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arXiv:quant-ph/0001083 · Physical Review Letters

Quantum Cryptography with 3-State Systems

Helle Bechmann-Pasquinucci, Asher Peres

Published Oct 9, 2000• 557 citations
arXivHTMLPDF

Abstract

We consider quantum cryptographic schemes where the carriers of information are 3-state particles. One protocol uses four mutually unbiased bases and appears to provide better security than obtainable with 2-state carriers. Another possible method allows quantum states to belong to more than one basis. Security is not better, but many curious features arise.

DOI
10.1103/physrevlett.85.3313

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We consider quantum cryptographic schemes where the carriers of information are 3-state particles. One protocol uses four mutually unbiased bases and appears to provide better security than obtainable with 2-state carriers. Another possible method allows quantum states to belong to more than one basis. Security is not better, but many curious features arise.
The problem of security of quantum key protocols is examined. In addition to the distribution of classical keys, the problem of encrypting quantum data and the structure of the operators which perform quantum encryption is studied. It is found that unitary bases are central to both encryption of quantum information, as well as the generation of states used in generalized quantum key distribution (which are called mutually unbiased bases). A one-to-one correspondence between certain unitary bases and mutually unbiased bases is found. Finally, a new protocol for making anonymous classical broadcasts is given along with a security proof. An experimental procedure to implement this protocol is also given. In order to prove these new results, some new bounds for accessible information of quantum sources are obtained.
Quantum cryptography lies at the intersection of information theory and quantum mechanics. Cryptosystems come in two major classes depending on whether the key is shared in public or in secret. Public key cryptosystems are special in that they allow two people, who have not yet met, to communicate securely by looking-up encryption methods in a public directory. In quantum cryptography, the sender and receiver have two types of communication channels: a classical public channel and a quantum channel. The best application of cryptography is to allow a secure communication. In the near future, quantum cryptography may be used in top-secret applications in the military, for example, as the basis of communication links. The first protocol for quantum cryptography was proposed in 1984 by C. H. Bennett and G. Brassard. Some of the basic quantum cryptographic systems are: four-states protocol, two-states protocol, 4+2 protocol and multi-photon and multi-stage protocol.
We investigate the security bounds of quantum-cryptographic protocols using ddd-level systems. In particular, we focus on schemes that use two mutually unbiased bases, thus extending the Bennett-Brassard 1984 quantum-key-distribution scheme to higher dimensions. Under the assumption of general coherent attacks, we derive an analytic expression for the ultimate upper security bound of such quantum-cryptography schemes. This bound is well below the predictions of optimal cloning machines. The possibility of extraction of a secret key beyond entanglement distillation is discussed. In the case of qutrits we argue that any eavesdropping strategy is equivalent to a symmetric one. For higher dimensions such an equivalence is generally no longer valid.