We consider a general and practical scenario of quantum key distribution (QKD) over an unknown, stationary, unital qubit channel. Furthermore, due to practical limitations, e.g., relative movement and rotation of communicating parties, a global shared reference frame cannot be established. This scenario can routinely appear in satellite QKD. We propose two methods to overcome the physical qubit noise and the lack of shared reference frame. The first proposed approach involves constructing the Pauli transfer matrix (PTM) description of the channel, which we achieve without requiring a shared reference frame, by absorbing the lack of shared reference frame in the channel definition. This is followed by the identification of singular vectors of PTM as the Bloch vectors for optimal signal states. In the optimized local bases, the resulting correlations are equivalent, up to outcome relabeling, to those of a Pauli channel, allowing us to show the optimality of the BB84 and six-state QKD protocols under these conditions. The second approach, called the sequential basis matching (SBM) involves sequentially identifying the channel-optimized local bases that enable QKD. We show that both of these approaches result in the same effective key exchange rate for QKD.
We consider a general and practical scenario of quantum key distribution (QKD) over an unknown, stationary, unital qubit channel. Furthermore, due to practical limitations, e.g., relative movement and rotation of communicating parties, a global shared reference frame cannot be established. This scenario can routinely appear in satellite QKD. We propose two methods to overcome the physical qubit noise and the lack of shared reference frame. The first proposed approach involves constructing the Pauli transfer matrix (PTM) description of the channel, which we achieve without requiring a shared reference frame, by absorbing the lack of shared reference frame in the channel definition. This is followed by the identification of singular vectors of PTM as the Bloch vectors for optimal signal states. In the optimized local bases, the resulting correlations are equivalent, up to outcome relabeling, to those of a Pauli channel, allowing us to show the optimality of the BB84 and six-state QKD protocols under these conditions. The second approach, called the sequential basis matching (SBM) involves sequentially identifying the channel-optimized local bases that enable QKD. We show that both of these approaches result in the same effective key exchange rate for QKD.
Reference-frame-independent quantum key distribution (RFI QKD) significantly alleviates alignment requirements for reference frame in practical quantum communication systems. While the original protocol requires Alice to prepare six quantum states in Z, X, and Y bases, its reliance on active modulation introduces inherent side-channel vulnerabilities from device imperfections. We address this security limitation by integrating a fully passive source into the RFI framework. In this paper, we propose a fully passive RFI QKD protocol. Our protocol avoids active modulation entirely, suppressing side-channel risks through passive quantum state generation. Moreover, by making full utilization of the quantum states generated by the fully passive source, we enhance the secure key rate of fully passive protocol. We establish a system model to analyze the performance of the protocol. Through the optimization of post-selection intervals and intensities, we obtain the maximum secure key transmission rate of the protocol. Under ideal circumstances, the secure key transmission rate of our protocol can reach more than 50% of that of the ideal QKD. Under practical conditions, we have considered the finite-length effect. When pulse number generated by the source reaches 1012, the maximum communication distances of the protocol can reach 167 km and 136 km with a reference frame misalignment of $0 $ and $45^{\circ} $ respectively. We believe that our protocol can contribute to the development of practical QKD systems.
In quantum key distribution (QKD), the users need to share the same reference frame. If their reference frames are inconsistent, the QKD system will not function properly. The most widely used method today is the active real-time calibration of both communication reference frames by using classical communication. In order to get rid of the real-time calibration operation of the reference frames, a QKD protocol independent of reference frame is proposed, called reference-frame-independent QKD (RFI-QKD). The RFI-QKD protocol is immune to the effects of slowly changing reference frame drift, requiring that only one set of bases should be aligned by Alice and Bob, and the remaining two sets of bases can slowly change in the channel. In the real QKD system, a set of basis vectors can always be found to maintain a stable alignment. However, some assumptions are made for the sources in most reported researches, i.e. with a trusted and fixed photon-number distribution (PND), which usually cannot be satisfied in practical implementations. Those unreasonable assumptions will inevitably compromise the security of practical QKD systems. To solve the problem, in this work, we present a passive light source monitoring (PLSM) scheme for RFI-QKD, which is accomplished by a passive monitoring module consisting of a beam splitter and two detectors on the source side. Through the PLSM module, we can have four monitoring events by using two local detectors and then precisely estimate the bounds of source distributions. Specifically, we take the three-intensity decoy-state-based RFI-QKD for example for illustraing the events. Compared with the original RFI-QKD, our PLSM method can passively monitor the PND and has many advantages, with light source fluctuations, finite-size effects and reference frame deflection angles taken into account.
