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This paper shows that the random privacy amplification is secure with a higher key rate than Mayers' evaluation at the same error rate in the BB84 protocol with one-way or two-way classical communications. There exists only Mayers' evaluation on the secure key rate with random privacy amplification that is applicable to the BB84 protocol with two-way classical communications. Our result improves the secure key rate of the random privacy amplification in the BB84 protocol with two-way classical communications.

We consider a variant of the BB84 protocol for quantum cryptography, the prototype of tomographically incomplete protocols, where the key is generated by one-way communication rather than the usual two-way communication. Our analysis, backed by numerical evidence, establishes thresholds for eavesdropping attacks on the raw data and on the generated key at quantum bit error rates of 10% and 6.15%, respectively. Both thresholds are lower than the threshold for unconditional security in the standard BB84 protocol.

Quantum cryptography uses quantum mechanics to guarantee secure communication. BB84 is a widely used quantum key distribution that provides a way for two parties, a sender, Alice, and a receiver, Bob, to share an unconditionally secure key in the presence of an eavesdropper, Eve.

Three different criteria can be assumed to study the BB84 protocol. They are the efficiency of the protocol, the probability that Eve remains undetected, and the amount of knowledge Eve has about Alice's bit sequence.

In a previous approach, we only considered the probability that Eve remains undetected. We viewed this protocol as a three player static game in which Alice and Bob were two cooperative players and Eve was a competitive one. In our game model, Alice's and Bob's objective was to maximize the probability of detecting Eve, while Eve's objective was to minimize this probability. In this paper, our previous effort is extended and we also consider the other two criteria, i.e. the efficiency of the protocol and the amount of knowledge Eve has about Alice's bit sequence. Using these models, we show how game theory can be used to find the strategies for Alice, Bob and Eve.

In this paper, we introduce a new quantum key distribution protocol, which we refer to as polarization-phase (PoP) protocol. In this protocol, two degrees of photonic freedom of the same particle in a hybrid manner are used to encode the information in the format of two- or high-dimensional quantum states (qubits and qudits, respectively). Here, we only discuss the qubit version of the general PoP protocol (we refer to two-dimensional PoP (TD-PoP) protocol) as an interesting extension for the standard BB84 protocol. We investigate the performance of the TD-PoP protocol using infinite-key analysis against restricted individual attacks, i.e. the intercept-resend and photon number splitting attacks, in both ideal single-photon and Poisson (attenuated laser) sources. In addition, we demonstrate that this protocol, despite using two physical dimensions, is simple and fully has empirical implementation capability. Ability to extract two bits of information from each detection event, and increasing the sifting parameter, the secure key rate, and the likelihood of detection of an eavesdropper, are the advantages of the TD-PoP protocol compared to the standard polarization- or phase-encoded BB84 protocol.

A relay-assisted scheme for quantum key distribution (QKD) over long atmospheric channels is proposed. In this scheme, a polarization orbital-angular-moment with measurement-device-independent (POAM-MDI) QKD for quantum relay is designed to both reconstruct the turbulence-degraded qubits and redirect the qubits to the next relay or to Bob who performs detection randomization. The proposed scheme will neither be time-consuming nor lead to unstable or even intermittent in volatile environments. Theoretical and numerical results show that the proposed relay-assisted scheme outperforms the conventional direct transmission over long atmospheric channels.