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arXiv:quant-ph/0412028

Information vs. Disturbance in Dimension D

P. Oscar Boykin, Vwani Roychowdhury

Published Dec 3, 2004• 1 citation
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Abstract

We show that for Eve to get information in one basis about a state, she must cause errors in all bases that are mutually unbiased to that basis. Our result holds in any dimension. We also show that this result holds for all functions of messages that are encrypted with a key.
DOI
10.48550/arxiv.quant-ph/0412028

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Alice communicates with words drawn uniformly amongst {∣j⟩}j=1..n\{\ket{j}\}_{j=1..n}{∣j⟩}j=1..n​, the canonical orthonormal basis. Sometimes however Alice interleaves quantum decoys {∣j⟩+i∣k⟩2}\{\frac{\ket{j}+i\ket{k}}{\sqrt{2}}\}{2​∣j⟩+i∣k⟩​} between her messages. Such pairwise superpositions of possible words cannot be distinguished from the message words. Thus as malevolent Eve observes the quantum channel, she runs the risk of damaging the superpositions (by causing a collapse). At the receiving end honest Bob, whom we assume is warned of the quantum decoys' distribution, checks upon their integrity with a measurement. The present work establishes, in the case of individual attacks, the tradeoff between Eve's information gain (her chances, if a message word was sent, of guessing which) and the disturbance she induces (Bob's chances, if a quantum decoy was sent, to detect tampering). Besides secure channel protocols, quantum decoys seem a powerful primitive for constructing n-dimensional quantum cryptographic applications. Moreover the methods employed in this article should be of strong interest to anyone concerned with the old but fundamental problem of how much information may be gained about a system, versus how much this will disturb the system, in quantum mechanics. Keywords: d-level systems cryptography
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