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Nonlinear Phenomena in Complex Systems

Unambiguous State Discrimination Attack on the B92 Protocol of Quantum Key Distribution with Single Photons

D. B. Horoshko, S. Ya. Kilin

Published Oct 12, 2021• 0 citations
Publisher

Abstract

We consider an unambiguous state discrimination attack on the B92 protocol of quantum key distribution, realized on the basis of polarization encoding of photons produced by a single-photon source. We calculate the secure key rate and the maximal tolerable loss for various overlaps between two signal states employed in this protocol. We make also a comparison with a physically impossible attack of perfect quantum cloning, and show that the unambiguous state discrimination is much more dangerous for the B92 protocol, than this attack, demonstrating thus, that the security of quantum key distribution is not always based on the no-cloning theorem.

DOI
10.33581/1561-4085-2021-24-3-222-229

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We consider an unambiguous state discrimination attack on the B92 protocol of quantum key distribution, realized on the basis of polarization encoding of photons produced by a single-photon source. We calculate the secure key rate and the maximal tolerable loss for various overlaps between two signal states employed in this protocol. We make also a comparison with a physically impossible attack of perfect quantum cloning, and show that the unambiguous state discrimination is much more dangerous for the B92 protocol, than this attack, demonstrating thus, that the security of quantum key distribution is not always based on the no-cloning theorem.
Abstract Quantum key distribution (QKD) has a promise of unconditionally secure communication between the remote sides. The real-world QKD implementations, however, have numerous loopholes, both of engeneering and physical origin, and compromise the security promise. In this work, we investigate two attack strategies on the passive side channel of the light source along with the optimal cloning attack on the BB84 protocol with decoy-states. We calculate an upper bound of a secret key rate for these situations and show that the joint measurement attack on the signal and side channel degree of freedom is more effective to the adversary.
The use of linearly independent signal states in realistic implementations of quantum key distribution (QKD) enables an eavesdropper to perform unambiguous state discrimination. We explore quantitatively the limits for secure QKD imposed by this fact taking into account that the receiver can monitor, to some extent the photon-number statistics of the signals even with todays standard detection schemes. We compare our attack to the beam-splitting attack and show that security against the beam-splitting attack does not necessarily imply security against the attack considered here.
We discuss the unconditional security of a quantum key distribution protocol in which bit values are encoded in the phase of a weak coherent-state pulse relative to a strong reference pulse, which is essentially the one proposed by Bennett in 1992 (the B92 scheme). In the BB84 protocol with a perfect single photon source, the key rate decreases linearly with the transmission T of the channel. If we simply replace this source with a weak coherent-state pulse, the key rate drops more rapidly (as O(η2)) since the presence of multiple photons favors the eavesdropper, Eve. The B92 protocol, if modified to be encoded on the polarization of a single photon, also shows O(η2) dependence. This comes from Eve's option of sending the vacuum state, which is always registered as an inconclusive result and never causes bit errors. In the original B92 scheme with phase coding, Eve has no such option--replacing the weak pulse by the vacuum cannot avoid errors completely, thanks to the strong reference pulse. This should make the scheme stronger against the loss in the channel even coherent-state pulses from conventional lasers are used. We have obtained an unconditional security proof allowing the presence of small bit errors, and confirmed the above observation in a rigorous way. The key rate is found to drop linearly with the transmission η, and it is lower than the BB84 with a perfect single-photon source only by a constant.
In this paper, we study unambiguous state discrimination regarding advanced attack on phase-coded quantum key distribution protocol.We propose the method of optimal unambiguous state discrimination probability derivation as a function of a priori probabilities for signal states.The expression obtained as an example in case of two signal states explicitly demonstrates the additional term dependent on small deviations from equal a priori probabilities that may take place in real quantum key distribution implementations.Precise estimation of optimal unambiguous state discrimination probability is significant for complete evaluation of quantum key distribution security.
Quantum key distribution schemes which employ encoding on vacuum-one-photon qubits are capable of transferring more information bits per particle than the standard schemes employing polarization or phase coding. We calculate the maximum number of classical bits per particle that can be securely transferred when the key distribution is performed with the BB84 and B92 protocols, respectively, using the vacuum-one-photon qubits. In particular, we show that for a generalized B92 protocol with the vacuum-one-photon qubits, a maximum of two bits per particle can be securely transferred. We also demonstrate the advantage brought about by performing a generalized measurement that is optimized for unambiguous discrimination of the encoded states: the parameter range where the transfer of two bits per particle can be achieved is dramatically enhanced as compared to the corresponding parameter range of projective measurements.