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Physical Review Letters

Quantum Cryptography Based on Split Transmission of One-Bit Information in Two Steps

Masato Koashi, Nobuyuki Imoto

Published Sep 22, 1997• 137 citations
Publisher

Abstract

We propose a simple quantum cryptographic scheme involving truly two orthogonal states. The security of the protocol is based on splitting the transfer of one-bit information into two steps, ensuring that only a fraction of the bit information is transmitted at a time. A particular implementation with an asymmetric interferometer is presented, which does not require the random timing of the packet sending as was used by Goldenberg and Vaidman [Phys. Rev. Lett. 75, 1239 (1995)].

DOI
10.1103/physrevlett.79.2383

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We propose a simple quantum cryptographic scheme involving truly two orthogonal states. The security of the protocol is based on splitting the transfer of one-bit information into two steps, ensuring that only a fraction of the bit information is transmitted at a time. A particular implementation with an asymmetric interferometer is presented, which does not require the random timing of the packet sending as was used by Goldenberg and Vaidman [Phys. Rev. Lett. 75, 1239 (1995)].
Since, in general, non-orthogonal states cannot be cloned, any eavesdropping attempt in a Quantum Communication scheme using non-orthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in Quantum Cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman [Phys. Rev. Lett. 75 (7), pp. 12391243, 1995] proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal states are superpositions of two localized wave packets which travel along separate channels, i.e. two different paths inside a balanced Mach-Zehnder interferometer. Here we present an experiment realizing this scheme.
Since, in general, nonorthogonal states cannot be cloned, any eavesdropping attempt in a quantum-communication scheme using nonorthogonal states as carriers of information introduces some errors in the transmission, leading to the possibility of detecting the spy. Usually, orthogonal states are not used in quantum-cryptography schemes since they can be faithfully cloned without altering the transmitted data. Nevertheless, L. Goldberg and L. Vaidman [Phys. Rev. Lett. 75, 1239 (1995)] proposed a protocol in which, even if the data exchange is realized using two orthogonal states, any attempt to eavesdrop is detectable by the legal users. In this scheme the orthogonal states are superpositions of two localized wave packets traveling along separate channels. Here we present an experiment realizing this scheme.
Abstract Quantum cryptography protocols are based on the use of quantum objects with at least two orthogonal states, for example, the polarization states of a photon. We propose a completely different cryptography protocol using a stochastic flow of single photons. Our method is based on the stochastic decay of an ensemble of radioactive nuclei randomly emitting a stream of γ -photons. We have experimentally demonstrated the transmission of classical information containing binary bits. Reading this information requires precise knowledge of the repetition rate of its sending. Otherwise, it is impossible to make the transmitted information visible, since it will be lost in the noise.
Summary form only given.One of the simplest protocols of quantum cryptography proposed so far is the one based on two nonorthogonal states. In this protocol, the receiver cannot determine every bit because there is no way to distinguish nonorthogonal states completely. Another simple protocol uses two orthogonal states, and the receiver can always discriminate between the two states that represent the bit values 0 and 1. In this protocol, however, the sender must mix the third states (vacuum states) in the bit stream to prevent eavesdropping. Thus the following question arises: do more simple protocols exist in which the sender switches between only two states and the receiver can obtain every bit value? Here we show that such a protocol does exist.
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.