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International Journal of Quantum Information

AN EFFICIENT PROTOCOL FOR SECURE AND DETERMINISTIC QUANTUM KEY EXPANSION

Xiang‐Bin Wang

Published Dec 1, 2006• 1 citation
Publisher

Abstract

We present a protocol for secure quantum key expansion. Our protocol costs almost zero classical communication and less qubits than that in the standard protocols. Since the bit value of the expanded key is deterministic, this protocol can also be used for direct communication. Our protocol includes the authentication steps, therefore, we do not worry about the case that Alice and Bob are completely isolated.

DOI
10.1142/s021974990600233x

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We present a protocol for secure quantum key expansion. Our protocol costs almost zero classical communication and less qubits than that in the standard protocols. Since the bit value of the expanded key is deterministic, this protocol can also be used for direct communication. Our protocol includes the authentication steps, therefore, we do not worry about the case that Alice and Bob are completely isolated.
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Recently, quantum key distribution (QKD) with classical Bob has been suggested and proven completely robust by Boyer et al. [Phys. Rev. Lett.99 (2007) 140501] in which quantum Alice has a fully-fledged quantum power, while classical Bob is restricted to preparing and measuring a particle in the computational basis, reflecting or reordering the particles. In this paper, we describe two related but simpler semi-quantum key distribution protocol that exempts classical Bob from measurement (hereafter called limited classical Bob for convenience) and, prove them completely robust. As limited classical Bob can deterministically prepare the qubits, we exploit this feature to construct a semi-quantum secure direct communication protocol, which is the direct communication of secret messages without first producing a shared secret key.
We present a protocol for deterministic and highly efficient quantum cryptography with entangled photon pairs in a 4x4-dimentional Hilbert space. Two communicating parties, Alice and Bob first share a both polarization- and path-entangled photon pair, and then each performs a complete Bell-state measurement on their own photon in one of two complementary Bell-state bases. It is demonstrated that each measurement in which both Alice and Bob register a photon can build certain perfect correlation and generate 1.5 key bits on average. The security of our protocol is guaranteed by the non-cloning theorem.
Quantum cryptography protocols using entangled qubit pairs can increase the rate and security of information exchange through a quantum channel. Usually those protocols are non-deterministic, i.e. a classical bit is encoded in a quantum state, but the actual bit value cannot be determined. Therefore they request the transmission of additional information through a public channel. By contrast, the ping-pong coding scheme based on entangled photons allows for deterministic and direct key distribution. No qubit has to be discarded and information can be decoded without the need for a subsequent transmission of additional information. Communication through a public channel nevertheless is necessary to ensure asymptotical security against arbitrary eavesdropping attacks.
In light of Lucamarini–Mancini's secure deterministic communication without entanglement [Phys. Rev. Lett94, (2005) 140501], by introducing an additional operation for encoding and additional classical information for decoding, we propose a new secure deterministic bidirectional communication protocol without using entanglement. In our protocol, two legitimate users can simultaneously exchange their different secret messages in a direct way with a set of communication devices. The proposed protocol is asymptotically secure in the limit of transmitting long messages.