
In recent years, traditional cryptography has faced a lot of threats with advancements in quantum computing technology. The objective of the work is to analyze the suitability of the BB84 protocol for quantum key distribution. The BB84 protocol uses the principles of superposition, entanglement, and the no-cloning theorem that provide a framework enabling the secure exchange of secret keys. Qiskit, an open-source software, is used for analysis and study. An ideal quantum channel is established between the two communicating parties using Qiskit. The analysis is done in the presence of an eavesdropper, and it is found that the eavesdropper’s incorrect basis choices alter the states of the qubits, and thereby, the communicating parties will come to know about the interception.
The security of quantum cryptography is guaranteed by the no-cloning theorem, which implies that an eavesdropper copying transmitted qubits in unknown states causes their disturbance. Nevertheless, in real cryptographic systems some level of disturbance has to be allowed to cover, e.g., transmission losses. An eavesdropper can attack such systems by replacing a noisy channel by a better one and by performing approximate cloning of transmitted qubits which disturb them but below the noise level assumed by legitimate users. We experimentally demonstrate such symmetric individual eavesdropping on the quantum key distribution protocols of Bennett and Brassard (BB84) and the trine-state spherical code of Renes (R04) with two-level probes prepared using a recently developed photonic multifunctional quantum cloner [Lemr et al., Phys. Rev. A 85, 050307(R) (2012)]. We demonstrated that our optimal cloning device with high-success rate makes the eavesdropping possible by hiding it in usual transmission losses. We believe that this experiment can stimulate the quest for other operational applications of quantum cloning.
We investigate the connection between the optimal collective eavesdropping attack and the optimal cloning attack where the eavesdropper employs an optimal cloner to attack the quantum key distribution (QKD) protocol. The analysis is done in the context of the security proof in Refs. [Proc. R. Soc. London A 461, 207 (2005); Phys. Rev. Lett. 95, 080501 (2005)] for discrete variable protocols in
d-dimensional Hilbert spaces. We consider a scenario in which the protocols and cloners are equipped with symmetries. These symmetries are used to define a quantum cloning scenario. We find that, in general, it does not hold that the optimal attack is an optimal cloner. However, there are classes of protocols, where we can identify an optimal attack by an optimal cloner. We analyze protocols with 2,
d and
d+1 mutually unbiased bases where
d is a prime, and show that for the protocols with 2 and
d+1 mutually unbiased bases (MUBs) the optimal attack is an optimal cloner but, for the protocols with
d MUBs, it is not. Finally, we give criteria to identify protocols which have different signal states, but the same optimal attack. Using these criteria, we present qubit protocols which have the same optimal attack as the Bennett-Brassard 1984 (BB84) protocol or the 6-state protocol.