![]() ![]() The detection efficiency matrices of two detectors Ρ i( λ) and ρ j( λ) ( λ includes wavelength, time, et al) Trace distance of different decoy states in all dimensions The intensity of reflected Trojan-horse photon | ω i⟩ and | ω j⟩ ( ω includes wavelength, time, et al) Considered imperfectionįidelity between practical states | γ i⟩ and ideal states | i⟩įidelity of different quantum state in other dimensions The detail calculation of these security parameters are descried in the main text. And is a matrix with element η 0( λ k, λ m) for k, m = 1, 2. The subscript of D k, l is the index of different decoy states k and l. The superscript i, j = 1, 2, 3, 4 are the index of four quantum states sent by Alice, which represent z 0, z 1, x 0, x 1 respectively. Alice and Bob can measure the required parameters for practical QKD system in experiment, then evaluate the security of QKD based on our model given in the following sections. Table 1. The considered imperfections in our model and the required parameters that used to evaluate these imperfections. Then we discuss the performance of QKD system based on this assumption. In fact, this assumption has been used to secure the single photon detectors (SPDs). In order to improve the key rate, a practical assumption is proposed, in which parts of loss in Bob's site can be carefully calibrated and monitored. Then the phase error is loss-dependent, which will rapidly worse the key rate even the source flaw is very small. When source flaws are taken into account, one major problem is that Eve could enhance the source flaws by exploiting the loss of system. The legitimate parties can first measure the required parameters for practical QKD system in experiment, then evaluate the final key rate based on our analysis in following. The considered imperfections and the required parameters to evaluate these imperfections are listed in table 1. In one model, the efficiency mismatch in detection and almost all of imperfections in source are taken into account together. In this paper, following the GLLP's analysis which is security under collective attack (if the source is independent and identically distributed, it is also security under coherent attack), the security of BB84 protocol with both source and detection imperfections are analyzed. However, in most of these security analysis, the flaws are considered individually with different models. In fact, based on different imperfections, many works have been done, such as GLLP's analysis, basis-dependent source flaws, Trojan-horse, decoy state and distinguishable decoy state, leaked source, detection mismatch, weak randomness of basis choice, and so on. But, when imperfections are taken into account,, then new method is required to estimate the upper bound of. If the QKD system is perfect, equals with the bit error in X-basis ( ). is the bit error in Z-basis, which is directly measured in experiment. If key is generated from both of two bases, equation ( 1) can be easily expended. įor BB84 protocol with single photon source (SPS), the key rate are given by Three typical device-independent protocols are full device-independent QKD, measurement-device-independent QKD and semi-device-independent QKD. The later one tries to propose new QKD protocol, in which the security can be proved with just a few of basic assumptions. In the former one, by adopting monitor or taking parameters of practical devices into the security model as many as possible, most of known quantum hacking can be defeated. In order to overcome the gap between theory and practice, two methods, security patch and device-independent QKD, are approached. Some detail information about the advances of QKD and quantum hacking can be found in recent review papers. In fact, some quantum attacks have been discovered and demonstrated by exploiting these imperfections of practical devices. However, it is well known that the imperfections of practical devices will compensate the security of generated key. Some quantum networks based on QKD are also available now. The unconditional security of QKD have been widely proved in theory and demonstrated in experiments based on fiber or free-space. Quantum key distribution (QKD), such as BB84, provides a way to share key between Alice and Bob with information-theoretical security.
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