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arXiv:1202.0456

Quantum Key Distribution with Qubits Encoded in Qutrit

Rupesh Kumar, Rafał Demkowicz-Dobrzański, Konrad Banaszek

Published Feb 2, 2012• 0 citations
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Abstract

We present a novel one-way quantum key distribution protocol based on 3-dimensional quantum state, a qutrit, that encodes two qubits in its 2-dimensional subspaces. The qubits hold the classical bit information that has to be shared between the legitimate users. Alice sends such a qutrit to Bob where he decodes one of the qubit and measures it along the random Pauli basis. This scheme has higher secure key rate at longer transmission distance than the standard BB84 protocol.

DOI
10.48550/arxiv.1202.0456

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We present a novel one-way quantum key distribution protocol based on 3-dimensional quantum state, a qutrit, that encodes two qubits in its 2-dimensional subspaces. The qubits hold the classical bit information that has to be shared between the legitimate users. Alice sends such a qutrit to Bob where he decodes one of the qubit and measures it along the random Pauli basis. This scheme has higher secure key rate at longer transmission distance than the standard BB84 protocol.
Quantum key distribution based on encoding in three-dimensional systems in the presence of several eavesdroppers is proposed. This extends the BB84 protocol in the presence of many eavesdroppers where two-level quantum systems (qubits) are replaced by three-level systems (qutrits). We discuss the scenarios involving two, three and four complementary bases. We derive the explicit form of Alice and Bob mutual information and the information gained by each eavesdropper. In particular, we show that, in the presence of only one eavesdropper, the protocol involving four bases is safer than the other ones. However, for two eavesdroppers, the security is strongly dependent on the attack probabilities. The effect of a large number of eavesdroppers is also investigated.
Quantum Key Distribution (QKD) provides a secure way of generating shared cryptographic keys between a sender (Alice) and a receiver (Bob). The original BB84 protocol uses a two-dimensional polarization basis, limiting the information content of a single photon to 1 bit. Using the transverse position of single photons as one basis and the Fourier space as a second basis, one can construct a pair of mutually unbiased higher-dimensional bases. This improves not only the security of the protocol, but also the key generation rate. We present experimental results with a Spatial-Light-Modulator-based encoding scheme employing two nearly orthogonal alphabets with on the order of 103symbols each and an information content of about 10 bit.
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In a deterministic quantum key distribution (DQKD) protocol with a two-way quantum channel, Bob sends a qubit to Alice who then encodes a key bit onto the qubit and sends it back to Bob. After measuring the returned qubit, Bob can obtain Alice's key bit immediately, without basis reconciliation. Since an eavesdropper may attack the qubits traveling on either the Bob-Alice channel or the Alice-Bob channel, the security analysis of DQKD protocol with a two-way quantum channel is complicated and its unconditional security has been controversial. This paper presents a security proof of a single-photon four-state DQKD protocol against general attacks.
A quantum key distribution protocol based on BB84 protocol and a challenge-response mechanism was proposed.Through a secure channel,Alice and Bob have pre-shared three different Hash functions(denoted by H_1,H_2 and H_3) and a random bit string S_O~(AB).Every time,Alice first generates two random bit strings S_r~A(challenge) and S_k~A(key),then prepares a photon sequence S_p~A based on BB84 protocol using S_r~B,S_k~B,S_O~(AB) and H_1.Alice sends S_r~A and S_p~A to Bob and Bob receives the corresponding S_r~B and S_p~B.Bob measures S_p~B according to BB84 protocol and gets corresponding S_k~B.In the ideal case,S_k~A should be the same as S_k~B.Bob uses S_r~B,S_k~B,S_O~(AB) and H_2 to generate S_2~B(response).At last,Alice and Bob use their own sequences and H_3 to generate S_O~A and S_O~B respectively,then they update their own S_O~(AB).In the proposed protocol,the utilization rate of photons is 100%.The security of the protocol is similar as that of the BB84 protocol.Furthermore,it is a one-way identification authentication protocol.