We describe a quantum key distribution protocol based on pairs of entangled qubits that generates a secure key between two partners in an environment of unknown and slowly varying reference frame. A direction of particle delivery is required, but the phases between the computational basis states need not be known or fixed. The protocol can simplify the operation of existing setups and has immediate applications to emerging scenarios such as earth-to-satellite links and the use of integrated photonic waveguides. We compute the asymptotic secret key rate for a two-qubit source, which coincides with the rate of the six-state protocol for white noise. We give the generalization of the protocol to higher-dimensional systems and detail a scheme for physical implementation in the three-dimensional qutrit case.
Reference-frame-independent measurement-deviceindependent quantum key distribution (RFI-MDI-QKD) can eschew the alignment of reference frames in practical systems and defeat all potential detector side channel attacks. Here, we propose the decoy-state RFI-MDI-QKD protocol with biased bases. In this protocol, two legitimate parties Alice and Bob prepare signal states in Z, X, and Y bases and decoy states in X and Y bases, which avoids the futility in Z basis for decoy states and simplifies the operation of existing systems. Considering the security against coherent attacks with statistical fluctuations, we investigate the performance of the decoy-state RFI-MDI-QKD protocol with biased bases in the environment of unknown and slowly drifting reference frames and make comparisons with the original decoy-state RFI-MDI-QKD protocol under the same conditions. Simulation results show that the proposed protocol can increase the achievable secret key rate and transmission distance obviously compared with the original protocol, which is very promising in real-life QKD systems.
Quantum key distribution (QKD) enables the establishment of shared keys between two distant users, Alice and Bob, based on the fundamental principles of quantum mechanics, and it has proven to possess information-theoretic security. In most of QKD systems, Alice and Bob require a shared reference frame, and real-time calibration of the reference frame increases system costs and reduces its performance. Fortunately, the reference-frame-independent QKD protocol has been proposed, overcoming reference-frame drift issues and receiving widespread attention. However, in practical QKD systems, the non-ideal characteristics of realistic devices introduce certain inconsistency between the theory and the practice. In real-world quantum key distribution systems, device imperfections can lead to security vulnerabilities, thereby reducing system security. For example, imperfections in the encoding apparatus at the source end may result in errors in the quantum states. The inherent defects in the detection part may cause after-pulse effects and dead-time effects, thus reducing the key rate. Therefore, in this work, we propose a practical state-preparation error tolerant reference-frame-independent quantum key distribution protocol by taking imperfections in both the source and the detectors into account. Moreover, a three-intensity decoy-state scheme for modeling analysis and numerical simulations is employed. In this protocol, we reduce the influence of state-preparation errors on the key rate by utilizing virtual state methods to precisely estimate the phase-error rate. Furthermore, by characterizing the effects of after-pulses and dead-time on the key rate, our protocol exhibits higher robustness and can effectively address issues related to detector imperfections. This approach can also be extended to other quantum key distribution protocols with higher security levels, such as measurement-device-independent quantum key distribution protocol and twin-field quantum key distribution, further mitigating the influence of device imperfections on practical implementation of QKD system. Therefore, our present work provide important reference value for putting the quantum key distributions into practical application.
We study a reference frame independent (RFI) quantum key distribution (QKD) protocol using six states for Alice and only four states for Bob, while previous RFI protocols require a six state analyzer for Bob. Our protocol can generate a secure key for any possible phase of the entangled state provided the variation is small compared to the measurement rate, as shown by our numerical key rate analysis. We perform a proof-of-principle experiment using polarization entangled photon pairs. In the presence of a varying rotational phase, we obtain a consistently low error rate of less than 4%, indicating the feasibility of this protocol for QKD. Our RFI protocol is hence beneficial but not limited to applications in a satellite or mobile free-space QKD, where a communication node must limit the resources and restrict the number of measured states to four instead of six.