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In this paper we provide a proof of unconditional security for a semiquantum key distribution protocol introduced in a previous work. This particular protocol demonstrated the possibility of using X basis states to contribute to the raw key of the two users (as opposed to using only direct measurement results) even though a semi-quantum participant cannot directly manipulate such states. In this work we provide a complete proof of security by deriving a lower bound of the protocol's key rate in the asymptotic scenario. Using this bound we are able to find an error threshold value such that for all error rates less than this threshold, it is guaranteed that A and B may distill a secure secret key; for error rates larger than this threshold, A and B should abort. We demonstrate that this error threshold compares favorably to several fully quantum protocols. We also comment on some interesting observations about the behavior of this protocol under certain noise scenarios.

Semi-quantum key distribution protocols are designed to allow two users to establish a secure secret key when one of the two users is limited to performing certain "classical" operations. There have been several such protocols developed recently, however, due to their reliance on a two-way quantum communication channel (and thus, the attacker's opportunity to interact with the qubit twice), their security analysis is difficult and little is known concerning how secure they are compared to their fully quantum counterparts. In this paper we prove the unconditional security of a particular semi-quantum protocol. We derive an expression for the key rate of this protocol, in the asymptotic scenario, as a function of the quantum channel's noise. Finally, we will show that this semi-quantum protocol can tolerate a maximal noise level comparable to certain fully quantum protocols. * This is an extended version of a paper published in IEEE ISIT 2015.

Quantum key distribution is one of the most fundamental cryptographic protocols. Quantum walks are important primitives for computing. In this paper we take advantage of the properties of quantum walks to design new secure quantum key distribution schemes. In particular, we introduce a secure quantum key-distribution protocol equipped with verification procedures against full man-in-the-middle attacks. Furthermore, we present a one-way protocol and prove its security. Finally, we propose a semi-quantum variation and prove its robustness against eavesdropping.

In this paper, we derive key-rate expressions for different quantum key distribution protocols. Our key-rate equations utilize multiple channel statistics, including those gathered from mismatched measurement bases - i.e., when Alice and Bob choose incompatible bases. In particular, we will consider an Extended B92 and a two-way semi-quantum protocol. For both these protocols, we demonstrate that their tolerance to noise is higher than previously thought - in fact, we will show the semi-quantum protocol can actually tolerate the same noise level as the fully quantum BB84 protocol. Along the way, we will also consider an optimal QKD protocol for various quantum channels. Finally, all the key-rate expressions which we derive in this paper are applicable to any arbitrary, not necessarily symmetric, quantum channel.

Quantum key distribution (QKD) protocols allow two parties to establish a shared secret key, secure against an all powerful adversary. This is a task impossible to achieve through classical communication only; indeed, to distribute a secret key through classical means requires one to assume computationally bounded adversaries. If, however, both parties are "quantum capable" then security may be attained assuming only that the adversary must obey the laws of physics. But "how quantum" must a protocol actually be to gain this advantage over classical communication? This is one of the questions semi-quantum cryptography seeks to answer.Semi-quantum communication, a model introduced in 2007 by M. Boyer, D. Kenigsberg, and T. Mor (PRL 99 140501), involves the use of fully-quantum users and semiquantum, or "classical" users. These classical users are only allowed to interact with the quantum channel in a limited, classical manner. Originally introduced to study the key-distribution problem, semi-quantum research has since expanded, and continues to grow, with new protocols, security proof methods, experimental implementations, and new cryptographic applications beyond key distribution. Research in the field of semi-quantum cryptography requires new insights into working with restricted protocols and, so, the tools and techniques derived in this field can translate to results in broader quantum information science. Furthermore, other questions such as the connection between quantum and classical processing, including how classical information processing can be used to counteract a quantum deficiency in a protocol, can shed light on important theoretical questions.This work surveys the history and current state-of-the-art in semi-quantum research. We discuss the model and several protocols offering the reader insight into how protocols are constructed in this realm. We discuss security proof methods and how classical post-processing can be used to counteract users' inability to perform certain quantum operations. Moving beyond key distribution, we survey current work in other * semi-quantum cryptographic protocols and current trends. We also survey recent work done in attempting to construct practical semi-quantum systems including recent experimental results in this field. Finally, as this is still a growing field, we highlight, throughout this survey, several open problems that we feel are important to investigate in the hopes that this will spur even more research in this topic.

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