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Chinese Physics

An efficient two-step quantum key distribution protocol with orthogonal product states

Yu‐Guang Yang, Wen Qiao-yan, Fu-Chen Zhu

Published Mar 20, 2007• 18 citations
Publisher

Abstract

An efficient two-step quantum key distribution (QKD) protocol with orthogonal product states in the n ⊗ n ( n ⩾3) Hilbert space is presented. In this protocol, the particles in the orthogonal product states form two particle sequences. The sender, Alice, first sends one sequence to the receiver, Bob. After Bob receives the first particle sequence, Alice and Bob check eavesdropping by measuring a fraction of particles randomly chosen. After ensuring the security of the quantum channel, Alice sends the other particle sequence to Bob. By making an orthogonal measurement on the two particle sequences, Bob can obtain the information of the orthogonal product states sent by Alice. This protocol has many distinct features such as great capacity, high efficiency in that it uses all orthogonal product states in distributing the key except those chosen for checking eavesdroppers.

DOI
10.1088/1009-1963/16/4/007

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An efficient two-step quantum key distribution (QKD) protocol with orthogonal product states in the n ⊗ n ( n ⩾3) Hilbert space is presented. In this protocol, the particles in the orthogonal product states form two particle sequences. The sender, Alice, first sends one sequence to the receiver, Bob. After Bob receives the first particle sequence, Alice and Bob check eavesdropping by measuring a fraction of particles randomly chosen. After ensuring the security of the quantum channel, Alice sends the other particle sequence to Bob. By making an orthogonal measurement on the two particle sequences, Bob can obtain the information of the orthogonal product states sent by Alice. This protocol has many distinct features such as great capacity, high efficiency in that it uses all orthogonal product states in distributing the key except those chosen for checking eavesdroppers.
The general conditions for the orthogonal product states of the multistate systems to be used in quantum key distribution (QKD) are proposed, and a novel QKD scheme with orthogonal product states in the $3\ifmmode\times\else\texttimes\fi{}3$ Hilbert space is presented. We show that this protocol has many distinct features such as great capacity and high efficiency. The generalization to $n\ifmmode\times\else\texttimes\fi{}n$ systems is also discussed and an asymptotic limit of 1/2 for the eavesdropper's success probability is obtained.
Quantum secret sharing (QSS) is a cryptographic protocol that utilizes fundamental principles of quantum mechanics to securely distribute and reconstruct secret information among multiple participants. Most existing protocols rely on entangled states (such as Bell and GHZ states), but in practical applications. The preparation of entangled state is constrained by a short quantum coherence time, low state fidelity, etc., which makes it difficult to implement entangled resource-dependent QSS protocols. In this work, a novel practical and verifiable multi-party QSS protocol is proposed based on orthogonal product states, which are easier to prepare than entangled states. During the protocol preparation stage, the secret distributor first converts pre-shared classical secret information into the corresponding orthogonal product states according to the encoding rules, and pre-shares a communication key with participants via quantum key distribution (QKD), which is used to hide the initial quantum sequence information through subsequent particle transformation operations. After preparing the orthogonal product states, the distributor reorganizes the particles by position, extracting particles at the same position from each state to form new sequences, shuffling their order, then applying Hadamard operations using a pre-shared key, inserting decoy particles, and sending the sequences to the participants. After receiving it, participants conduct eavesdropping detection, use the same key for the inverse transformations, retain one particle from each sequence, and sequentially pass the remaining particles until the last participant receives a complete set, triggering state verification with the arbiter distributor. If the verification is successful, the particles will be returned to the first participant and the return stage will follow the same procedure. Only after both the transmission and return stage verifications have passed, will the distributor reveal the initial particle positions, allowing participants to collaboratively reconstruct the secret. In the protocol, the secret distributor acts as an arbitrator to verify the particle state information together with participants at designated points (the end of the transmission stage and the end of the return stage) in order to determine whether the particle-state information is error-free during transmission. If the verification fails at either stage, the protocol will be terminated immediately. Meanwhile, considering that the number of participants may change during the execution of the protocol, a dynamic scheme for personnel changes is designed to ensure the flexibility of the protocol. Through the analysis of possible internal and external attacks, It can be proven that our protocol can effectively resist the existing common attack. Using Qiskit simulation experiments, the core quantum procedures of the protocol can be successfully modeled. The experimental results provide strong computational validation of the theoretical feasibility of the protocol.
The evolution of Quantum Key Distribution (QKD) relies on innovative methods to enhance its security and efficiency. Unextendible Product Bases (UPBs) hold promise in quantum cryptography due to their inherent indistinguishability, yet they are underutilized in QKD protocols. This work introduces a protocol utilizing UPBs to establish quantum keys between distant parties. Specifically, we propose a protocol utilizing a 3×33\times 33×3 tile UPB, where Alice sequentially transmits subsystem states to Bob through quantum channels. The protocol's security is underpinned by the no-cloning theorem, prohibiting the cloning of orthogonal states. We analyze potential attacks, including intercept-resend and detector blinding attacks when quantum channels are noiseless, and discuss the challenges posed by the indistinguishability of our protocol for eavesdroppers, thereby enhancing QKD security.
A protocol for quantum secure direct communication using blocks of Einstein-Podolsky-Rosen (EPR) pairs is proposed. A set of ordered N EPR pairs is used as a data block for sending secret message directly. The ordered N EPR set is divided into two particle sequences, a checking sequence and a message-coding sequence. After transmitting the checking sequence, the two parties of communication check eavesdropping by measuring a fraction of particles randomly chosen, with random choice of two sets of measuring bases. After insuring the security of the quantum channel, the sender Alice encodes the secret message directly on the message-coding sequence and sends them to Bob. By combining the checking and message-coding sequences together, Bob is able to read out the encoded messages directly. The scheme is secure because an eavesdropper cannot get both sequences simultaneously. We also discuss issues in a noisy channel.