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arXiv:quant-ph/9906073

Quantum memory in quantum cryptography

Tal Mor

Published Jun 21, 1999• 7 citations

Abstract

[Shortened abstract:] This thesis investigates the importance of quantum memory in quantum cryptography, concentrating on quantum key distribution schemes. In the hands of an eavesdropper -- a quantum memory is a powerful tool, putting in question the security of quantum cryptography; Classical privacy amplification techniques, used to prove security against less powerful eavesdroppers, might not be effective when the eavesdropper can keep quantum states for a long time. In this work we suggest a possible direction for approaching this problem. We define strong attacks of this type, and show security against them, suggesting that quantum cryptography is secure. We start with a complete analysis regarding the information about a parity bit (since parity bits are used for privacy amplification). We use the results regarding the information on parity bits to prove security against very strong eavesdropping attacks, which uses quantum memories and all classical data (including error correction codes) to attack the final key directly. In the hands of the legitimate users, a quantum memory is also a useful tool. We suggest a new type of quantum key distribution scheme where quantum memories are used instead of quantum channels. This scheme is especially adequate for networks of many users. The use of quantum memory also allows reducing the error rate to improve large scale quantum cryptography, and to enable the legitimate users to work with reasonable error rate.

DOI: 10.48550/arxiv.quant-ph/9906073

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[Shortened abstract:] This thesis investigates the importance of quantum memory in quantum cryptography, concentrating on quantum key distribution schemes. In the hands of an eavesdropper -- a quantum memory is a powerful tool, putting in question the security of quantum cryptography; Classical privacy amplification techniques, used to prove security against less powerful eavesdroppers, might not be effective when the eavesdropper can keep quantum states for a long time. In this work we suggest a possible direction for approaching this problem. We define strong attacks of this type, and show security against them, suggesting that quantum cryptography is secure. We start with a complete analysis regarding the information about a parity bit (since parity bits are used for privacy amplification). We use the results regarding the information on parity bits to prove security against very strong eavesdropping attacks, which uses quantum memories and all classical data (including error correction codes) to attack the final key directly. In the hands of the legitimate users, a quantum memory is also a useful tool. We suggest a new type of quantum key distribution scheme where quantum memories are used instead of quantum channels. This scheme is especially adequate for networks of many users. The use of quantum memory also allows reducing the error rate to improve large scale quantum cryptography, and to enable the legitimate users to work with reasonable error rate.

Quantum cryptography was designed to provide a new approach to the problem of distributing keys for private-key cryptography. The principal idea is that security can be ensured by exploiting the laws of quantum physics and, in particular, by the fact that any attempt to measure a quantum state will change it uncontrollably. This change can be detected by the legitimate users of the communication channel and so reveal to them the presence of an eavesdropper. In this paper I explain (briefly) how quantum key distribution works and some of the progress that has been made towards making this a viable technology. With the principles of quantum communication and quantum key distribution firmly established, it is perhaps time to consider how efficient it can be made. It is interesting to ask, in particular, how many bits of information might reasonably be encoded securely on each photon. The use of photons entangled in their time of arrival might make it possible to achieve data rates in excess of 10 bits per photon.

We address the question whether quantum memory is more powerful than classical memory. In particular, we consider a setting where information about a random n-bit string X is stored in s classical or quantum bits, for s<n, i.e., the stored information is bound to be only partial. Later, a randomly chosen predicate F about X has to be guessed using only the stored information. The maximum probability of correctly guessing F(X) is then compared for the cases where the storage device is classical or quantum mechanical, respectively. We show that, despite the fact that the measurement of quantum bits can depend arbitrarily on the predicate F, the quantum advantage is negligible already for small values of the difference n-s. Our setting generalizes the setting of Ambainis et al. who considered the problem of guessing an arbitrary bit (i.e., one of the n bits) of X. An implication for cryptography is that privacy amplification by universal hashing remains essentially equally secure when the adversary's memory is allowed to be quantum rather than only classical. Since privacy amplification is a main ingredient of many quantum key distribution (QKD) protocols, our result can be used to prove the security of QKD in a generic way.

Unlike classical bits, quantum bits cannot be duplicated and the quantum-entangled states cannot be identified. This property of quantum information was used to suggest an information-theoretic secure cryptography-quantum cryptography. This paper concentrates on quantum key distribution over a long-distance quantum network, it has many nodes and control centers which are connected by quantum channels. Quantum bits are storage on the quantum control centers and using entanglement states swapping to transfer over large distances between nodes and centers. An eavesdropper will inevitably increase the quantum bit error rate and the legitimate users will detect the eavesdropper and hence not use the key.

Strong attacks against quantum key distribution use quantum memories and quantum gates to attack directly the final key. In this paper we extend a novel security result recently obtained, to demonstrate proofs of security against a wide class of such attacks. To reach this goal we calculate information-dependent reduced density matrices, we study the geometry of quantum mixed states, and we find bounds on the information leaked to an eavesdropper. Our result suggests that quantum cryptography is ultimately secure.

Abstract An important advantage of quantum cryptography over classical cryptography consists in the fact that the security of the transmitted keys is not related to the assumptions about the eavesdropper capabilities and is guaranteed by the laws of nature. Nevertheless, in some situations it makes sense to consider some reasonable assumptions about the eavesdropper capabilities, which can increase the secret key distribution rate. Methods are proposed for legitimate users to employ some practical limitations, and attacks are constructed that the eavesdropper can apply under the conditions of these limitations.